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Radiation Oncology Physics: 
A Handbook for Teachers and Students
E.B. Podgorsak
Technical Editor
Sponsored by the IAEA and endorsed by the COMP/CCPM, EFOMP, ESTRO, IOMP, PAHO and WHO
Cover photograph courtesy of E. Izewski
A HAN
RADIATION ONCOLOGY PHYSICS:
DBOOK FOR TEACHERS AND STUDENTS
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IN
DIATION ONCOLOGY 
SICS: A HANDBOOK FOR 
CHERS AND STUDENTS
TERNATIONAL ATOMIC ENERGY AGENCY
VIENNA, 2005
IAEA
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tion oncology physics : a handbook for teachers and students / editor 
. B. Podgorsak ; sponsored by IAEA 
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p.; 24 cm. 
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ncludes bibliographical references.
. Radiation dosimetry — Handbooks, manuals, etc. 2. Dosimeters 
Handbooks, manuals, etc. 3. Radiation — Measurement — 
ndbooks, manuals, etc. 4. Radiation — Dosage — Handbooks, 
nuals, etc. 5. Radiotherapy — Handbooks, manuals, etc. 6. Photon 
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., ed. II. International Atomic Energy Agency.
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FOREWORD
In the late 1990s the IAEA initiated for its Member States a systematic 
and comprehensive plan to support the development of teaching programmes 
in medical radiation physics. Multiple projects were initiated at various levels 
that, together with the well known short term training courses and 
specialization fellowships funded by the IAEA Technical Cooperation 
programme, a
based master o
One of 
development 
harmonizing th
carried out du
report used for
teachers’ guide
expanded to fo
material to be
prepared acco
was appointed
book became 
coverage deep
expanded con
contributors. T
placed on the I
This han
physicists initi
advances in ra
large number o
necessary to d
expected that t
for medical ra
largest possibl
will contribute
value to newc
medical physic
technologists.
Endorsem
international 
Organization 
Therapeutic R
Organisations 
imed at supporting countries to develop their own university 
f science programmes in medical radiation physics.
the early activities of the IAEA in this period was the 
of a syllabus in radiotherapy physics, which had the goal of 
e various levels of training that the IAEA provided. This was 
ring 1997–1998, and the result of this work was released as a 
 designing IAEA training courses. In 1999–2000 a more detailed 
 was developed, in which the various topics in the syllabus were 
rm a detailed ‘bullet list’ containing the basic guidelines of the 
 included in each topic so that lectures to students could be 
rdingly. During the period 2001–2002 E.B. Podgorsak (Canada) 
 editor of the project and redesigned the contents so that the 
a comprehensive handbook for teachers and students, with 
er than a simple teachers’ guide. The initial list of topics was 
siderably by engaging an enhanced list of international 
he handbook was published as working material in 2003 and 
nternet in order to seek comments, corrections and feedback.
dbook aims at providing the basis for the education of medical 
ating their university studies in the field. It includes the recent 
diotherapy techniques; however, it is not designed to replace the 
f textbooks available on radiotherapy physics, which will still be 
eepen knowledge in the specific topics reviewed here. It is 
his handbook will successfully fill a gap in the teaching material 
diation physics, providing in a single manageable volume the 
e coverage available today. Its wide dissemination by the IAEA 
 to the harmonization of education in the field and will be of 
omers as well as to those preparing for their certification as 
ists, radiation oncologists, medical dosimetrists and radiotherapy 
ent of this handbook has been granted by the following 
organizations and professional bodies: the International 
for Medical Physics (IOMP), the European Society for 
adiology and Oncology (ESTRO), the European Federation of 
for Medical Physics (EFOMP), the World Health Organization 
(WHO), the Pan American Health Organization (PAHO), the Canadian 
Organization of Medical Physicists (COMP) and the Canadian College of 
Physicists in Medicine (CCPM).
The following international experts are gratefully acknowledged for 
making major contributions to the development of an early version of the 
syllabus: B. Nilsson (Sweden), B. Planskoy (United Kingdom) and 
J.C. Rosenwald (France). The following made majorcontributions to this 
handbook: R. 
and N. Sunth
officers respon
J. Izewska and
Although 
contained in th
responsibility fo
The use o
judgement by the
of their authoriti
The menti
as registered) do
construed as an 
The autho
IAEA to repro
copyrights.
Alfonso (Cuba), G. Rajan (India), W. Strydom (South Africa) 
aralingam (United States of America). The IAEA scientific 
sible for the project were (in chronological order) P. Andreo, 
 K.R. Shortt.
EDITORIAL NOTE
great care has been taken to maintain the accuracy of information 
is publication, neither the IAEA nor its Member States assume any 
r consequences which may arise from its use.
f particular designations of countries or territories does not imply any 
 publisher, the IAEA, as to the legal status of such countries or territories, 
es and institutions or of the delimitation of their boundaries.
on of names of specific companies or products (whether or not indicated 
es not imply any intention to infringe proprietary rights, nor should it be 
endorsement or recommendation on the part of the IAEA.
rs are responsible for having obtained the necessary permission for the 
duce, translate or use material from sources already protected by 
PREFACE
Radiotherapy, also referred to as radiation therapy, radiation oncology or 
therapeutic radiology, is one of the three principal modalities used in the 
treatment of malignant disease (cancer), the other two being surgery and 
chemotherapy. In contrast to other medical specialties that rely mainly on the 
clinical knowledge and experience of medical specialists, radiotherapy, with its 
use of ionizing
technology an
coordinated te
The rad
physicists, dos
characterized 
link — the nee
interaction of
specialized are
proficiency in 
aspires to ach
radiotherapy t
by technologic
imaging; howe
physics.
This boo
that train pr
compilation of
will be usefu
programmes, t
and radiothera
material cover
however, the b
same. The tex
certification e
dosimetry or r
The inten
textbooks on m
knowledge in 
oncology phy
professionals, 
medicine that u
diagnosis of di
 radiation in the treatment of cancer, relies heavily on modern 
d the collaborative efforts of several professionals whose 
am approach greatly influences the outcome of the treatment.
iotherapy team consists of radiation oncologists, medical 
imetrists and radiation therapy technologists: all professionals 
by widely differing educational backgrounds and one common 
d to understand the basic elements of radiation physics, and the 
 ionizing radiation with human tissue in particular. This 
a of physics is referred to as radiation oncology physics, and 
this branch of physics is an absolute necessity for anyone who 
ieve excellence in any of the four professions constituting the 
eam. Current advances in radiation oncology are driven mainly 
al development of equipment for radiotherapy procedures and 
ver, as in the past, these advances rely heavily on the underlying 
k is dedicated to students and teachers involved in programmes 
ofessionals for work in radiation oncology. It provides a 
 facts on the physics as applied to radiation oncology and as such 
l to graduate students and residents in medical physics 
o residents in radiation oncology, and to students in dosimetry 
py technology programmes. The level of understanding of the 
ed will, of course, be different for the various student groups; 
asic language and knowledge for all student groups will be the 
t will also be of use to candidates preparing for professional 
xaminations, whether in radiation oncology, medical physics, 
adiotherapy technology.
t of the text is to serve as a factual supplement to the various 
edical physics and to provide basic radiation oncology physics 
the form of a syllabus covering all modern aspects of radiation 
sics. While the text is mainly aimed at radiation oncology 
certain parts of it may also be of interest in other branches of 
se ionizing radiation not for the treatment of disease but for the 
sease (diagnostic radiology and nuclear medicine). The contents 
may also be useful for physicists who are involved in studies of radiation 
hazards and radiation protection (health physics).
This book represents a collaborative effort by professionals from many 
different countries who share a common goal of disseminating their radiation 
oncology physics knowledge and experience to a broad international audience 
of teachers and students. Special thanks are due to J. Denton-MacLennan for 
critically reading and editing the text and improving its syntax.
E.B. Podgorsak
CONTRIBUTORS
Andreo, P. University of Stockholm, Karolinska Institute, 
Sweden
Evans, M.D.C. McGill University Health Centre, Canada
Hendry, J.H.
Horton, J.L.
Izewska, J.
Mijnheer, B.J.
Mills, J.A.
Olivares, M.
Ortiz López, P.
Parker, W.
Patrocinio, H.
Podgorsak, E.B.
Podgorsak, M.B
Rajan, G.
Seuntjens, J.P.
Shortt, K.R.
Strydom, W.
Suntharalingam
Thwaites, D.I.
Tolli, H. 
International Atomic Energy Agency
University of Texas MD Anderson Cancer Center, 
United States of America
International Atomic Energy Agency
Netherlands Cancer Institute, Netherlands
Walsgrave Hospital, United Kingdom
McGill University Health Centre, Canada
International Atomic Energy Agency
McGill University Health Centre, Canada
McGill University Health Centre, Canada
McGill University Health Centre, Canada
. Roswell Park Cancer Institute, United States of 
America
Bhabha Atomic Research Centre, India
McGill University Health Centre, Canada
International Atomic Energy Agency
Medical University of Southern Africa, 
South Africa
, N. Thomas Jefferson University Hospital, United 
States of America
University of Edinburgh, United Kingdom
International Atomic Energy Agency
BL
AN
K
CONTENTS
CHAPTER 1. BASIC RADIATION PHYSICS . . . . . . . . . . . . . . . . . . . 1
1.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1. Fundamental physical constants (rounded off to four 
1.1.2.
1.1.3.
1.1.4.
1.1.5.
1.1.6.
1.1.7.
1.1.8.
1.1.9.
1.2. ATOMI
1.2.1.
1.2.2.
1.2.3.
1.2.4.
1.2.5.
1.2.6.
1.2.7.
1.2.8.
1.2.9.
1.3. ELECT
1.3.1.
1.3.2.
1.3.3.
1.3.4.
1.4. PHOTO
1.4.1.
1.4.2.
1.4.3.
1.4.4.
1.4.5.
significant figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Important derived physical constants and relationships . . 1
Physical quantities and units . . . . . . . . . . . . . . . . . . . . . . . . 3
Classification of forces in nature . . . . . . . . . . . . . . . . . . . . . 4
Classification of fundamental particles . . . . . . . . . . . . . . . . 4
Classification of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Classification of ionizing photon radiation . . . . . . . . . . . . . 6
Einstein’s relativistic mass, energy and momentum 
relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Radiation quantities and units . . . . . . . . . . . . . . . . . . . . . . . 7
C AND NUCLEAR STRUCTURE . . . . . . . . . . . . . . . . . . 7
Basic definitions for atomic structure . . . . . . . . . . . . . . . . 7
Rutherford’s model of the atom . . . . . . . . . . . . . . . . . . . . . 9
Bohr’s model of the hydrogen atom . . . . . . . . . . . . . . . . . . 10
Multielectron atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Nuclear structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Activation of nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 19
Modes of radioactive decay . . . . . . . . . . . . . . . . . . . . . . . . 20
RON INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Electron–orbital electron interactions . . . . . . . . . . . . . . . . 23
Electron–nucleus interactions . . . . . . . . . . . . . . . . . . . . . . . 23
Stopping power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Mass scattering power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
N INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Types of indirectly ionizing photon radiation . . . . . . . . . . . 26
Photon beam attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Types of photon interaction . . . . . . . . . . . . . . . . . . . . . . . . . 28
Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Coherent (Rayleigh) scattering . . . . . . . . . . . . . . . . . . . . . . 29
1.4.6. Compton effect (incoherent scattering) . . . . . . . . . . . . . . . 30
1.4.7. Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.4.8. Photonuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.4.9. Contributions to attenuation coefficients . . . . . . . . . . . . . . 34
1.4.10. Relative predominance of individual effects . . . . . . . . . . . 36
1.4.11. Effects following photon interactions . . . . . . . . . . . . . . . . . 37
1.4.12. Summary of photon interactions . . . . . . . . . . . . . . . . . . . . . 38
1.4.13.
1.4.14.
BIBLIO
CHAPTER 2.
2.1. INTRO
2.2. PHOTO
2.3. KERMA
2.4. CEMA 
2.5. ABSOR
2.6. STOPPI
2.7. RELAT
QUANT
2.7.1.
2.7.2.
2.7.3.
2.7.4.
2.8. CAVITY
2.8.1.
2.8.2.
2.8.3.
2.8.4.
2.8.5.
2.8.6.
BIBLIO
Example of photon attenuation . . . . . . . . . . . . . . . . . . . . . 40
Production of vacancies in atomic shells . . . . . . . . . . . . . . . 41
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
DOSIMETRIC PRINCIPLES, 
QUANTITIES AND UNITS . . . . . . . . . . . . . . . . . . . . . . 45
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
N FLUENCE AND ENERGY FLUENCE . . . . . . . . . . . . 45
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
BED DOSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
NG POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
IONSHIPS BETWEEN VARIOUS DOSIMETRIC 
ITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Energy fluence and kerma (photons) . . . . . . . . . . . . . . . . . 54
Fluence and dose (electrons) . . . . . . . . . . . . . . . . . . . . . . . . 56
Kerma and dose (charged particle equilibrium) . . . . . . . . 57
Collision kerma and exposure . . . . . . . . . . . . . . . . . . . . . . . 60
 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Bragg–Gray cavity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Spencer–Attix cavity theory . . . . . . . . . . . . . . . . . . . . . . . . . 62
Considerations in the application of cavity theory to 
ionization chamber calibration and dosimetry protocols . 64
Large cavities in photon beams . . . . . . . . . . . . . . . . . . . . . . 66
Burlin cavity theory for photon beams . . . . . . . . . . . . . . . . 66
Stopping power ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
CHAPTER 3. RADIATION DOSIMETERS . . . . . . . . . . . . . . . . . . . . . 71
3.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2. PROPERTIES OF DOSIMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.1. Accuracy and precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.1.1. Type A standard uncertainties . . . . . . . . . . . . . . 72
3.2.1.2. Type B standard uncertainties . . . . . . . . . . . . . . 73
3.2.2.
3.2.3.
3.2.4.
3.2.5.
3.2.6.
3.2.7.
3.2.8.
3.3. IONIZA
3.3.1.
3.3.2.
3.3.3.
3.3.4.
3.3.5.
3.4. FILM D
3.4.1.
3.4.2.
3.5. LUMIN
3.5.1.
3.5.2.
3.5.3.
3.6. SEMIC
3.6.1.
3.6.2.
3.7. OTHER
3.7.1.
3.7.2.
3.7.3.
3.2.1.3. Combined and expanded uncertainties . . . . . . . 73
Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Dose rate dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Energy dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Directional dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Spatial resolution and physical size . . . . . . . . . . . . . . . . . . . 76
Readout convenience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Convenience of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
TION CHAMBER DOSIMETRY SYSTEMS . . . . . . . . . 77
Chambers and electrometers . . . . . . . . . . . . . . . . . . . . . . . . 77
Cylindrical (thimble type) ionization chambers . . . . . . . . 78
Parallel-plate (plane-parallel) ionization chambers . . . . . 79
Brachytherapy chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Extrapolation chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
OSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Radiographic film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Radiochromic film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
ESCENCE DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Thermoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Thermoluminescent dosimeter systems . . . . . . . . . . . . . . . 86
Optically stimulated luminescence systems . . . . . . . . . . . . 88
ONDUCTOR DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . 89
Silicon diode dosimetry systems . . . . . . . . . . . . . . . . . . . . . 89
MOSFET dosimetry systems . . . . . . . . . . . . . . . . . . . . . . . . 90
 DOSIMETRY SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Alanine/electron paramagnetic resonance dosimetry 
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Plastic scintillator dosimetry system . . . . . . . . . . . . . . . . . . 92
Diamond dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.7.4. Gel dosimetry systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.8. PRIMARY STANDARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.8.1. Primary standard for air kerma in air . . . . . . . . . . . . . . . . . 95
3.8.2. Primary standards for absorbed dose to water . . . . . . . . . 95
3.8.3. Ionometric standard for absorbed dose to water . . . . . . . . 96
3.8.4. Chemical dosimetry standard for absorbed dose to water 96
3.8.5.
3.9. SUMMA
SYSTEM
BIBLIO
CHAPTER 4.
4.1. INTRO
4.2. OPERA
RADIA
4.3. AREA 
4.3.1.
4.3.2.
4.3.3.
4.3.4.
4.3.5.
4.3.6.
4.3.7.
4.3.8.
4.3.9.
4.4. INDIVI
4.4.1.
Calorimetric standard for absorbed dose to water . . . . . . 97
RY OF SOME COMMONLY USED DOSIMETRIC 
S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
RADIATION MONITORING INSTRUMENTS . . . . 101
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 101
TIONAL QUANTITIES FOR 
TION MONITORING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
SURVEY METERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Ionization chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Proportional counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Neutron area survey meters . . . . . . . . . . . . . . . . . . . . . . . . . 105
Geiger–Müller counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Scintillator detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Commonly available features of area survey meters . . . . 108
Calibration of survey meters . . . . . . . . . . . . . . . . . . . . . . . . 108
Properties of survey meters . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.9.1. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.9.2. Energy dependence . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.9.3. Directional dependence . . . . . . . . . . . . . . . . . . . . 111
4.3.9.4. Dose equivalent range . . . . . . . . . . . . . . . . . . . . 111
4.3.9.5. Response time . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.9.6. Overload characteristics . . . . . . . . . . . . . . . . . . . 111
4.3.9.7. Long term stability . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.9.8. Discrimination between different types 
of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.9.9. Uncertainties in area survey measurements . . . 112
DUAL MONITORING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Film badge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.4.2. Thermoluminescence dosimetry badge . . . . . . . . . . . . . . . . 115
4.4.3. Radiophotoluminescent glass dosimetry systems . . . . . . . 116
4.4.4. Optically stimulated luminescence systems . . . . . . . . . . . . 116
4.4.5. Direct reading personal monitors . . . . . . . . . . . . . . . . . . . . 117
4.4.6. Calibration of personal dosimeters . . . . . . . . . . . . . . . . . . . 118
4.4.7. Properties of personal monitors . . . . . . . . . . . . . . . . . . . . . . 118
4.4.7.1. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
BIBLIO
CHAPTER 5.
5.1. INTRO
5.2. X RAY 
5.2.1.
5.2.2.
5.2.3.
5.2.4.
5.2.5.
5.2.6.
5.3. GAMM
5.3.1.
5.3.2.
5.3.3.
5.3.4.
5.3.5.
5.3.6.
5.4. PARTIC
5.4.1.
5.4.2.
5.4.3.
4.4.7.2. Energy dependence . . . . . . . . . . . . . . . . . . . . . . . 119
4.4.7.3. Uncertainties in personal monitoring 
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4.7.4. Equivalent dose range . . . . . . . . . . . . . . . . . . . . . 119
4.4.7.5. Directional dependence . . . . . . . . . . . . . . . . . . . 120
4.4.7.6. Discrimination between different types 
of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
TREATMENT MACHINES FOR EXTERNAL 
BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . 123
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
BEAMS AND X RAY UNITS . . . . . . . . . . . . . . . . . . . . . . . 124
Characteristic X rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Bremsstrahlung (continuous) X rays . . . . . . . . . . . . . . . . . 124
X ray targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Clinical X ray beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
X ray beam quality specifiers . . . . . . . . . . . . . . . . . . . . . . . 127
X ray machines for radiotherapy . . . . . . . . . . . . . . . . . . . . . 127
A RAY BEAMS AND GAMMA RAY UNITS . . . . . . . . 129
Basic properties of gamma rays . . . . . . . . . . . . . . . . . . . . . . 129
Teletherapy machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Teletherapy sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Teletherapy source housing . . . . . . . . . . . . . . . . . . . . . . . . . 131
Dose delivery with teletherapy machines . . . . . . . . . . . . . . 132
Collimator and penumbra . . . . . . . . . . . . . . . . . . . . . . . . . 132
LE ACCELERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Betatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Cyclotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Microtron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.5. LINACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.5.1. Linac generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.5.2. Safety of linac installations . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.5.3. Components of modern linacs . . . . . . . . . . . . . . . . . . . . . . . 138
5.5.4. Configuration of modern linacs . . . . . . . . . . . . . . . . . . . . . . 138
5.5.5. Injection system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.5.6. Radiofrequency power generation system . . . . . . . . . . . . . 143
5.5.7.
5.5.8.
5.5.9.
5.5.10.
5.5.11.
5.5.12.
5.5.13.
5.5.14.
5.5.15.
5.6. RADIO
HEAVY
5.7. SHIELD
5.8. COBAL
5.9. SIMUL
TOMOG
5.9.1.
5.9.2.
5.10. TRAIN
BIBLIO
CHAPTER 6.
6.1. INTRO
6.2. QUANT
6.2.1.
6.2.2.
6.2.3.
6.2.4.
6.2.5.
6.3. PHOTO
Accelerating waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Microwave power transmission . . . . . . . . . . . . . . . . . . . . . . 144
Auxiliary system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Electron beam transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Linac treatment head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Production of clinical photon beams in a linac . . . . . . . . . 147
Beam collimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Production of clinical electron beams in a linac . . . . . . . . . 149
Dose monitoring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
THERAPY WITH PROTONS, NEUTRONS AND 
 IONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
ING CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 152
T-60 TELETHERAPY UNITS VERSUS LINACS . . . . . 153
ATORS AND COMPUTED 
RAPHY SIMULATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Radiotherapy simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Computed tomography simulator . . . . . . . . . . . . . . . . . . . . 158
ING REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
EXTERNAL PHOTON BEAMS: 
PHYSICAL ASPECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
ITIES USED IN DESCRIBING A PHOTON BEAM . . 161
Photon fluence and photon fluence rate . . . . . . . . . . . . . . 162
Energy fluence and energy fluence rate . . . . . . . . . . . . . . . 162
Air kerma in air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Exposure in air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Dose to small mass of medium in air . . . . . . . . . . . . . . . . . . 164
N BEAMSOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.4. INVERSE SQUARE LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.5. PENETRATION OF PHOTON BEAMS INTO A 
PHANTOM OR PATIENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.5.1. Surface dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.5.2. Buildup region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.5.3. Depth of dose maximum zmax . . . . . . . . . . . . . . . . . . . . . . . . 172
6.5.4. Exit dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.6. RADIA
6.6.1.
6.6.2.
6.6.3.
6.6.4.
6.7. CENTR
SOURC
6.7.1.
6.7.2.
6.8. CENTR
DISTAN
6.8.1.
6.8.2.
6.8.3.
6.8.4.
6.8.5.
6.8.6.
6.8.7.
6.9. OFF-AX
6.9.1.
6.9.2.
6.10. ISODO
6.11. SINGLE
6.11.1.
TION TREATMENT PARAMETERS . . . . . . . . . . . . . . . 172
Radiation beam field size . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Collimator factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Peak scatter factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Relative dose factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
AL AXIS DEPTH DOSES IN WATER: 
E TO SURFACE DISTANCE SET-UP . . . . . . . . . . . . . . . 179
Percentage depth dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Scatter function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
AL AXIS DEPTH DOSES IN WATER: SOURCE TO AXIS 
CE SET-UP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Tissue–air ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Relationship between TAR(d, AQ, hn) and 
PDD(d, A, f, hn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Scatter–air ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Relationship between SAR(d, AQ, hn) and S(z, A, f, hn) . 190
Tissue–phantom ratio and tissue–maximum ratio . . . . . . 190
Relationship between TMR(z, AQ, hn) and 
PDD(z, A, f, hn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Scatter–maximum ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
IS RATIOS AND BEAM PROFILES . . . . . . . . . . . . . . 194
Beam flatness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Beam symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
SE DISTRIBUTIONS IN WATER PHANTOMS . . . . . . . 197
 FIELD ISODOSE DISTRIBUTIONS IN PATIENTS . . 199
Corrections for irregular contours and oblique 
beam incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.11.1.1. Effective source to surface distance method . . . 201
6.11.1.2. Tissue–air ratio or tissue–maximum ratio 
method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.11.1.3. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 202
6.11.2. Missing tissue compensation . . . . . . . . . . . . . . . . . . . . . . . . 202
6.11.2.1. Wedge filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.11.2.2. Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.11.2.3. Compensators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.11.3. Corrections for tissue inhomogeneities . . . . . . . . . . . . . . . . 204
6.11.4. Model based algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
6.12. CLARK
6.13. RELAT
IONIZA
6.14. DELIV
EXTER
6.15. EXAMP
6.16. SHUTT
BIBLIO
CHAPTER 7.
7.1. INTRO
7.2. VOLUM
7.2.1.
7.2.2.
7.2.3.
7.2.4.
7.2.5.
7.3. DOSE S
7.4. PATIEN
7.4.1.
7.4.2.
7.4.3.
7.4.4.
7.4.5.
7.4.6.
SON SEGMENTAL INTEGRATION . . . . . . . . . . . . . . . . 206
IVE DOSE MEASUREMENTS WITH 
TION CHAMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
ERY OF DOSE WITH A SINGLE 
NAL BEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
LE OF DOSE CALCULATION . . . . . . . . . . . . . . . . . . . . 213
ER CORRECTION TIME . . . . . . . . . . . . . . . . . . . . . . . . . . 215
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
CLINICAL TREATMENT PLANNING 
IN EXTERNAL PHOTON BEAM 
RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
E DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Gross tumour volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Clinical target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Internal target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Planning target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Organ at risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
PECIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
T DATA ACQUISITION AND SIMULATION . . . . . . 223
Need for patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Nature of patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7.4.2.1. Two dimensional treatment planning . . . . . . . . 223
7.4.2.2. Three dimensional treatment planning . . . . . . . 224
Treatment simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Patient treatment position and immobilization devices . . 226
Patient data requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Conventional treatment simulation . . . . . . . . . . . . . . . . . . . 229
7.4.6.1. Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.4.6.2. Localization of the target volume and 
organs at risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.4.6.3. Determination of the treatment beam geometry 230
7.4.6.4. Acquisition of patient data . . . . . . . . . . . . . . . . . 230
7.4.7. Computed tomography based conventional 
treatment simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.4.7.1. Computed tomography based patient data 
7.4.8.
7.4.9.
7.4.10.
7.4.11.
7.5. CLINIC
7.5.1.
7.5.2.
7.5.3.
7.5.4.
7.5.5.
7.5.6.
7.5.7.
acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.4.7.2. Determination of the treatment beam 
geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Computed tomography based virtual simulation . . . . . . . 233
7.4.8.1. Computed tomography simulator . . . . . . . . . . . . 233
7.4.8.2. Virtual simulation . . . . . . . . . . . . . . . . . . . . . . . . . 233
7.4.8.3. Digitally reconstructed radiographs . . . . . . . . . . 234
7.4.8.4. Beam’s eye view . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.4.8.5. Virtual simulation procedure . . . . . . . . . . . . . . . 235
Conventional simulator versus computed tomography 
simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Magnetic resonance imaging for treatment planning . . . . 238
Summary of simulation procedures . . . . . . . . . . . . . . . . . . . 240
AL CONSIDERATIONS FOR PHOTON BEAMS . . . . 241
Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Wedge filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Compensating filters . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 245
Corrections for contour irregularities . . . . . . . . . . . . . . . . . 246
7.5.5.1. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 246
7.5.5.2. Effective attenuation coefficient method . . . . . 248
7.5.5.3. Tissue–air ratio method . . . . . . . . . . . . . . . . . . . . 248
Corrections for tissue inhomogeneities . . . . . . . . . . . . . . . . 248
7.5.6.1. Tissue–air ratio method . . . . . . . . . . . . . . . . . . . . 249
7.5.6.2. Batho power law method . . . . . . . . . . . . . . . . . . . 250
7.5.6.3. Equivalent tissue–air ratio method . . . . . . . . . . 250
7.5.6.4. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 250
Beam combinations and clinical application . . . . . . . . . . . 251
7.5.7.1. Weighting and normalization . . . . . . . . . . . . . . . 251
7.5.7.2. Fixed source to surface distance versus isocentric 
techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
7.5.7.3. Parallel opposed beams . . . . . . . . . . . . . . . . . . . . 252
7.5.7.4. Multiple coplanar beams . . . . . . . . . . . . . . . . . . . 253
7.5.7.5. Rotational techniques . . . . . . . . . . . . . . . . . . . . . 254
7.5.7.6. Multiple non-coplanar beams . . . . . . . . . . . . . . . 255
7.5.7.7. Field matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
7.6. TREATMENT PLAN EVALUATION . . . . . . . . . . . . . . . . . . . . . . . 256
7.6.1. Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.6.2. Orthogonal planes and isodose surfaces . . . . . . . . . . . . . . . 257
7.6.3.
7.6.4.
7.6.5.
7.7. TREAT
CALCU
7.7.1.
7.7.2.
7.7.3.
7.7.4.
7.7.5.
BIBLIO
CHAPTER 8.
8.1. CENTR
8.1.1.
8.1.2.
8.1.3.
8.1.4.
8.1.5.
8.1.6.
Dose statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Dose–volume histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
7.6.4.1. Direct dose–volume histogram . . . . . . . . . . . . . . 259
7.6.4.2. Cumulative dose–volume histogram . . . . . . . . . 259
Treatment evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
7.6.5.1. Port films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.6.5.2. On-line portal imaging . . . . . . . . . . . . . . . . . . . . . 262
MENT TIME AND MONITOR UNIT 
LATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Treatment time and monitor unit calculations for a fixed 
source to surface distance set-up . . . . . . . . . . . . . . . . . . . . . 265
Monitor unit and treatment time calculations for 
isocentric set-ups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Normalization of dose distributions . . . . . . . . . . . . . . . . . . 270
Inclusion of output parameters in the dose 
distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Treatment time calculation for orthovoltage 
and cobalt-60 units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
ELECTRON BEAMS: 
PHYSICAL AND CLINICAL ASPECTS . . . . . . . . . . . 273
AL AXIS DEPTH DOSE DISTRIBUTIONS IN WATER 273
General shape of the depth dose curve . . . . . . . . . . . . . . . . 273
Electron interactions with an absorbing medium . . . . . . . 274
Inverse square law (virtual source position) . . . . . . . . . . . 276
Range concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Buildup region (depths between the surface and 
z (i.e. 0 £ z £ zmax )) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Dose distribution beyond zmax (z > zmax) . . . . . . . . . . . . . . 279
max
8.2. DOSIMETRIC PARAMETERS OF ELECTRON BEAMS . . . . 281
8.2.1. Electron beam energy specification . . . . . . . . . . . . . . . . . . 281
8.2.2. Typical depth dose parameters as a function of energy . . 281
8.2.3. Percentage depth dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.2.3.1. Percentage depth doses for small electron 
field sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.2.3.2. Percentage depth doses for oblique beam 
8.2.4.
8.2.5.
8.2.6.
8.2.7.
8.3. CLINIC
BEAM 
8.3.1.
8.3.2.
8.3.3.
8.3.4.
8.3.5.
8.3.6.
8.3.7.
8.3.8.
8.3.9.
8.3.10.
BIBLIO
CHAPTER 9.
9.1. INTRO
incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Therapeutic range R90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Profiles and off-axis ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Flatness and symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
AL CONSIDERATIONS IN ELECTRON 
THERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Dose specification and reporting . . . . . . . . . . . . . . . . . . . . . 286
Small field sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Field shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
8.3.4.1. Electron applicators . . . . . . . . . . . . . . . . . . . . . . . 289
8.3.4.2. Shielding and cut-outs . . . . . . . . . . . . . . . . . . . . . 289
8.3.4.3. Internal shielding . . . . . . . . . . . . . . . . . . . . . . . . . 290
8.3.4.4. Extended source to surface distance 
treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Irregular surface correction . . . . . . . . . . . . . . . . . . . . . . . . . 291
Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Inhomogeneity corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 292
8.3.7.1. Coefficient of equivalent thickness . . . . . . . . . . 292
8.3.7.2. Scatter perturbation (edge) effects . . . . . . . . . . . 293
Electron beam combinations . . . . . . . . . . . . . . . . . . . . . . . . 295
8.3.8.1. Matched (abutted) electron fields . . . . . . . . . . . 295
8.3.8.2. Matched photon and electron fields . . . . . . . . . . 295
Electron arc therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Electron therapy treatment planning . . . . . . . . . . . . . . . . . 298
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
CALIBRATION OF PHOTON AND ELECTRON 
BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.1.1. Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
9.1.2. Fricke dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.1.3. Ionization chamber dosimetry . . . . . . . . . . . . . . . . . . . . . . . 304
9.1.4. Mean energy expended in air per ion pair formed . . . . . . 304
9.1.5. Reference dosimetry with ionization chambers . . . . . . . . . 305
9.1.5.1. Standard free air ionization chambers . . . . . . . 305
9.1.5.2. Cavity ionization chambers . . . . . . . . . . . . . . . . 306
9.1.6.
9.1.7.
9.2. IONIZA
9.2.1.
9.2.2.
9.2.3.
9.3. CHAM
INFLUE
9.3.1.
9.3.2.
9.3.3.
9.3.4.
9.3.5.
9.4. DETER
CALIB
9.4.1.
9.4.2.
9.5. STOPPI
9.5.1.
9.5.2.
9.6. MASS–
9.7. PERTU
9.7.1.
9.7.2.
9.1.5.3. Phantom embedded extrapolation chambers . . 306
Clinical beam calibration and measurement chain . . . . . . 307
Dosimetry protocols . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 307
TION CHAMBER BASED DOSIMETRY SYSTEMS . 308
Ionization chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Electrometer and power supply . . . . . . . . . . . . . . . . . . . . . . 309
Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
BER SIGNAL CORRECTION FOR 
NCE QUANTITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Air temperature, pressure and humidity 
effects: kT,P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Chamber polarity effects: polarity correction 
factor kpol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Chamber voltage effects: recombination correction 
factor ksat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Chamber leakage currents . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Chamber stem effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
MINATION OF ABSORBED DOSE USING 
RATED IONIZATION CHAMBERS . . . . . . . . . . . . . . . . . 319
Air kerma based protocols . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Absorbed dose to water based protocols . . . . . . . . . . . . . . 323
NG POWER RATIOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
Stopping power ratios for electron beams . . . . . . . . . . . . . 326
Stopping power ratios for photon beams . . . . . . . . . . . . . . 327
ENERGY ABSORPTION COEFFICIENT RATIOS . . . 328
RBATION CORRECTION FACTORS . . . . . . . . . . . . . . . 329
Displacement perturbation factor pdis and effective 
point of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
Chamber wall perturbation factor pwall . . . . . . . . . . . . . . . . 331
9.7.3. Central electrode perturbation pcel . . . . . . . . . . . . . . . . . . . 333
9.7.4. Cavity or fluence perturbation correction pcav . . . . . . . . . . 334
9.8. BEAM QUALITY SPECIFICATION . . . . . . . . . . . . . . . . . . . . . . . 335
9.8.1. Beam quality specification for kilovoltage 
photon beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
9.8.2. Beam quality specification for megavoltage 
9.8.3.
9.9. CALIB
AND E
9.9.1.
9.9.2.
9.9.3.
9.9.4.
9.10. KILOV
9.10.1.
9.10.2.
9.10.3.
9.10.4.
9.10.5.
9.11. ERROR
CHAM
9.11.1.
9.11.2.
9.11.3.
BIBLIO
photon beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Beam quality specification for megavoltage 
electron beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
RATION OF MEGAVOLTAGE PHOTON 
LECTRON BEAMS: PRACTICAL ASPECTS . . . . . . . . . 342
Calibration of megavoltage photon beams based on the air 
kerma in air calibration coefficient NK,Co . . . . . . . . . . . . . 342
Calibration of megavoltage photon beams based on 
the dose to water calibration coefficient ND,w,Co . . . . . . . . 343
Calibration of megavoltage electron beams based on the 
air kerma in air calibration coefficient NK,Co . . . . . . . . . . . 345
Calibration of high energy electron beams based on the 
dose to water calibration coefficient ND,w,Co . . . . . . . . . . . . 346
OLTAGE DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Specific features of kilovoltage beams . . . . . . . . . . . . . . . . 347
Air kerma based in-phantom calibration method 
(medium energies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Air kerma based backscatter method (low and medium 
photon energies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Air kerma in air based calibration method for very 
low energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Absorbed dose to water based calibration method . . . . . . 351
 AND UNCERTAINTY ANALYSIS FOR IONIZATION 
BER MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Errors and uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Classification of uncertainties . . . . . . . . . . . . . . . . . . . . . . . 352
Uncertainties in the calibration chain . . . . . . . . . . . . . . . . . 352
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
CHAPTER 10. ACCEPTANCE TESTS AND COMMISSIONING 
MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
10.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
10.2. MEASUREMENT EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . 355
10.2.1. Radiation survey equipment . . . . . . . . . . . . . . . . . . . . . . . . 355
10.2.2. Ionometric dosimetry equipment . . . . . . . . . . . . . . . . . . . . 356
10.2.3.
10.2.4.
10.2.5.
10.3. ACCEP
10.3.1.
10.3.2.
10.3.3.
Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
10.2.5.1. Radiation field analyser and water phantom . . 357
10.2.5.2. Plastic phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . 357
TANCE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
Safety checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
10.3.1.1. Interlocks, warning lights and patient 
monitoring equipment . . . . . . . . . . . . . . . . . . . . . 359
10.3.1.2. Radiation survey . . . . . . . . . . . . . . . . . . . . . . . . . . 359
10.3.1.3. Collimator and head leakage . . . . . . . . . . . . . . . 360
Mechanical checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
10.3.2.1. Collimator axis of rotation . . . . . . . . . . . . . . . . . 361
10.3.2.2. Photon collimator jaw motion . . . . . . . . . . . . . . . 361
10.3.2.3. Congruence of light and radiation field . . . . . . . 362
10.3.2.4. Gantry axis of rotation . . . . . . . . . . . . . . . . . . . . . 363
10.3.2.5. Patient treatment table axis of rotation . . . . . . . 363
10.3.2.6. Radiation isocentre . . . . . . . . . . . . . . . . . . . . . . . 364
10.3.2.7. Optical distance indicator . . . . . . . . . . . . . . . . . . 364
10.3.2.8. Gantry angle indicators . . . . . . . . . . . . . . . . . . . . 365
10.3.2.9. Collimator field size indicators . . . . . . . . . . . . . . 365
10.3.2.10. Patient treatment table motions . . . . . . . . . . . . . 365
Dosimetry measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
10.3.3.1. Photon energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
10.3.3.2. Photon beam uniformity . . . . . . . . . . . . . . . . . . . 366
10.3.3.3. Photon penumbra . . . . . . . . . . . . . . . . . . . . . . . . . 366
10.3.3.4. Electron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
10.3.3.5. Electron beam bremsstrahlung contamination . 367
10.3.3.6. Electron beam uniformity . . . . . . . . . . . . . . . . . . 368
10.3.3.7. Electron penumbra . . . . . . . . . . . . . . . . . . . . . . . . 368
10.3.3.8. Monitor characteristics . . . . . . . . . . . . . . . . . . . . 368
10.3.3.9. Arc therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
10.4. COMMISSIONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
10.4.1. Photon beam measurements . . . . . . . . . . . . . . . . . . . . . . . . 370
10.4.1.1. Central axis percentage depth doses . . . . . . . . . 370
10.4.1.2. Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
10.4.1.3. Blocking tray factors . . . . . . . . . . . . . . . . . . . . . .373
10.4.1.4. Multileaf collimators . . . . . . . . . . . . . . . . . . . . . . 373
10.4.1.5. Central axis wedge transmission factors . . . . . . 374
10.4.2.
10.5. TIME R
BIBLIO
CHAPTER 11
11.1. INTRO
11.2. SYSTEM
11.2.1.
11.2.2.
11.3. SYSTEM
11.3.1.
11.3.2.
11.3.3.
11.3.4.
11.3.5.
11.3.6.
11.3.7.
10.4.1.6. Dynamic wedge . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
10.4.1.7. Transverse beam profiles/off-axis energy 
changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
10.4.1.8. Entrance dose and interface dosimetry . . . . . . . 376
10.4.1.9. Virtual source position . . . . . . . . . . . . . . . . . . . . . 377
Electron beam measurements . . . . . . . . . . . . . . . . . . . . . . . 378
10.4.2.1. Central axis percentage depth dose . . . . . . . . . . 378
10.4.2.2. Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
10.4.2.3. Transverse beam profiles . . . . . . . . . . . . . . . . . . . 383
10.4.2.4. Virtual source position . . . . . . . . . . . . . . . . . . . . . 383
EQUIRED FOR COMMISSIONING . . . . . . . . . . . . . . . . 384
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
. COMPUTERIZED TREATMENT PLANNING 
SYSTEMS FOR EXTERNAL PHOTON BEAM 
RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
 HARDWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
Treatment planning system hardware . . . . . . . . . . . . . . . . . 388
Treatment planning system configurations . . . . . . . . . . . . . 389
 SOFTWARE AND CALCULATION ALGORITHMS 390
Calculation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
Beam modifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
11.3.2.1. Photon beam modifiers . . . . . . . . . . . . . . . . . . . . 393
11.3.2.2. Electron beam modifiers . . . . . . . . . . . . . . . . . . 394
Heterogeneity corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Image display and dose–volume histograms . . . . . . . . . . . 395
Optimization and monitor unit calculations . . . . . . . . . . . . 396
Record and verify systems . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Biological modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
11.4. DATA ACQUISITION AND ENTRY . . . . . . . . . . . . . . . . . . . . . . . 397
11.4.1. Machine data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
11.4.2. Beam data acquisition and entry . . . . . . . . . . . . . . . . . . . . . 398
11.4.3. Patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
11.5. COMMISSIONING AND QUALITY ASSURANCE . . . . . . . . . . 400
11.5.1. Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
11.5.2.
11.5.3.
11.5.4.
11.5.5.
11.5.6.
11.5.7.
11.6. SPECIA
BIBLIO
CHAPTER 12
12.1. INTRO
12.1.1.
12.1.2.
12.1.3.
12.1.4.
12.2. MANAG
12.2.1.
12.2.2.
12.3. QUALI
FOR EQ
12.3.1.
Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Spot checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Normalization and beam weighting . . . . . . . . . . . . . . . . . . . 402
Dose–volume histograms and optimization . . . . . . . . . . . . 403
Training and documentation . . . . . . . . . . . . . . . . . . . . . . . . 403
Scheduled quality assurance . . . . . . . . . . . . . . . . . . . . . . . . . 403
L CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
. QUALITY ASSURANCE OF EXTERNAL 
BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . 407
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
12.1.1.1. Quality assurance . . . . . . . . . . . . . . . . . . . . . . . . . 407
12.1.1.2. Quality assurance in radiotherapy . . . . . . . . . . . 407
12.1.1.3. Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
12.1.1.4. Quality standards . . . . . . . . . . . . . . . . . . . . . . . . . 408
Need for quality assurance in radiotherapy . . . . . . . . . . . . 408
Requirements on accuracy in radiotherapy . . . . . . . . . . . . 409
Accidents in radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . 411
ING A QUALITY ASSURANCE PROGRAMME . . . 414
Multidisciplinary radiotherapy team . . . . . . . . . . . . . . . . . . 414
Quality system/comprehensive quality assurance 
programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
TY ASSURANCE PROGRAMME 
UIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
Structure of an equipment quality 
assurance programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
12.3.1.1. Equipment specification . . . . . . . . . . . . . . . . . . . 419
12.3.1.2. Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
12.3.1.3. Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
12.3.1.4. Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
12.3.2. Uncertainties, tolerances and action levels . . . . . . . . . . . . . 421
12.3.3. Quality assurance programme for cobalt-60 
teletherapy machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
12.3.4. Quality assurance programme for linacs . . . . . . . . . . . . . . 425
12.3.5. Quality assurance programme for treatment 
12.3.6.
12.3.7.
12.3.8.
12.4. TREAT
12.4.1.
12.4.2.
12.4.3.
12.4.4.
12.5. QUALI
12.5.1.
12.5.2.
12.5.3.
BIBLIO
CHAPTER 13
13.1. INTRO
13.2. PHOTO
13.2.1.
simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
Quality assurance programme for computed 
tomography scanners and computed tomography 
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Quality assurance programme for treatment 
planning systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
Quality assurance programme for test equipment . . . . . . 431
MENT DELIVERY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
Patient charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
Portal imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
12.4.2.1. Portal imaging techniques . . . . . . . . . . . . . . . . . . 436
12.4.2.2. Future developments in portal imaging . . . . . . . 439
In vivo dose measurements . . . . . . . . . . . . . . . . . . . . . . . . . 439
12.4.3.1. In vivo dose measurement techniques . . . . . . . . 440
12.4.3.2. Use of electronic portal imaging systems for 
in vivo dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 443
Record and verify systems . . . . . . . . . . . . . . . . . . . . . . . . . . 443
TY AUDIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
Practical quality audit modalities . . . . . . . . . . . . . . . . . . . . . 446
12.5.2.1. Postal audit with mailed dosimeters . . . . . . . . . 446
12.5.2.2. Quality audit visits . . . . . . . . . . . . . . . . . . . . . . . . 446
What should be reviewed in a quality audit visit? . . . . . . . 447
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 448
. BRACHYTHERAPY: 
PHYSICAL AND CLINICAL ASPECTS . . . . . . . . . . . 451
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
N SOURCE CHARACTERISTICS . . . . . . . . . . . . . . . . . . 455
Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
13.2.2. Physical characteristics of some photon emitting 
brachytherapy sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
13.2.3. Mechanical source characteristics . . . . . . . . . . . . . . . . . . . . 456
13.2.4. Source specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
13.2.4.1. Specification of g ray sources . . . . . . . . . . . . . . . 457
13.2.4.2. Specification of b ray sources . . . . . . . . . . . . . . . 459
13.3. CLINIC
13.3.1.
13.3.2.
13.3.3.
13.3.4.
13.3.5.
13.3.6.
13.4. DOSE S
13.4.1.
13.4.2.
13.5. DOSE D
13.5.1.
13.5.2.
13.5.3.
AL USE AND DOSIMETRY SYSTEMS . . . . . . . . . . . . . 460
Gynaecology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
13.3.1.1. Types of source . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
13.3.1.2. Dose specification . . . . . . . . . . . . . . . . . . . . . . . . . 460
13.3.1.3. Source arrangement . . . . . . . . . . . . . . . . . . . . . . 460
13.3.1.4. Applicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
13.3.1.5. Rectal and bladder dose monitoring . . . . . . . . . 461
Interstitial brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
13.3.2.1. Patterson–Parker system . . . . . . . . . . . . . . . . . . . 461
13.3.2.2. Quimby system . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
13.3.2.3. Paris system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
Remote afterloading systems . . . . . . . . . . . . . . . . . . . . . . . . 463
Permanent prostate implants . . . . . . . . . . . . . . . . . . . . . . . . 464
13.3.4.1. Choice of radionuclide for prostate 
implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
13.3.4.2. Planning technique: ultrasound or computed 
tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
13.3.4.3. Preplanning, seed placement and dose 
distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
13.3.4.4. Post-implant dose distributions 
and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
Eye plaques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Intravascular brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . 466
PECIFICATION AND REPORTING . . . . . . . . . . . . . . . . 467
Intracavitary treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Interstitial treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
ISTRIBUTIONS AROUND SOURCES . . . . . . . . . . . . . 468
AAPM TG 43 algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
Other calculation methods for point sources . . . . . . . . . . . 471
Linear sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
13.5.3.1. Unfiltered line source in air . . . . . . . . . . . . . . . . . 473
13.5.3.2. Filtered line source in air . . . . . . . . . . . . . . . . . . . 474
13.5.3.3. Filtered line source in water . . . . . . . . . . . . . . . . 475
13.6. DOSE CALCULATION PROCEDURES . . . . . . . . . . . . . . . . . . . . 475
13.6.1. Manual dose calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
13.6.1.1. Manual summation of doses . . . . . . . . . . . . . . . . 475
13.6.1.2. Precalculated dose distributions (atlases) . . . . . 475
13.6.2.
13.6.3.
13.7. COMM
TREAT
13.7.1.
13.7.2.
13.7.3.
13.7.4.
13.8. SOURC
13.8.1.
13.8.2.
13.8.3.
13.9. QUALI
13.9.1.
13.9.2.
13.9.3.
13.9.4.
13.9.5.
Computerized treatment planning . . . . . . . . . . . . . . . . . . . 476
13.6.2.1. Source localization . . . . . . . . . . . . . . . . . . . . . . . . 476
13.6.2.2. Dose calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 476
13.6.2.3. Dose distribution display . . . . . . . . . . . . . . . . . . . 476
13.6.2.4. Optimization of dose distribution . . . . . . . . . . . . 477
Calculation of treatment time . . . . . . . . . . . . . . . . . . . . . . . 477
13.6.3.1. Use of Patterson–Parker tables . . . . . . . . . . . . . 477
13.6.3.2. Choice of reference points . . . . . . . . . . . . . . . . . . 478
13.6.3.3. Decay corrections . . . . . . . . . . . . . . . . . . . . . . . . . 478
ISSIONING OF BRACHYTHERAPY COMPUTER 
MENT PLANNING SYSTEMS . . . . . . . . . . . . . . . . . . . . . . 479
Check of the reconstruction procedure . . . . . . . . . . . . . . . 479
Check of consistency between quantities and units . . . . . . 479
Computer versus manual dose calculation for 
a single source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
Check of decay corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 479
E COMMISSIONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
Wipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
Autoradiography and uniformity checks of activity . . . . . 480
Calibration chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
TY ASSURANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Constancy check of a calibrated dosimeter . . . . . . . . . . . . 481
Regular checks of sources and applicators . . . . . . . . . . . . . 481
13.9.2.1. Mechanical properties . . . . . . . . . . . . . . . . . . . . . 481
13.9.2.2. Source strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
13.9.2.3. Wipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
Checks of source positioning with afterloading devices . . 482
Radiation monitoring around patients . . . . . . . . . . . . . . . . 482
Quality management programme . . . . . . . . . . . . . . . . . . . . 482
13.10. BRACHYTHERAPY VERSUS EXTERNAL BEAM 
RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
CHAPTER 14. BASIC RADIOBIOLOGY . . . . . . . . . . . . . . . . . . . . . . . . 485
14.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
14.2. CLASS
14.3. CELL C
14.4. IRRAD
14.4.1.
14.4.2.
14.4.3.
14.5. TYPE O
14.5.1.
14.5.2.
14.5.3.
14.5.4.
14.5.5.
14.5.6.
14.5.7.
14.6. CELL S
14.7. DOSE R
14.8. MEASU
14.9. NORM
THERA
14.10. OXYGE
14.11. RELAT
14.12. DOSE R
14.13. RADIO
BIBLIO
 CHAPTER 1
15.1. INTRO
15.2. STERE
15.2.1.
15.2.2.
IFICATION OF RADIATIONS IN RADIOBIOLOGY . 486
YCLE AND CELL DEATH . . . . . . . . . . . . . . . . . . . . . . . . 487
IATION OF CELLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
Direct action in cell damage by radiation . . . . . . . . . . . . . . 488
Indirect action in cell damage by radiation . . . . . . . . . . . . 488
Fate of irradiated cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
F RADIATION DAMAGE . . . . . . . . . . . . . . . . . . . . . . . . . 489
Timescale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
Classification of radiation damage . . . . . . . . . . . . . . . . . . . 490
Somatic and genetic effects . . . . . . . . . . . . . . . . . . . . . . . . . 490
Stochastic and deterministic (non-stochastic) effects . . . . 491
Acute versus late tissue or organ effects . . . . . . . . . . . . . . . 491
Total body radiation response . . . . . . . . . . . . . . . . . . . .. . . 491
Foetal irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
URVIVAL CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
ESPONSE CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
REMENT OF RADIATION DAMAGE IN TISSUE . . . 496
AL AND TUMOUR CELLS: 
PEUTIC RATIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
N EFFECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
IVE BIOLOGICAL EFFECTIVENESS . . . . . . . . . . . . . . 500
ATE AND FRACTIONATION . . . . . . . . . . . . . . . . . . . . . 501
PROTECTORS AND RADIOSENSITIZERS . . . . . . . . . 503
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
5. SPECIAL PROCEDURES AND TECHNIQUES 
IN RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
DUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
OTACTIC IRRADIATION . . . . . . . . . . . . . . . . . . . . . . . . . 506
Physical and clinical requirements for radiosurgery . . . . . 506
Diseases treated with stereotactic irradiation . . . . . . . . . 507
15.2.3. Equipment used for stereotactic radiosurgery . . . . . . . . . 507
15.2.4. Historical development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
15.2.5. Radiosurgical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 509
15.2.5.1. Gamma Knife . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
15.2.5.2. Linac based radiosurgery . . . . . . . . . . . . . . . . . . . 509
15.2.5.3. Miniature linac on robotic arm . . . . . . . . . . . . . . 511
15.2.6. Uncertainty in radiosurgical dose delivery . . . . . . . . . . . . . 512
15.2.7.
15.2.8.
15.2.9.
15.2.10.
15.2.11.
15.3. TOTAL
15.3.1.
15.3.2.
15.3.3.
15.3.4.
15.3.5.
15.3.6.
15.3.7.
15.3.8.
15.4. TOTAL
15.4.1.
15.4.2.
15.4.3.
15.4.4.
15.4.5.
15.4.6.
15.4.7.
15.4.8.
15.5. INTRA
15.5.1.
15.5.2.
Dose prescription and dose fractionation . . . . . . . . . . . . . . 513
Commissioning of radiosurgical equipment . . . . . . . . . . . . 514
Quality assurance in radiosurgery . . . . . . . . . . . . . . . . . . . . 514
Gamma Knife versus linac based radiosurgery . . . . . . . . . 515
Frameless stereotaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
 BODY IRRADIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
Clinical total body irradiation categories . . . . . . . . . . . . . . 516
Diseases treated with total body irradiation . . . . . . . . . . . 517
Technical aspects of total body irradiation . . . . . . . . . . . . . 517
Total body irradiation techniques . . . . . . . . . . . . . . . . . . . . 518
Dose prescription point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
Commissioning of total body irradiation procedure . . . . . 519
Test of total body irradiation dosimetry protocol . . . . . . . 521
Quality assurance in total body irradiation . . . . . . . . . . . . 521
 SKIN ELECTRON IRRADIATION . . . . . . . . . . . . . . . . . 522
Physical and clinical requirements for total skin electron 
irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
Current total skin electron irradiation techniques . . . . . . 523
Selection of total skin electron irradiation technique . . . . 524
Dose calibration point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
Skin dose rate at the dose prescription point . . . . . . . . . . . 525
Commissioning of the total skin electron irradiation 
procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
Measurement of clinical total skin electron irradiation 
dose distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
Quality assurance in total skin electron irradiation . . . . . 526
OPERATIVE RADIOTHERAPY . . . . . . . . . . . . . . . . . . . 527
Physical and clinical requirements for intraoperative 
radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
Intraoperative radiotherapy radiation modalities and 
techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
15.5.3. Commissioning of an intraoperative radiotherapy 
programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
15.5.4. Quality assurance in intraoperative radiotherapy . . . . . . . 528
15.6. ENDOCAVITARY RECTAL IRRADIATION . . . . . . . . . . . . . . . 529
15.6.1. Physical and clinical requirements for endorectal 
irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
15.6.2.
15.6.3.
15.7. CONFO
15.7.1.
15.7.2.
15.7.3.
15.7.4.
15.7.5.
15.7.6.
15.7.7.
15.7.8.
15.7.9.
15.8. IMAGE
15.8.1.
15.8.2.
15.8.3.
15.8.4.
15.8.5.
15.8.6.
15.9. ADAPT
15.10. RESPIR
15.11. POSITR
TOMOG
TOMOG
IMAGE
BIBLIO
Endorectal treatment technique . . . . . . . . . . . . . . . . . . . . . 530
Quality assurance in endorectal treatments . . . . . . . . . . . . 531
RMAL RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . 531
Basic aspects of conformal radiotherapy . . . . . . . . . . . . . . 531
Multileaf collimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
Acceptance testing of multileaf collimators . . . . . . . . . . . . 533
Commissioning of multileaf collimators . . . . . . . . . . . . . . . 534
Quality assurance programme for multileaf collimators . 534
Intensity modulated radiotherapy . . . . . . . . . . . . . . . . . . . . 534
Commissioning of intensity modulated radiotherapy 
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Quality assurance for intensity modulated radiotherapy 
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Dose verification for intensity modulated radiotherapy 
treatment plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
 GUIDED RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . 538
Cone beam computed tomography . . . . . . . . . . . . . . . . . . . 539
Computed tomography Primatom . . . . . . . . . . . . . . . . . . . 540
Tomotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
BAT system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
ExacTrac ultrasonic module . . . . . . . . . . . . . . . . . . . . . . . . . 542
CyberKnife . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
IVE RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
ATORY GATED RADIOTHERAPY . . . . . . . . . . . . . . . 544
ON EMISSION TOMOGRAPHY/COMPUTED 
RAPHY SCANNERS AND POSITRON EMISSION 
RAPHY/COMPUTED TOMOGRAPHY 
 FUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
CHAPTER 16. RADIATION PROTECTION AND SAFETY IN 
RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
16.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549
16.2. RADIATION EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
16.2.1. Deterministic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
16.2.2. Stochastic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
16.2.3.
16.3. INTER
STAND
16.4. TYPES
16.5. QUANT
PROTE
16.5.1.
16.5.2.
16.5.3.
16.6. BASIC 
16.7. GOVER
INFRA
16.8. SCOPE
16.9. RESPO
OF BAS
16.10. SAFET
EQUIP
16.10.1.
16.10.2.
16.10.3.Effects on the embryo and foetus . . . . . . . . . . . . . . . . . . . . 551
NATIONAL CONSENSUS AND RADIATION SAFETY 
ARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
 OF RADIATION EXPOSURE . . . . . . . . . . . . . . . . . . . . . . 552
ITIES AND UNITS USED IN RADIATION 
CTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Physical quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Radiation protection quantities . . . . . . . . . . . . . . . . . . . . . . 554
16.5.2.1. Organ dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
16.5.2.2. Equivalent dose . . . . . . . . . . . . . . . . . . . . . . . . . . 555
16.5.2.3. Effective dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
16.5.2.4. Committed dose . . . . . . . . . . . . . . . . . . . . . . . . . . 557
16.5.2.5. Collective dose . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
Operational quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
16.5.3.1. Ambient dose equivalent . . . . . . . . . . . . . . . . . . . 558
16.5.3.2. Directional dose equivalent . . . . . . . . . . . . . . . . 558
16.5.3.3. Personal dose equivalent . . . . . . . . . . . . . . . . . . . 559
FRAMEWORK OF RADIATION PROTECTION . . . . . 559
NMENTAL REGULATION AND NATIONAL 
STRUCTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
 OF THE BASIC SAFETY STANDARDS . . . . . . . . . . . . 561
NSIBILITIES FOR IMPLEMENTATION 
IC SAFETY STANDARDS REQUIREMENTS . . . . . . . 562
Y IN THE DESIGN OF RADIATION SOURCES AND 
MENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
Sealed sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
Safety in the design of facilities and ancillary 
equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
16.10.3.1. Manual brachytherapy . . . . . . . . . . . . . . . . . . . . . 567
16.10.3.2. Remote control brachytherapy and 
external beam radiotherapy . . . . . . . . . . . . . . . . 569
16.11. SAFETY ASSOCIATED WITH ACCEPTANCE TESTS, 
COMMISSIONING AND OPERATION . . . . . . . . . . . . . . . . . . . . 570
16.11.1. Safe operation of external beam radiotherapy . . . . . . . . . 572
16.11.2. Safe operation of brachytherapy . . . . . . . . . . . . . . . . . . . . . 572
16.11.2.1. Safe operation of manual brachytherapy . . . . . . 574
16.11.2.2. Safe operation of remote control 
afterloading brachytherapy . . . . . . . . . . . . . . . . . 575
16.12. SECUR
16.13. OCCUP
16.13.1.
16.13.2.
16.13.3.
16.13.4.
16.13.5.
16.13.6.
16.13.7.
16.13.8.
16.13.9.
16.13.10
16.13.11
16.14. MEDIC
16.14.1.
16.14.2.
16.14.3.
16.14.4.
16.14.5.
16.14.6.
16.14.7.
16.14.8.
16.14.9.
16.15. PUBLIC
16.15.1.
16.15.2.
16.15.3.
16.15.4.
16.16. POTEN
16.16.1.
ITY OF SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
ATIONAL EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
Responsibilities and conditions of service . . . . . . . . . . . . . 577
Use of dose constraints in radiotherapy . . . . . . . . . . . . . . 577
Investigation levels for staff exposure in radiotherapy . . . 578
Pregnant workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Classification of areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
Local rules and supervision . . . . . . . . . . . . . . . . . . . . . . . . . 579
Protective equipment and tools . . . . . . . . . . . . . . . . . . . . . . 580
Individual monitoring and exposure assessment . . . . . . . . 580
Monitoring of the workplace . . . . . . . . . . . . . . . . . . . . . . . . 581
. Health surveillance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581
. Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
AL EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
Responsibilities for medical exposure . . . . . . . . . . . . . . . . . 583
Justification of medical exposure . . . . . . . . . . . . . . . . . . . . . 584
Optimization of exposure and protection . . . . . . . . . . . . . . 584
Calibration of radiotherapy sources and machines . . . . . . 585
Clinical dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
Quality assurance for medical exposure . . . . . . . . . . . . . . . 587
Constraints for comforters and visitors . . . . . . . . . . . . . . . . 589
Discharge of patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
Investigation of accidental medical exposure . . . . . . . . . . 590
 EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Access control for visitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Radioactive waste and sources no longer in use . . . . . . . . 591
Monitoring of public exposure . . . . . . . . . . . . . . . . . . . . . . . 592
TIAL EXPOSURE AND EMERGENCY PLANS . . . . . 592
Potential exposure and safety assessment . . . . . . . . . . . . . 592
16.16.2. Mitigation of consequences: emergency plans . . . . . . . . . . 593
16.16.2.1. Lost source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
16.16.2.2. Stuck source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594
16.16.2.3. Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
16.16.2.4. Off-site accidents . . . . . . . . . . . . . . . . . . . . . . . . . 595
16.16.2.5. Patient accidental exposure . . . . . . . . . . . . . . . . . 595
16.17. GENER
16.17.1.
16.17.2.
16.17.3.
16.18. TYPICA
16.18.1.
16.18.2.
16.18.3.
16.18.4.
16.18.5.
16.18.6.
16.18.7.
16.18.8.
16.19. SHIELD
FACILI
BIBLIO
INTERNATIO
ABBREVIAT
SYMBOLS . . 
BIBLIOGRA
INDEX . . . . . 
AL SHIELDING CALCULATIONS . . . . . . . . . . . . . . . . 596
Step one: Design dose in occupied areas 
(annual dose and weekly dose) . . . . . . . . . . . . . . . . . . . . . . 597
Step two: Calculation of the radiation field 
(air kerma in air) in the occupied area without shielding . 598
Step three: Attenuation by shielding barriers . . . . . . . . . . 599
L LINAC INSTALLATION . . . . . . . . . . . . . . . . . . . . . . . . 600
Workload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
Calculation of the primary barrier transmission factor . . . 602
Calculation of the scatter barrier transmission factor . . . . 603
Calculation of the leakage barrier transmission factor . . . 603
Determination of barrier thickness . . . . . . . . . . . . . . . . . . . 604
Consideration of neutron production in a high 
energy linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Door of a linac room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
ING DESIGN FOR BRACHYTHERAPY 
TIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
GRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
NAL ORGANIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 611
IONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619
PHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 627
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
BL
AN
K
Chapter 1
BASIC RADIATION PHYSICS
E.B. PODGORSAK
Department of Medical Physics,
McGill U
Montrea
1.1. INTROD
1.1.1. Funda
signifi
● Avogadr
● Avogadr
● Speed of
● Electron
● Electron
● Positron 
● Proton re
● Neutron 
● Atomic m
● Planck’s 
● Permittiv
● Permeab
● Newtonia
● Proton m
● Specific c
1.1.2. Impor
● Speed of
c = 1
e m0
1
niversity Health Centre,
l, Quebec, Canada
UCTION
mental physical constants (rounded off to four 
cant figures)
o’s number: NA = 6.022 × 10
23 atoms/g-atom.
o’s number: NA = 6.022 × 10
23 molecules/g-mole.
 light in vacuum: c = 299 792 458 m/s (ª3 × 108 m/s).
 charge: e = 1.602 × 10–19 C.
 rest mass: me– = 0.5110 MeV/c
2. 
rest mass: me+ = 0.5110 MeV/c
2.
st mass: mp = 938.3 MeV/c
2.
rest mass: mn = 939.6 MeV/c
2.
ass unit: u = 931.5 MeV/c2. 
constant: h = 6.626 × 10–34 J·s.
ity of vacuum: e0 = 8.854 × 10
–12 C/(V·m).
ility of vacuum: m0 = 4p × 10
–7 (V·s)/(A·m).
n gravitation constant: G = 6.672 × 10–11 m3·kg–1·s–2.
ass/electron mass: mp/me = 1836.0.
harge of electron: e/me = 1.758 × 10
11 C/kg. 
tant derived physical constants and relationships
 light in a vacuum:
(1.1)ª ¥3 108
0
 m/s
CHAPTER 1
2
● Reduced Planck’s constant × speed of light in a vacuum:
● Fine structure constant:
● Bohr rad
● Rydberg
● Rydberg
● Classical
● Compton
=c h c= = ◊ ª ◊
2
197 3 200
p
. MeV fm MeV fm
a
pe
= e 2
4 0
a
m0
= =
a
E mR = 12
R
E• = 2p
r
e
e
0
=
4pe
lC
e
= h
m c
(1.2)
(1.3)
ius:
(1.4)
 energy:
(1.5)
 constant:
(1.6)
 electron radius:
(1.7)
 wavelength of the electron:
(1.8)
=
c
1 1
137=
c
c e
c
m ce
0
e
 = ==pe2 2 224 0 5292( ) . Å
c
e m c
ce 0
e eV= ÊËÁ ˆ˜¯ =12 4 13 612 2 2 2 22a pe ( ) .=
c
m c
c
e m c
c
-= = ÊËÁ ˆ˜¯ =R e 0 e cm4 14 4 109 7372 2 2 2 23ap p pe= = =( ) 11
m ce
 fm=2 2 2 818.
 = 0 0243. Å
BASIC RADIATION PHYSICS
1.1.3. Physical quantities and units
● Physical quantities are characterized by their numerical value 
(magnitude) and associated unit.
● Symbols for physical quantities are set in italic type, while symbols for 
units are set in roman type (e.g. m = 21 kg; E = 15 MeV).
● The numerical value and the unit of a physical quantity must be separated 
by a spac
● The curre
national 
abbrevia
physical q
Length l:
Mass m: 
Time t: se
Electric c
Tempera
Amount 
Luminou
All other
and units (see 
TABLE 1.1. 
QUANTITIES
OF UNITS AN
Physical 
quantity
Sy
Length
Mass
Time
Current
Charge
Force
Momentum
Energy
3
e (e.g. 21 kg and not 21kg; 15 MeV and not 15MeV).
ntly used metric system of units is known as the Système inter-
d’unités (International System of Units), with the international 
tion SI. The system is founded on base units for seven basic 
uantities:
 metre (m).
kilogram (kg).
cond (s).
urrent I: ampere (A).
ture T: kelvin (K).
of substance: mole (mol).
s intensity: candela (cd).
 quantities and units are derived from the seven base quantities 
Table 1.1).
 THE BASIC AND SEVERAL DERIVED PHYSICAL 
 AND THEIR UNITS IN THE INTERNATIONAL SYSTEM 
D IN RADIATION PHYSICS
mbol
Unit
in SI
Units used in 
radiation physics
Conversion
l m nm, Å, fm 1 m = 109 nm = 1010 Å = 1015 fm
m kg MeV/c2 1 MeV/c2 = 1.78 × 10–30 kg
t s ms, ms, ns, ps 1 s = 103 ms = 106 ms = 109 ns = 1012 ps
I A mA, mA, nA, pA 1 A = 103 mA = 106 mA = 109 nA 
Q C e 1 e = 1.602 × 10–19 C
F N 1 N = 1 kg·m·s–2
p N·s 1 N·s = 1 kg·m·s–1
E J eV, keV, MeV 1 eV = 1.602 × 10–19 J = 10–3 keV 
CHAPTER 1
4
1.1.4. Classification of forces in nature
There are four distinct forces observed in the interaction between various 
types of particle (see Table 1.2). These forces, listed in decreasing order of 
strength, are the strong force, electromagnetic (EM) force, weak force and 
gravitational force, with relative strengths of 1, 1/137, 10–6 and 10–39, 
respectively.
● The ran
dependen
● The rang
order of 
Each force res
— Strong ch
gluons; 
— Electric c
— Weak cha
— Energy f
called gra
1.1.5. Classi
Two class
● Quarks a
uents of 
(2/3 or –1
called co
strange, c
TABLE 1.2. T
Force
Strong
EM
Weak
Gravitational
ges of the EM and gravitational forces are infinite (1/r2
ce, where r is the separation between two interacting particles);
es of the strong and weak forces are extremely short (of the 
a few femtometres).
ults from a particular intrinsic property of the particles, such as:
arge for the strong force transmitted by massless particles called 
harge for the EM force transmitted by photons; 
rge for the weak force transmitted by particles called W and Z0;
or the gravitational force transmitted by hypothetical particles 
vitons.
fication of fundamental particles
es of fundamental particle are known: quarks and leptons.
re particles that exhibit strong interactions. They are constit-
hadrons (protons and neutrons) with a fractional electric charge 
/3) and are characterized by one of three types of strong charge 
lour: red, blue and green. There are six known quarks: up, down, 
harm, top and bottom.
HE FOUR FUNDAMENTAL FORCES IN NATURE
Source Transmitted particle Relative strength
Strong charge Gluon 1
Electric charge Photon 1/137
Weak charge W and Z0 10–6
Energy Graviton 10–39
BASIC RADIATION PHYSICS
● Leptons are particles that do not interact strongly. Electrons (e), muons 
(m), taus (t) and their corresponding neutrinos (ne, nm, nt) are in this 
category.
1.1.6. Classification of radiation
As shown in Fig. 1.1, radiation is classified into two main categories, non-
ionizing and io
potential of ato
from a few ele
● Non-ioni
● Ionizing 
—Direct
a part
—Indirec
g rays)
Directly 
Coulomb inte
orbital electron
Indirectly
medium throu
● In the fir
release e
● In the se
medium 
atoms in 
Radiation
5
nizing, depending on its ability to ionize matter. The ionization 
ms (i.e. the minimum energy required to ionize an atom) ranges 
ctronvolts for alkali elements to 24.5 eV for helium (noble gas).
zing radiation (cannot ionize matter).
radiation (can ionize matter either directly or indirectly):
ly ionizing radiation (charged particles): electrons, protons, 
icles and heavy ions.
tly ionizing radiation (neutral particles): photons (X rays and 
, neutrons.
ionizing radiation deposits energy in the medium through direct 
ractions between the directly ionizing charged particle and 
s of atoms in the medium.
 ionizing radiation (photons or neutrons) deposits energy in the 
gh a two step process: 
st step a charged particle is released in the medium (photons 
lectrons or positrons, neutrons release protons or heavier ions);
cond step the released charged particles deposit energy to the 
through direct Coulomb interactions with orbital electrons of the 
the medium.
Non-ionizing
Ionizing
 
 
 
 
Directly ionizing (charged particles) 
electrons, protons, etc.
Indirectly ionizing (neutral particles) 
photons, neutrons
FIG. 1.1. Classification of radiation.
CHAPTER 1
6
Both directly and indirectly ionizing radiations are used in the treatment 
of disease, mainly but not exclusively for malignant disease. The branch of 
medicine that uses radiation in the treatment of disease is called radiotherapy, 
therapeutic radiology or radiation oncology. Diagnostic radiology and nuclear 
medicine are branches of medicine that use ionizing radiation in the diagnosis 
of disease.
1.1.7. Classi
● Characteshells.
● Bremsstr
● g rays: re
● Annihila
1.1.8. Einste
E = m(u)
E0 = m0c
EK = E –
E2 = E0
2 +
where 
u is the p
c is the s
b is the n
m(u) is the p
m0 is the p
E is the t
E0 is the r
EK is the k
p is the m
m( )u =
fication of ionizing photon radiation
ristic X rays: resulting from electron transitions between atomic 
ahlung: resulting from electron–nucleus Coulomb interactions.
sulting from nuclear transitions.
tion quanta: resulting from positron–electron annihilation.
in’s relativistic mass, energy and momentum relationships
(1.9) 
c2 (1.10)
2 (1.11)
 E0 = (g – 1)E0 (1.12)
 p2c2 (1.13)
article velocity;
peed of light in a vacuum;
ormalized particle velocity (i.e. b = u/c);
article mass at velocity u ;
article rest mass (at velocity u = 0);
otal energy of the particle;
est energy of the particle;
inetic energy of the particle;
omentum of the particle.
m
c
m
m
u b
g- ÊËÁ ˆ˜¯ = - =0 0 01 12 2
BASIC RADIATION PHYSICS
● For photons, E = hn and E0 = 0; thus using Eq. (1.13) we obtain p = hn/c = 
h/l, where n and l are the photon frequency and wavelength, respec-
tively.
1.1.9. Radiation quantities and units
The most important radiation quantities and their units are listed in 
Table 1.3. Also
relationships b
1.2. ATOMIC
1.2.1. Basic 
The cons
electrons. Prot
the atom.
● Atomic n
atom.
● Atomic m
protons Z
● There is n
furnishes
● Atomic m
1/12 of th
smaller t
because 
(nucleon
● Atomic g
atoms of
number)
A grams
g-atom o
Avogadr
Z =
1 98.
7
 listed are the definitions of the various quantities and the 
etween the old and the SI units for these quantities.
 AND NUCLEAR STRUCTURE
definitions for atomic structure 
tituent particles forming an atom are protons, neutrons and 
ons and neutrons are known as nucleons and form the nucleus of 
umber Z: number of protons and number of electrons in an 
ass number A: number of nucleons in an atom (i.e. number of 
 plus number of neutrons N in an atom: A = Z + N).
o basic relation between A and Z, but the empirical relationship
(1.14)
 a good approximation for stable nuclei.
ass M: expressed in atomic mass units u, where 1 u is equal to 
e mass of the 12C atom or 931.5 MeV/c2. The atomic mass M is 
han the sum of the individual masses of constituent particles 
of the intrinsic energy associated with binding the particles 
s) within the nucleus.
-atom (gram-atom): number of grams that correspond to NA
 an element, where NA = 6.022 × 10
23 atoms/g-atom (Avogadro’s 
. The atomic mass numbers of all elements are defined such that 
 of every element contain exactly NA atoms. For example: 1 
f 60Co is 60 g of 60Co. In 60 g of 60Co (1 g-atom) there is 
o’s number of 60Co atoms.
A
A+ 0 0155 2 3. /
CHAPTER 1
8
● Number 
● Number 
TABLE 1.3. RADIATION QUANTITIES, UNITS AND CONVERSION 
BETWEEN OLD AND SI UNITS
Quantity Definition SI unit Old unit Conversion
Exposure 
(X)
Dose (D)
Equivalent 
dose (H)
H
Activity (A) A
DQ is the cha
Dmair is the ma
DEab is the abs
Dm is the ma
wR is the rad
l is the dec
N is the num
R stands fo
Gy stands fo
Sv stands fo
Bq stands fo
Ci stands fo
STP stands fo
X
Q
m
= DD air 2.58 10 Ckg air4¥ - 1R esucm air3 STP= 1 2 58 10 4 R Ckg air= ¥ -.
D
N
m
N
A
a A=
Z
N
V
 a =
of atoms Na per mass of an element:
of electrons per volume of an element:
1 Gy = 100 rad
 = DwR 1 Sv 1 rem 1 Sv = 100 rem
 = lN 1 Bq = 1 s–1 1 Ci = 3.7 × 1010 s–1
rge of either sign collected;
ss of air;
orbed energy;
ss of medium;
iation weighing factor;
ay constant;
ber of radioactive atoms;
r roentgen;
r gray;
r sievert;
r becquerel;
r curie;
r standard temperature (273.2 K) and standard pressure (101.3 kPa). 
E
m
= DD ab 1 Gy 1 Jkg= 1 rad 100 ergg=
1 Bq 
1 Ci
3.7 1010
= ¥
Z
N
m
Z
N
A
a A=r r
BASIC RADIATION PHYSICS
● Number of electrons per mass of an element: 
 
Note that (Z/A) ª 0.5 for all elements, with the one notable exception of 
hydrogen, for which (Z/A) = 1. Actually, (Z/A) slowly decreases from 0.5 
for low Z elements to 0.4 for high Z elements.
● In nuclea
A is the 
the 60Co 
● In ion ph
For exam
for a dou
● If we assu
of the a
compoun
the g-mo
atomic m
a g-mole 
18 g of w
3NA atom
three ato
1.2.2. Ruthe
The mod
and Marsden in
tested the vali
positive charge
spherical atom
Theoretical ca
scattered on su
10–3500, while th
104 a particles 
From the
1911 conclude
concentrated i
electrons are 
ångströms).
In a part
Coulomb inter
Z
N
m
Z
A
N a A=
9
r physics the convention is to designate a nucleus X as AZX, where 
atomic mass number and Z is the atomic number; for example, 
nucleus is identified as 6027Co, the 
226Ra nucleus as 22688Ra.
ysics the convention is to designate ions with + or – superscripts. 
ple, 42He
+ stands for a singly ionized 4He atom and 42He
2+ stands 
bly ionized 4He atom, which is the a particle.
me that the mass of a molecule is equal to the sum of the masses 
toms that make up the molecule, then for any molecular 
d there are NA molecules per g-mole of the compound, where 
le (gram-mole or mole) in grams is defined as the sum of the 
ass numbers of the atoms making up the molecule; for example, 
of water is 18 g of water and a g-mole of CO2 is 44 g of CO2. Thus 
ater or 44 g of carbon dioxide contain exactly NA molecules (or 
s, since each molecule of water and carbon dioxide contains 
ms).
rford’s model of the atom
el is based on the results of an experiment carried out by Geiger 
 1909 with a particles scattered on thin gold foils. The experiment 
dity of the Thomson atomic model, which postulated that the 
s and negative electrons were uniformly distributed over the 
ic volume, the radius of which was of the order of a few ångström. 
lculations predict that the probability for an a particle to be 
ch an atom with a scattering angle exceeding 90º is of the order of 
e Geiger–Marsden experiment showed that approximately 1 in 
was scattered with a scattering angle q > 90º (probability 10–4).
 findings of the Geiger–Marsden experiment, Rutherford in 
d that the positive charge and most of the mass of the atom are 
n the atomic nucleus (diameter a few femtometres) and negative 
smeared over on the periphery of the atom (diameter a few
icle scattering the positively charged a particle has a repulsive 
action with the more massive and positively charged nucleus. 
CHAPTER 1
10
The interaction produces a hyperbolic trajectory of the a particle, and the 
scattering angle q is a function of the impact parameter b. The limiting case is a 
direct hit with b = 0 and q = p (backscattering) that, assuming conservation of 
energy, determines the distance of closest approach D
a–N in the backscattering 
interaction:
(1.15)
where 
z
α 
is the a
ZN is the a
EK(a) is the i
The repu
nucleus (charg
resulting in the
The diffe
follows:
1.2.3. Bohr’s
Bohr exp
postulates that
of angular mom
electron entitie
ionized lithium
E
z Z e
D
z Z e
K
N N( ) a a a= fi =2 2
FCoul 4
=
b D= 1
2 a
d
d R
sWÊËÁ ˆ˜¯ =
tomic number of the a particle;
tomic number of the scattering material; 
nitial kinetic energy of the a particle. 
lsive Coulomb force between the a particle (charge +2e) and the 
e +Ze) is governed by 1/r2 as follows:
(1.16)
 following b versus θ relationship:
(1.17)
rential Rutherford scattering cross-section is then expressed as 
(1.18)
 model of the hydrogen atom
anded Rutherford’s atomic model in 1913 and based it on four 
 combine classical, non-relativistic mechanics with the concept 
entum quantization. Bohr’s model successfully deals with one-
s such as thehydrogen atom, singly ionized helium atom, doubly 
 atom, etc.
D E0 N
N
0 K( )pe pe aa
a- -4 4
Ze
r0
2 2
2pe
- 2qN cot
4
1
sin /2
 N 4 q
aÊËÁ ˆ˜¯-D 2 ( )
BASIC RADIATION PHYSICS
The four Bohr postulates are as follows:
● Postulate 1: Electrons revolve about the Rutherford nucleus in well 
defined, allowed orbits (shells). The Coulomb force of attraction FCoul = 
Ze2/(4pe0r
2) between the negative electrons and the positively charged 
nucleus is balanced by the centrifugal force Fcent = meu
2/r, where Z is the 
number of protons in the nucleus (atomic number), r is the radius of the 
orbit, me
orbit.
● Postulate
being co
basic law
part of it
● Postulate
allowed 
referred 
Planck’s 
stipulates
a basic va
● Postulate
transition
with quan
The radiu
where a0 is the
The velo
where a is the 
The ener
hydrogen, sing
r an = ÊËÁ0
u an c= ÊËÁ
E En = -
11
 is the electron mass and u is the velocity of the electron in the 
 2: While in orbit, the electron does not lose any energy despite 
nstantly accelerated (this postulate is in contravention of the 
 of nature, which is that an accelerated charged particle will lose 
s energy in the form of radiation).
 3: The angular momentum L = meur of the electron in an 
orbit is quantized and given as L=n�, where n is an integer 
to as the principal quantum number and � =h/(2p), where h is 
constant. The simple quantization of angular momentum 
 that the angular momentum can have only integral multiples of 
lue (�).
 4: An atom or ion emits radiation when an electron makes a 
 from an initial orbit with quantum number ni to a final orbit 
tum number nf for ni > nf.
s rn of a one-electron Bohr atom is given by:
(1.19)
 Bohr radius (a0 = 0.529 Å).
city un of the electron in a one-electron Bohr atom is:
(1.20)
fine structure constant (a = 1/137).
gy levels for orbital electron shells in monoelectronic atoms (e.g. 
ly ionized helium and doubly ionized lithium) are given by:
(1.21)
n
Z
n
Z
ˆ˜¯ = ÊËÁ ˆ˜¯ 2 20 529. Å
Z
n
c Z
n
ˆ˜¯ = ÊËÁ ˆ˜¯137
Z
n
Z
n
ÊËÁ ˆ˜¯ = - ÊËÁ ˆ˜¯R eV 2 213 6.
CHAPTER 1
12
where
ER is the Rydberg energy (13.61 eV);
n is the principal quantum number (n = 1, ground state; n > 1, excited state);
Z is the atomic number (Z = 1 for a hydrogen atom, Z = 2 for singly ionized 
helium, Z = 3 for doubly ionized lithium, etc.).
The wave
where R
•
 is th
Bohr’s m
shown in Fig. 1
1.2.4. Multie
For mult
theory provid
electron transi
shells, but the n
number (the p
● The K s
estimated
where Ze
the scree
● Excitatio
shell to a
complem
● Ionizatio
(i.e. the e
energy in
● Excitatio
possible 
amount 
k R= =1
l
EB(K) =
 number k of the emitted photon is given by:
(1.22)
e Rydberg constant.
odel results in the energy level diagram for the hydrogen atom 
.2.
lectron atoms 
ielectron atoms the fundamental concepts of the Bohr atomic 
e qualitative data for orbital electron binding energies and 
tions resulting in emission of photons. Electrons occupy allowed 
umber of electrons per shell is limited to 2n2, where n is the shell 
rincipal quantum number).
hell binding energies EB(K) for atoms with Z > 20 may be 
 with the following relationship: 
(1.23)
ff, the effective atomic number, is given by Zeff = Z – s, where s is 
ning constant equal to 2 for K shell electrons. 
n of an atom occurs when an electron is moved from a given 
 higher n shell that is either empty or does not contain a full 
ent of electrons.
n of an atom occurs when an electron is removed from the atom 
lectron is supplied with enough energy to overcome its binding 
 a shell). 
n and ionization processes occur in an atom through various 
interactions in which orbital electrons are supplied with a given 
of energy. Some of these interactions are: (i) Coulomb 
Z
n n
Z
n n
-ÊËÁ ˆ˜¯ = -ÊËÁ ˆ˜¯• -1 1 109 737 1 12 2 2 1 2 2 2f i f i cm
E Z E Z s E ZR eff R R( ) ( )= - = -2 2 22
BASIC RADIATION PHYSICS
interactio
Compton
electron 
● An orbit
lower n a
either em
transferr
atom as a
● Energy l
electron 
larger en
● The num
photons)
fluoresce
0
Excite
states
n > 1
Elect
boun
state
Continuum 
of electron 
kinetic 
energies
FIG. 1.2. Energy
13
n with a charged particle; (ii) the photoelectric effect; (iii) the 
 effect; (iv) triplet production; (v) internal conversion; (vi) 
capture; (vii) the Auger effect; and (viii) positron annihilation. 
al electron from a higher n shell will fill an electron vacancy in a 
tomic shell. The energy difference between the two shells will be 
itted in the form of a characteristic photon or it will be 
ed to a higher n shell electron, which will be ejected from the 
n Auger electron.
evel diagrams of multielectron atoms resemble those of one-
structures, except that inner shell electrons are bound with much 
ergies, as shown for a lead atom in Fig. 1.3.
ber of characteristic photons (sometimes called fluorescent 
 emitted per orbital electron shell vacancy is referred to as 
nt yield w, while the number of Auger electrons emitted per orbital 
d 
ron 
d 
s
Ground 
state
n = 1
n = 1
–13.6 eV
Discrete 
energy 
levels
–0.9 eV
–1.5 eV
–3.4 eV
n = 2
n = 3
 level diagram for a hydrogen atom (ground state: n = 1, excited states: n > 1).
CHAPTER 1
14
electron vacancy is equal to (1 – w). The fluorescent yield depends on the 
atomic number Z of the atom and on the principal quantum number of a 
shell. For atoms with Z < 10 the fluorescent yield wK = 0; for Z ª 30 the 
fluorescent yield wK ª 0.5; and for high atomic number atoms wK = 0.96, 
where wK refers to the fluorescent yield for the K shell (see Fig. 1.9).
1.2.5. Nuclear structure 
Most of t
of Z protons a
atomic mass nu
Excite
states
n > 1
Electr
bound
states
FIG. 1.3. Energ
are referred to a
low n shells are 
X ray energy ra
optical transition
he atomic mass is concentrated in the atomic nucleus consisting 
nd (A – Z) neutrons, where Z is the atomic number and A is the 
mber of a given nucleus.
0
d 
on 
 
Ground 
state
n = 1
–88 keV
Discrete 
energy 
levels
Continuum 
of electron 
kinetic 
energies
–3 keV
–15 keV
n = 1 K Two electrons 
n = 2 L Eight electrons 
n = 3 M Eighteen electrons
y level diagram for a multielectron atom (lead). The n = 1, 2, 3, 4… shells 
s the K, L, M, O… shells, respectively. Electronic transitions that end in 
referred to as X ray transitions because the resulting photons are in the 
nge. Electronic transitions that end in high n shells are referred to as 
s because they result in ultraviolet, visible or infrared photons.
BASIC RADIATION PHYSICS
● The radius r of the nucleus is estimated from:
(1.24)
where r0 is a constant (~1.4 fm) assumed equal to ½ of re, the classical 
electron radius.
● Protons and neutrons are commonly referred to as nucleons and are 
bound in
gravitatio
distance 
a very sh
femtome
force, exc
● The bind
number o
broad ma
be calcula
where 
M is t
931
mpc
2 is th
mnc
2 is th
1.2.6. Nucle
Much of
experiments in
The projectile
scattering (no
trajectory); (ii)
emitted with le
(the projectile 
a different par
r r A= 0 3
EB
nucleon
15
 the nucleus with the strong force. In contrast to electrostatic and 
nal forces, which are inversely proportional to the square of the 
between two particles, the strong force between two nucleons is 
ort range force, active only at distances of the order of a few 
tres. At these short distances the strong force is the predominant 
eeding other forces by several orders of magnitude.
ing energy EB per nucleon in a nucleus varies slowly with the 
f nucleons A, is of the order of ~8 MeV/nucleonand exhibits a 
ximum of 8.7 MeV/nucleon at A ª 60. For a given nucleus it may 
ted from the energy equivalent of the mass deficit Dm as follows:
(1.25)
he nuclear mass in atomic mass units u (note that uc2 = 
.5 MeV);
e proton rest energy;
e neutron rest energy.
ar reactions
 the present knowledge of the structure of nuclei comes from 
 which a particular nuclide A is bombarded with a projectile a. 
 undergoes one of three possible interactions: (i) elastic 
 energy transfer occurs; however, the projectile changes 
 inelastic scattering (the projectile enters the nucleus and is re-
ss energy and in a different direction); or (iii) nuclear reaction 
a enters the nucleus A, which is transformed into nucleus B and 
ticle b is emitted).
mc A Zm c A Z m c Mc Ap n/ ]/= = + - -D 2 2 2 2[ ( )
CHAPTER 1
16
● Nuclear reactions are designated as follows:
a + A Æ B + b or A(a, b)B (1.26)
● A number of physical quantities are rigorously conserved in all nuclear 
reactions. The most important of these quantities are charge, mass 
number, linear momentum and mass–energy.
● The thre
value of 
place. Th
relativist
where m
and prod
1.2.7. Radio
Radioact
into a more sta
chain of decay
laws that gove
formulated by
1910.
● The activ
product 
N(t): 
A(t) = lN
● The simp
nucleus 
nucleus D
—The nu
govern
EK
thr a( ) =
P D
PÆl
shold energy for a nuclear reaction is defined as the smallest 
a projectile’s kinetic energy at which a nuclear reaction can take 
e threshold kinetic energy EK
thr(a) of projectile a is derived from 
ic conservation of energy and momentum as:
(1.27)
A, ma, mB and mb are the rest masses of the target A, projectile a 
ucts B and b, respectively. 
activity
ivity is characterized by a transformation of an unstable nucleus 
ble entity that may be unstable and will decay further through a 
s until a stable nuclear configuration is reached. The exponential 
rn the decay and growth of radioactive substances were first 
 Rutherford and Soddy in 1902 and then refined by Bateman in 
ity A(t) of a radioactive substance at time t is defined as the 
of the decay constant l and the number of radioactive nuclei 
(t) (1.28)
lest radioactive decay is characterized by a radioactive parent 
P decaying with a decay constant lP into a stable daughter 
:
(1.29)
mber of radioactive parent nuclei NP(t) as a function of time t is 
ed by the following relationship:
m c m c m c m c
m c
B b A a
A
( ) ( )+ - +2 2 2 2 2 2
22
BASIC RADIATION PHYSICS
(1.30)
where NP(0) is the initial number of parent nuclei at time t = 0.
—Similarly, the activity of parent nuclei AP(t) at time t is given as:
(1.31)
where 
● The half-
number 
present a
● The deca
follows:
● The spec
where N
number. 
● The aver
average l
time t = 0
● The deca
lP = 1/tP
resulting
N t N e tP P P( ) ( )= -0 l
A AP P P( ) ( )t e
t= -0 l
N t tP( = 1
lP = ln
/
2
1 2t
a
m
= =AP
AP P( )0 t
17
AP(0) is the initial activity of parent nuclei at time t = 0.
life t1/2 of a radioactive substance is the time during which the 
of radioactive nuclei decays to half of the initial value NP(0) 
t time t = 0: 
(1.32)
y constant lP and half-life (t1/2)P for the parent are thus related as 
(1.33)
ific activity a is defined as the parent’s activity per unit mass:
(1.34)
A is Avogadro’s number and AP is the parent’s atomic mass 
age (mean) life tP of a radioactive substance represents the 
ife expectancy of all parent radioactive atoms in the substance at 
:
(1.35)
y constant lP and average life tP are thus related as follows:
(1.36)
 in the following relationship between (t1/2)P and tP: 
N N e tP P P) ( / ) ( ) ( )/ /= = -2 1 2 0 0 1 2l
N
m
N
A
N
A t
= =P P A
P
A
P P (
l
l
ln
)/
2
1 2
A AP P
P
P d( )
( )
0
0
0
l
l= =-•Ú e tt
CHAPTER 1
18
(t1/2)P = tP ln 2 (1.37)
● A more complicated radioactive decay occurs when a radioactive parent 
nucleus P decays with a decay constant lP into a daughter nucleus D 
which in turn is radioactive and decays with a decay constant lD into a 
stable granddaughter G:
—The ac
where 
t = 0 (i
at t = 0
—The m
under 
● Special c
ships:
—For lD
relatio
—For lD
—For lD
AD/AP 
P D
P DÆl l
AD( )t
tmax =
A
A
D
P
=
A
A
D
P
=
(1.38)
tivity of the daughter A D(t) may then be expressed as:
(1.39)
AP(0) is the initial activity of the parent nuclei present at time 
.e. AP(0) = lPNP(0), where NP(0) is the number of parent nuclei 
).
aximum activity of daughter nuclei occurs at time tmax given by:
(1.40)
the condition that ND = 0 at time t = 0.
onsiderations in parent Æ daughter Æ granddaughter relation-
 < lP or (t1/2)D > (t1/2)P we obtain the following general 
nship:
(1.41)
 > lP or (t1/2)D < (t1/2)P we obtain transient equilibrium with:
for t >> tmax (1.42)
 >> lP or (t1/2)D << (t1/2)P we obtain secular equilibrium and
ª 1 (1.43)
 GÆ
AD
D P
P
P D( )( )e et t= - -- -ll l l l0
ln( )-l ll lD PD P/
D
D P
 D P- - - -ll l l l[ ]( )1 e t
D
D P-ll l
BASIC RADIATION PHYSICS
1.2.8. Activation of nuclides
Activation of nuclides occurs when a stable parent isotope P is 
bombarded with neutrons in a nuclear reactor and transforms into a 
radioactive daughter D that decays into a granddaughter G:
(1.44)
The probabilit
nuclear reactio
● Activity 
where NP
● This resu
which an
turn deca
P Æ D Æ
section fo
rate of ne
● The time
process is
● In situat
Eq. (1.45
● An impo
isotope b
P D G
DÆ Æsf l
AD( )t =
tmax
l=
lD
AD( )t =s
27
59 Co + n
19
y for activation is determined by the cross-section s for the 
n, usually expressed in barns per atom, where 1 barn = 10–24 cm2.
of the daughter AD(t) is expressed as:
(1.45)
(0) is the initial number of parent nuclei.
lt is similar to the P Æ D Æ G relationship above (Eq. (1.39)) in 
 unstable parent P decays into an unstable daughter D that in 
ys into granddaughter G. However, the decay constant lP in the 
 G decay relationship is replaced by sf, where s is the cross-
r activation of the parent nuclei (cm2/atom) and f is the fluence 
utrons in the reactor (cm–2·s–1).
 tmax at which the maximum activity AD occurs in the activation 
 then, similarly to Eq. (1.40), given by:
(1.46)
ions where sf << lD, the daughter activity relationship of 
) transforms into a simple exponential growth relationship:
(1.47)
rtant example of nuclear activation is the production of the 60Co 
y bombarding 59Co with thermal neutrons in a nuclear reactor:
(1.48)
D
D
P
D( )( )N e et t- -- -sfll sf sf l0
n -lsfsfD
P
D( )( )N e t- -f l0 1
 Co + 27
60Æ g
CHAPTER 1
20
or in shorthand notation 5927Co(n, g)
60
27Co, with an activation cross-section s
of 37 × 10–24 cm2/atom (37 barn/atom with 1 barn = 10–24 cm2) and typical 
reactor neutron fluence rates f of the order of 1013 cm–2·s–1.
1.2.9. Modes of radioactive decay 
A radioactive parent X with atomic number Z and atomic mass number A
decays into a d
b+, electron ca
a decay:
where 42He(a) 
decay is the de
b– decay:
A neutro
n
—
e, sharing the
decay is the d
5.26 years:
b+ decay:
A proton
sharing the av
decay is the de
Z
A X Æ
88
226 Ra Æ
Z
A X Æ
27
60 Co Æ
Z
A X Æ
7
13
6
13NÆ
aughter Y through the following possible modes of decay: a, b–, 
pture g and internal conversion.
(1.49)
is a 4He nucleus referred to as an a particle. An example of a
cay of 226Ra into 222Rn with a half-life of 1600 years:
(1.50)
(1.51)
n transforms into a proton, and an electron b– and antineutrino 
 availableenergy, are ejected from the nucleus. An example of b–
ecay of 60Co nuclei into excited 60Ni nuclei with a half-life of 
(1.52)
(1.53)
 transforms into a neutron, and a positron b+ and neutrino ne, 
ailable energy, are ejected from the nucleus. An example of b+
cay of 13N into 13C:
(1.54)
Z
A Y + He2
4-- 24 ( )a
 Rn + He86
222
2
4
Z
A Y + + e+ -1 b n
 Ni + + 28
60 *
e
-b n
Z
A Y + + e- +1 b n
C e+ ++b n
BASIC RADIATION PHYSICS
Electron capture:
(1.55)
The nucleus captures one of its own K shell orbital electrons, a proton 
transforms into a neutron and a neutrino ne is ejected. An example of electron 
capture is the decay of 125I into 125Te in an excited state, which decays to the 
125Te ground st
The resu
and the transit
photons or Au
g decay:
An excit
attains its grou
example of g d
decay of 60Co, 
of 1.17 and 1.3
Internal conver
Rather th
may be transfe
energy equal t
The resulting K
the transition e
electrons. An 
which results f
emission of 35
Z
A
Z
AX e YK e+ Æ +- -1 n
53
125 I eK+ -
Z
A X* Æ
Z
A X * Æ
21
ate through g decay and internal conversion:
(1.56)
lting K shell vacancy is filled with a higher level orbital electron 
ion energy is emitted from the atom in the form of characteristic 
ger electrons.
(1.57)
ed nucleus AZX
*, generally produced through b– or b+ decay, 
nd state AZX through emission of one or several g photons. An 
ecay is the transition of the excited 6028Ni
*, resulting from the b–
into stable 6028Ni through an emission of two g rays with energies 
3 MeV.
sion:
(1.58)
an being emitted as a g photon, the nuclear excitation energy 
rred to a K shell orbital electron that is ejected with a kinetic 
o the excitation energy less the orbital electron binding energy. 
 shell vacancy is filled with a higher level orbital electron and 
nergy is emitted in the form of characteristic photons or Auger 
example of internal conversion is the decay of excited 125Te, 
rom an electron capture decay of 125I, into stable 125Te through 
 keV g rays (7%) and internal conversion electrons (93%).
52
125 Te eÆ +* n
Z
A X + g
Z
A X + eK
-
CHAPTER 1
22
1.3. ELECTRON INTERACTIONS
As an energetic electron traverses matter, it interacts with matter through 
Coulomb interactions with atomic orbital electrons and atomic nuclei. Through 
these collisions the electrons may lose their kinetic energy (collision and 
radiative losses) or change their direction of travel (scattering). Energy losses 
are described by stopping power; scattering is described by scattering power. 
The colli
nucleus of an
electron is defl
inelastic collisi
energy is trans
strahlung. En
traverse an ab
of multiple sca
with orbital ele
The type
of radius a dep
perpendicular 
and the atomic
FIG. 1.4. Interac
impact paramete
sions between the incident electron and an orbital electron or 
 atom may be elastic or inelastic. In an elastic collision the 
ected from its original path but no energy loss occurs, while in an 
on the electron is deflected from its original path and some of its 
ferred to an orbital electron or emitted in the form of brems-
ergetic electrons experience thousands of collisions as they 
sorber, hence their behaviour is described by a statistical theory 
ttering embracing the individual elastic and inelastic collisions 
ctrons and nuclei.
 of interaction that the electron undergoes with a particular atom 
ends on the impact parameter b of the interaction, defined as the 
distance between the electron direction before the interaction 
 nucleus (see Fig. 1.4).
Electron trajectory
Nucleus
Electron cloud
tion of an electron with an atom, where a is the atomic radius and b is the 
r.
BASIC RADIATION PHYSICS
● For b >> a the electron will undergo a soft collision with the whole atom 
and only a small amount of energy will be transferred from the incident 
electron to orbital electrons.
● For b ª a the electron will undergo a hard collision with an orbital 
electron and an appreciable fraction of the electron’s kinetic energy will 
be transferred to the orbital electron.
● For b << a the incident electron undergoes a radiative interaction 
(collision
(bremsst
kinetic e
depends 
impact pa
1.3.1. Electr
● Coulomb
of an abs
—Ionizat
—Excita
allowe
● Atomic e
are chara
1.3.2. Electr
● Coulomb
absorber
through 
energy lo
● Bremsstr
which sta
accelerat
accelerat
● The ang
proportio
accelerat
charge w
P
q a= 2
6pe 0
23
) with the atomic nucleus. The electron will emit a photon 
rahlung) with energy between zero and the incident electron 
nergy. The energy of the emitted bremsstrahlung photon 
on the magnitude of the impact parameter b; the smaller the 
rameter, the higher the energy of the bremsstrahlung photon.
on–orbital electron interactions 
 interactions between the incident electron and orbital electrons 
orber result in ionizations and excitations of absorber atoms:
ion: ejection of an orbital electron from the absorber atom;
tion: transfer of an orbital electron of the absorber atom from an 
d orbit to a higher allowed orbit (shell).
xcitations and ionizations result in collisional energy losses and 
cterized by collision (ionization) stopping powers.
on–nucleus interactions
 interactions between the incident electron and nuclei of the 
 atom result in electron scattering and energy loss of the electron 
production of X ray photons (bremsstrahlung). These types of 
ss are characterized by radiative stopping powers.
ahlung production is governed by the Larmor relationship, 
tes that the power P emitted in the form of photons from an 
ed charged particle is proportional to the square of the particle 
ion a and the square of the particle charge q, or:
(1.59)
ular distribution of the emitted photons (bremsstrahlung) is 
nal to sin2 q/(1 – b cos q)5, where q is the angle between the 
ion of the charged particle and a unit vector connecting the 
ith the point of observation and b is the standard relativistic u/c. 
c
2
3
CHAPTER 1
24
● At small velocities u of the charged particle (b Æ 0) the angular distri-
bution goes as sin2 q and exhibits a maximum at q = 90º. However, as the 
velocity of the charged particle increases from 0 towards c, the angular 
distribution of the emitted photons becomes increasingly more forward 
peaked.
● The angle at which the photon emission intensity is maximum can be 
calculated from the following relationship:
that for b
in the di
ray phot
megavolt
direction
● The ener
with the 
The radia
range (~1
range it a
1.3.3. Stopp
The inela
density r are d
represents the 
(S/r)tot consist
resulting from
ionizations), a
electron–nucle
(S/r)tot =
● (S/r)col h
the medi
qmax ar=
( )S/ totr =
(1.60)
 Æ 0 gives qmax = p/2 and for b Æ 1 gives qmax = 0, indicating that 
agnostic radiology energy range (orthovoltage beams) most X 
ons are emitted at 90º to the electron path, while in the 
age range (linac beams) most photons are emitted in the 
 of the electron beam striking the target.
gy loss by radiation and the radiative yield g increase directly 
absorber atomic number Z and the kinetic energy of electrons. 
tion yield for X ray targets in the diagnostic radiology energy 
00 keV) is of the order of 1%, while in the megavoltage energy 
mounts to 10–20%.
ing power
stic energy losses by an electron moving through a medium with 
escribed by the total mass–energy stopping power (S/r)tot, which 
kinetic energy EK loss by the electron per unit path length x, or:
(1.61)
s of two components: the mass collision stopping power (S/r)col, 
 electron–orbital electron interactions (atomic excitations and 
nd the mass radiative stopping power (S/r)rad,resulting from 
us interactions (bremsstrahlung production):
 (S/r)col + (S/r)rad (1.62)
as an important role in radiation dosimetry, since the dose D in 
um may be expressed as:
b
bccos ( )+ -ÈÎÍ ˘˙˚13 1 15 12
)
E
x
d
d
 (MeV cm /gK 2
r
◊1
BASIC RADIATION PHYSICS
D = f(S/r)col (1.63)
where f is the fluence of electrons.
● (S/r)tot is used in the calculation of electron range R as follows:
(1.64)
where Ek
● Both (S/r
(also refe
● The stop
through a
one is int
medium 
absorptio
average e
of specifi
● In radiat
introduce
power (S
that resu
radiation
energy th
of 1 mm i
high kine
this ener
particle a
1.3.4. Mass s
When a 
electrons unde
the incident e
spread of a pe
bution. The m
an absorbing 
R
S
E E
E= ÊËÁ ˆ˜¯ -Ú r ( )K KdKi 1
0
Y
E
= 1
Ki
25
i is the initial kinetic energy of the electron.
)rad and (S/r)tot are used in the determination of radiation yield 
rred to as bremsstrahlung efficiency) Y as:
(1.65)
ping power focuses on the energy loss by an electron moving 
 medium. When attention is focused on the absorbing medium, 
erested in the linear rate of energy absorption by the absorbing 
as the electron traverses the medium. The rate of energy 
n, called the linear energy transfer (LET), is defined as the 
nergy locally imparted to the absorbing medium by an electron 
ed energy in traversing a given distance in the medium.
ion dosimetry the concept of restricted stopping power (S
D
/r) is 
d, which accounts for that fraction of the collisional stopping 
/r)col that includes all the soft collisions plus those hard collisions 
lt in delta rays with energies less than a cut-off value D. In 
 dosimetry this cut-off energy is usually taken as 10 keV, an 
at allows an electron just to traverse an ionization chamber gap 
n air. Delta rays are defined as electrons that acquire sufficiently 
tic energies through hard collisions so as to enable them to carry 
gy a significant distance away from the track of the primary 
nd produce their own ionizations of absorber atoms.
cattering power
beam of electrons passes through an absorbing medium, the 
rgo multiple scattering through Coulomb interactions between 
lectrons and nuclei of the absorber. The angular and spatial 
ncil electron beam can be approximated by a Gaussian distri-
ultiple scattering of electrons traversing a path length l through 
medium is commonly described by the mean square angle of 
tot
S
S
E
EÚ
0
rad
tot
K
/
/
 d
Ki ( )
( )
r
r
CHAPTER 1
26
scattering that is proportional to the mass thickness rl of the absorber. 
Analogously to the definition of stopping power, the International Commission 
on Radiation Units and Measurements (ICRU) defines the mass scattering 
power T/r as:
(1.66)
The scattering 
number and in
1.4. PHOTON
1.4.1. Types
Dependi
into one of the
● Bremsstr
interactio
● Characte
from one
● g rays (d
● Annihila
positron–
1.4.2. Photo
The inten
by an attenuat
where 
I(0) is the
m(hn, Z) is the
hn an
q 2
T
l
T
lr r
q
r
q
r
= =1 2 2d
d
 or 
I x I( ) (=
power varies approximately as the square of the absorber atomic 
versely as the square of the electron kinetic energy.
 INTERACTIONS
 of indirectly ionizing photon radiation
ng on their origin, the indirectly ionizing photon radiations fall 
 following four categories:
ahlung (continuous X rays), emitted through electron–nucleus 
ns.
ristic X rays (discrete), emitted in transitions of orbital electrons 
 allowed orbit to a vacancy in another allowed orbit.
iscrete), emitted through nuclear transitions in g decay.
tion radiation (discrete, typically 0.511 MeV), emitted through 
electron annihilation.
n beam attenuation 
sity I(x) of a narrow monoenergetic photon beam, attenuated 
or of thickness x, is given as:
(1.67)
 original intensity of the unattenuated beam;
 linear attenuation coefficient, which depends on photon energy 
d attenuator atomic number Z.
e h Z x) ( , )-0 m n
BASIC RADIATION PHYSICS
● The half-value layer (HVL or x1/2) is defined as that thickness of the 
attenuator that attenuates the photon beam intensity to 50% of its 
original value:
x1/2 = HVL = (ln 2)/m (1.68)
● Similarly, the tenth-value layer (TVL or x1/10) is defined as that thickness 
of the att
original v
x1/10 = TV
● HVL and
● The mas
and elect
attenuati
where r,
number, 
● Typical u
coefficien
implying
g/cm2, at
● For use in
defined: 
coefficien
to m as fo
and
x x1 10/ =
m rm= m
m mtr = Eh
27
enuator that attenuates the photon beam intensity to 10% of its 
alue:
L = (ln 10)/m (1.69)
 TVL are thus related as follows:
(1.70)
s attenuation coefficient mm, atomic attenuation coefficient am
ronic attenuation coefficient em are proportional to the linear 
on coefficient m through the following relationships:
(1.71)
 Z and A are the density, atomic number and atomic mass 
respectively, of the attenuator.
nits for the linear, mass, atomic and electronic attenuation 
ts are: cm–1, cm2/g, cm2/atom and cm2/electron, respectively, 
 that thickness x in the exponent (–mx) must be given in cm, 
oms/cm2 and electrons/cm2, respectively.
 radiation dosimetry two additional attenuation coefficients are 
the energy transfer coefficient mtr and the energy absorption 
t mab (often designated as men). The two coefficients are related 
llows:
(1.72)
x1 2 1 23 3/ /.=ln 10ln 2
r
m
r
m= =A a A eNA N ZA
n
tr 
CHAPTER 1
28
(1.73)
where 
is the average energy transferred to charged particles (electrons and 
positrons) in the attenuator;
is th
atten
● The ener
mab are re
mab = mtr(
1.4.3. Types
Photons 
attenuator; the
energy hn of th
● The phot
atom as a
of the n
electron 
● In the c
orbital el
than, the
energy th
● During t
electric e
coherent
1.4.4. Photo
In the ph
photon interac
disappears, wh
electron with a
EK = hn –
m m
nab
ab= E
h
Etr
Eab
 e average energy deposited by charged particles in the 
uator.
gy transfer coefficient mtr and the energy absorption coefficient 
lated through the radiative fraction g as follows:
1 – g) (1.74)
 of photon interaction
may undergo various possible interactions with the atoms of an 
 probability or cross-section for each interaction depends on the 
e photon and on the atomic number Z of the attenuator. 
on interactions may be with a tightly bound electron (i.e. with an 
 whole (photoelectric effect, coherent scattering)), with the field 
ucleus (pair production) or with an essentially free orbital 
(Compton effect, triplet production).
ontext of photon interactions, a tightly bound electron is an 
ectron with a binding energy of the order of, or slightly larger 
 photon energy, while a free electron is an electron with a binding 
at is much smaller than the photon energy. 
he interaction the photon may completely disappear (photo-
ffect, pair production, triplet production) or it may be scattered 
ly (coherent scattering) or incoherently (Compton effect).
electric effect
otoelectric effect (sometimes referred to as the photoeffect) the 
ts with a tightly bound orbital electron of an attenuator and 
ile the orbital electron is ejected from the atom as a photo-
 kinetic energy EK given as:
 EB (1.75)
BASIC RADIATION PHYSICS
where hn is the incident photon energy and EB is the binding energy of the 
electron.
● The atomic attenuation coefficient for the photoelectric effect at is 
proportional to Z4/(hn)3, while the mass attenuation coefficient for the 
photoelectric effect tm is proportional to (Z/hn)
3, where Z is the atomic 
number of the attenuator and hn is the photon energy.
● In additio
versush
binding e
discontin
than the 
with elec
the bindi
● The aver
to electro
where EB
electron)
occur in 
range of 
numbers
1.4.5. Coher
In coher
orbital electron
elastic in the s
scattered throu
photon to cha
transfer coeffic
● The atom
(Z/hn)2 a
Z/(hn)2.
● In tissue
Rayleigh
as it con
coefficien
( )K tr
PEE =
29
n to a steady decrease in tm with an increasing hn, the plot of tm
n also shows sharp discontinuities in tm when hn equals the 
nergy for a particular electronic shell of the attenuator. These 
uities, called absorption edges, reflect the fact that for hn less 
binding energy photons cannot undergo the photoelectric effect 
trons in that particular shell, while for hn greater than or equal to 
ng energy they can.
age energy transferred from the photon with energy hn > EB(K) 
ns (E–K)tr
PE in the photoelectric effect is given as follows:
(1.76)
(K) is the binding energy of the K shell orbital electron (photo-
, PK is the fraction of all photoelectric effect interactions that 
the K shell and wK is the fluorescent yield for the K shell. The 
PK is from 1.0 at low atomic numbers Z to 0.8 at high atomic 
 (see Fig. 1.9).
ent (Rayleigh) scattering
ent (Rayleigh) scattering the photon interacts with a bound 
 (i.e. with the combined action of the whole atom). The event is 
ense that the photon loses essentially none of its energy and is 
gh only a small angle. Since no energy transfer occurs from the 
rged particles, Rayleigh scattering plays no role in the energy 
ient; however, it contributes to the attenuation coefficient.
ic cross-section for Rayleigh scattering asR is proportional to 
nd the mass attenuation coefficient sR/r is proportional to
 and tissue equivalent materials the relative importance of 
 scattering in comparison with other photon interactions is small, 
tributes only a few per cent or less to the total attenuation 
t.
(K)K K Bh P E-n w
CHAPTER 1
30
1.4.6. Compton effect (incoherent scattering)
The Compton effect (incoherent scattering) represents a photon 
interaction with an essentially ‘free and stationary’ orbital electron. The 
incident photon energy hn is much larger than the binding energy of the orbital 
electron. The photon loses part of its energy to the recoil (Compton) electron 
and is scattered as photon hn ¢ through a scattering angle q, as shown schemati-
cally in Fig. 1
direction and t
● The cha
Compton
Dl = lC(1
where lC
● The relat
vation of
hn + mec
and
where e i
lC
e
= h
m c
h
c
h
c
n n= ¢
0 = ¢h
c
n
si
e n= h
m ce
2
.5. Angle f represents the angle between the incident photon 
he direction of the recoil electron.
nge in photon wavelength Dl is given by the well known 
 relationship: 
 – cos q) (1.77)
 is the Compton wavelength of the electron, expressed as:
(1.78)
ionship for Dl is calculated from equations representing conser-
 energy and momentum in the Compton process:
2 = hn ¢ + mec
2 + EK (1.79)
(1.80)
(1.81)
s the normalized incident photon energy: 
 = 0 024. Å
m
c
q
u
u
f+ - ÊËÁ ˆ˜¯cos cose1 2
1
2
- - ÊËÁ ˆ˜¯
m
c
q
u
u
fn sine
BASIC RADIATION PHYSICS
and EK is
conservat
momentu
● The scatt
the follow
cot f = (1
From Eq
p (photo
for any a
photon e
● The Com
essentiall
atomic C
Recoil electron
2
Ê ˆ
m n
n
epe =
pn¢ cos q
pe sin f
y
FIG. 1.5. Schem
interacts with a 
from the atom a
photon with ener
31
 the kinetic energy of the recoil electron. Equation (1.79) represents 
ion of energy; Eqs (1.80) and (1.81) represent conservation of 
m along the x axis and y axis, respectively, of Fig. 1.5. 
ering angle q and the recoil electron angle f are related through 
ing relationship:
 + e) tan(q/2) (1.82)
. (1.82) it is evident that the range of angle f is between 0 for q = 
n backscattering) and p/2 for q = 0 (photon forward scattering) 
rbitrary photon energy. For a given q, the higher the incident 
nergy, the smaller is the recoil electron angle f.
pton interaction represents a photon interaction with an 
y free and stationary electron (hn >> EB). Consequently, the 
ompton attenuation coefficient asC depends linearly on the atomic 
1-
Ë
Á
¯
˜c
Incident photon
h
c
pn =
pn¢ sin q
Scattered photon
hn¢
c
pn¢ = 
pe cos f
f
q x
atic diagram of Compton scattering. An incident photon with energy hn
loosely bound (essentially free) atomic electron. The electron is ejected 
s a recoil (Compton) electron with kinetic energy EK and a scattered 
gy hn ¢ = hn – EK is produced (see Eq. (1.79)).
CHAPTER 1
32
number Z of the attenuator, while esC and sC/r, the electronic and mass 
Compton attenuation coefficients, respectively, are independent of Z.
● The electronic Compton attenuation coefficient esC steadily decreases 
with hn from a value of 0.665 × 10–24 cm2/electron at low photon energies 
to 0.21 × 10–24 cm2/electron at hn = 1 MeV; 0.051 × 10–24 cm2/electron at hn
= 10 MeV; and 0.008 × 10–24 cm2/electron at hn = 100 MeV.
● The scattered photon energy hn and the kinetic energy of the Compton 
electron 
● The ener
which fo
mec
2 and
● The max
fractions
electron 
nation o
coefficien
● For exam
a Compt
kinetic en
200 keV. 
● On aver
produce 
100 keV 
scattered
electron 
produce 
1.4.7. Pair p
In pair p
with a combin
Coulomb field
h h¢ =n n
h ¢ =n q( 9
EK are given as follows:
(1.83)
gy of photons scattered at 90º and 180º is thus given as:
(1.84)
r large incident photon energies (e = hn/(mec
2) Æ • results in 
 0.5 mec
2 for q = 90º and q = 180º, respectively.
imum (for q = 180º (i.e. photon backscattering)) and mean 
 of the incident photon energy transferred to the Compton recoil 
are given in Fig. 1.6. The mean fraction is used in the determi-
f the Compton effect contribution to the energy transfer 
t. 
ple, from Fig. 1.6 we determine that a 1 MeV photon undergoing 
on backscattering event would result in a recoil electron with a 
ergy of 800 keV and a backscattered photon with an energy of 
age, a 1 MeV photon undergoing Compton scattering will 
a 440 keV recoil electron and a 560 keV scattered photon; a 
photon will produce a 15 keV recoil electron and a 85 keV 
 photon; a 10 MeV photon will produce a 6.9 MeV recoil 
and a 3.1 MeV scattered photon; and a 100 MeV photon will 
an 80 MeV recoil electron and a 20 MeV scattered photon.
roduction
roduction the photon disappears and an electron–positron pair 
ed kinetic energy equal to hn – 2mec
2 is produced in the nuclear 
.
E h+ - = -+ -e q n e qe q11 1 11 1( cos ) and ( cos )( cos )K
h
h
h= + ¢ = = +ne n q n e) and ( )o o0 1 180 1 2
BASIC RADIATION PHYSICS
● Since ma
positron 
energy re
● When pa
is referre
positron 
threshold
● The prob
threshold
threshold
● The atom
attenuati
and Z, re
Maximum fraction
Mean fraction
1.0 
0.8 
0.6 
0.4
0.2
0.0
0.
M
ax
im
um
 a
nd
 m
ea
n 
fr
ac
tio
n 
of
 in
ci
d
en
t
p
ho
to
n 
en
er
gy
 g
iv
en
 t
o 
C
om
p
to
n 
el
ec
tr
on
FIG. 1.6. Max
Compton recoil 
obtained from th
DC (www.nist.go
33
ss is produced out of photon energy in the form of an electron–
pair, pair production has an energy threshold (minimum photon 
quired for the effect to happen) of 2mec
2 = 1.02 MeV.
ir production occurs in the field of an orbital electron, the effect 
d to as triplet production, and three particles (an electron–
pair and the orbital electron) share the available energy. The 
 for this effect is 4mec
2.
ability for pair production is zero for photon energies below the 
 energy and increases rapidly with photon energy above the 
. 
ic attenuationcoefficient for pair production ak and the mass 
on coefficient for pair production k/r vary approximately as Z2
spectively, where Z is the atomic number of the attenuator.
 
 
01 0.1 1 10 100
Photon energy (MeV)
imum and mean fractions of incident photon energy transferred to a 
electron in the photon energy range from 10 keV to 100 MeV. Data are 
e National Institute of Science and Technology (NIST) in Washington, 
v).
CHAPTER 1
34
1.4.8. Photonuclear reactions
Photonuclear reactions (also referred to as photodisintegration reactions) 
occur when a high energy photon is absorbed by the nucleus of an atom, 
resulting in an emission of a neutron ((x, n) reaction) or proton ((x, p) reaction) 
and a transformation of the nucleus into a radioactive reaction product. 
● The thre
reaction 
nuclei (w
threshold
● The prob
other pho
coefficien
reaction 
● While ph
attenuati
therapy t
(x, n) re
treatmen
reaction.
personne
machine 
room do
and abso
(six to eig
low react
1.4.9. Contr
For a g
coefficient m, e
mab are given a
energy absorpt
m = t + s
m ttr tr=
shold for a particular photonuclear reaction depends on the 
and the nucleus and is of the order of 10 MeV or higher for most 
ith the exception of the deuteron and 9Be nuclei, for which the 
 is of the order of 2 MeV). 
ability for photonuclear reactions is much smaller than that for 
ton interactions, and their contribution to the total attenuation 
t amounts to only a few per cent at photon energies above the 
threshold.
otonuclear reactions do not play an active role in photon 
on considerations, they are of concern in high energy radio-
reatment rooms because of the neutron production through the 
actions and because of the radioactivity that is induced in the 
t room air and in machine components through the (x, n) 
 Both the neutrons and the radioactivity pose a health hazard to 
l and must be dealt with in the treatment room and treatment 
design. The neutron problem is dealt with special treatment 
ors incorporating borated hydrogenous materials to thermalize 
rb the neutrons, the radioactivity with adequate room ventilation 
ht air changes per hour) and use of machine components with a 
ion cross-section and short half-life of the reaction product.
ibutions to attenuation coefficients
iven photon energy hn and attenuator Z, the attenuation 
nergy transfer coefficient mtr and energy absorption coefficient 
s a sum of coefficients for individual photon interactions (the 
ion coefficient is often designated as men):
R + sC + k (1.85)
(1.86)s k t
n
s
n
k
nC tr tr
K tr
PE
C
K tr
CE
K tr
PP( ) ( ) ( )+ + = + +( ) E
h
E
h
E
h
BASIC RADIATION PHYSICS
mab = men = mtr(1 – g) (1.87)
where g is the radiative fraction, and the average energies transferred to 
charged particles (electrons and positrons) for the photoelectric effect, the 
Compton effect and pair production are designated as (E–K)tr
PE, (E–K)tr
CE and 
(E–K)tr
PP, respectively.
● (E–K)tr
PE m
binding e
electric e
fluoresce
● (E–K)tr
CE is
Fig. 1.6.
● (E–K)tr
PP = 
● Note tha
Rayleigh
nor to th
The ind
summed, resul
energy absorpt
Figure 1.
energy transfe
r) in (b) for lea
m
r
t
r
= +
m
r
t
r
tr tr=
= ÊËÁ1r
m
r
m
r
ab t=
35
ay be approximated by hn – PKwKEB(K), where EB(K) is the 
nergy of the K shell electron, PK is the fraction of all photo-
ffect interactions that occur in the K shell and wK is the 
nt yield for the K shell.
 obtained from tabulated values or from the graph shown in 
hn – 2mec
2.
t in Rayleigh scattering no energy transfer occurs and therefore 
 scattering contributes neither to the energy transfer coefficient 
e energy absorption coefficient.
ividual components of the attenuation coefficients, when 
t in the total mass attenuation, mass–energy transfer and mass– 
ion coefficients as follows:
(1.88)
(1.89)
(1.90)
7 shows the mass attenuation coefficient m/r in (a) and the mass–
r coefficient (m
tr
/r) and mass–energy absorption coefficient (m
ab
/
d in the photon energy range from 10 keV to 100 MeV. 
s
r
s
r
k
r
+ +R C
s
r
k
r
C tr tr+ +( )
- + + - ˆ˜¯2 2t n w
n
s
n
k
n
n
h P E
h
E
h
h m c
h
K K B
C
K tr
CE
eK) ( )(
r -( )1 g
CHAPTER 1
36
1.4.10. Relati
The pro
interaction ph
photon and on
photoelectric e
at intermediate
Figure 1.
important ind
display the po
thus delineate 
energies, Com
sc/r
s
0.01 
oe
ffi
ci
en
t 
(c
m
2 /
g)
 c
oe
ffi
ci
en
t 
(c
m
2 /
g)
1000 
100 
10 
1000 
100 
10 
1 
0.1 
0.01
M
as
s 
at
te
nu
at
io
n 
co
ef
fic
ie
nt
 (c
m
2 /
g)
(a) (b)
K edge
L edgesL edges
K edge
FIG. 1.7. Mass
mass–energy abs
10 keV and 100 M
while the solid cu
by Eq. (1.88) for 
MeV, m
tr
/r ª m
ab
/r
MeV, g increase
transfer and mas
ve predominance of individual effects
bability for a photon to undergo any one of the various 
enomena with an attenuator depends on the energy hn of the 
 the atomic number Z of the attenuating material. In general, the 
ffect predominates at low photon energies, the Compton effect 
 energies and pair production at high photon energies. 
8 shows the regions of relative predominance of the three most 
ividual effects with hn and Z as parameters. The two curves 
ints in the (hn, Z) diagram for which asC = at or asC = ak and 
the regions of photoelectric effect predominance at low photon 
pton effect predominance at intermediate energies and pair 
t /r
m /r
k /r
R /r mab/r
m t r/r
tt r/r
sCtr
/r
mab/r
m t r/r
kt r/r
0.01 0.1 1 10 1000.1 1 10 100
Photon energy (MeV)Photon energy (MeV)
M
as
s–
en
er
gy
 t
ra
ns
fe
r 
c
an
d
m
as
s–
en
er
gy
 a
b
so
rp
tio
n
1 
0.1 
0.01
 attenuation coefficient m/r (a); mass–energy transfer coefficient m
tr
/r and 
orption coefficient m
ab
/r (b) for lead in the photon energy range between 
eV. The dotted–dashed curves represent contributions of individual effects, 
rves represent the sum of the contributions of the individual effects as given 
m/r, Eq. (1.89) for m
tr
/r and Eq. (1.90) for m
ab
/r. For photon energies below 2 
, because the radiative fraction g in this energy region is negligible. Above 2 
s with photon energy, causing the divergence between the mass–energy 
s–energy absorption coefficients.
BASIC RADIATION PHYSICS
production pre
photon will in
electric effect 
Compton effec
predominantly
the Compton e
1.4.11. Effect
In the ph
vacancies are 
electrons. For 
FIG. 1.8. Region
with matter. The
photoelectric eff
region where t
coefficient (asC =
37
dominance at high photon energies. For example, a 100 keV 
teract with lead (Z = 82) predominantly through the photo-
and with soft tissue (Zeff = 7.5) predominantly through the 
t. A 10 MeV photon, on the other hand, will interact with lead 
 through pair production and with tissue predominantly through 
ffect.
s following photon interactions
otoelectric effect, the Compton effect and triplet production, 
produced in atomic shells through the ejection of orbital 
the orthovoltage and megavoltage photons used in the diagnosis 
s of relative predominance of the three main forms of photon interaction 
 left curve represents the region where the atomic coefficients for the 
ect and Compton effect are equal (at = asC), the right curve is for the 
he atomic Compton coefficient equals the atomic pair production 
 ak).
CHAPTER 1
38
and treatment of disease with radiation, the shell vacancies occur mainly ininner atomic shells and are followed by characteristic X rays or Auger 
electrons, the probability for the former given by the fluorescent yield w (see 
Fig. 1.9), while the probability for the Auger effect is 1 – w. 
Pair production and triplet production are followed by the annihilation of 
the positron with a ‘free’ and stationary electron, producing two annihilation 
quanta, most commonly with energies of 0.511 MeV each and emitted at 180º 
from each othe
An annihilatio
referred to as
exceeding 0.51
1.4.12. Summ
Table 1.
Rayleigh scatte
1.
0.
0.
0.
0.
0
Fl
uo
re
sc
en
t 
yi
el
d
s 
w
K
 
an
d
 
w
L
FIG. 1.9. Fluor
lfractions P
K
 for 
were obtained fro
Wiley, New York (
r to satisfy the conservation of charge, momentum and energy. 
n of a positron before it has expended all of its kinetic energy is 
 annihilation in flight and produces photons with energies 
1 MeV.
ary of photon interactions
4 summarizes the main characteristics of the photoeffect, 
ring, the Compton effect and pair production. 
Atomic number Z
wK wL
PK
PK
PL
0 20 40 60 80
Atomic number Z
0 
8 
6 
4 
2 
1.0 
0.8 
0.6 
0.4 
0.2 
0
Fr
ac
ti
o
ns
 P
K
 a
nd
 P
L
escent yields w
K
 for hn > (E
B
)
K
 and w
L
 for (E
B
)
L
 < hn < (E
B
)
K
 as well as
hn > (E
B
)
K
 and P
L
 for (E
B
)
L
 < hn < (E
B
)
K
 against the atomic number Z. Data
m F.H. Attix, Introduction to Radiological Physics and Radiation Dosimetry,
1986).
BASIC RADIATION PHYSICS
TABLE 1.4. MAIN CHARACTERISTICS OF THE PHOTOELECTRIC 
EFFECT, RAYLEIGH SCATTERING, THE COMPTON EFFECT AND 
PAIR PRODUCTION
 Photoelectric 
 effect
 Rayleigh 
 scattering
 Compton 
 effect
Pair
production
Photon 
interaction
With whole atom With bound With free With nuclear 
Mode of photon
interaction
Energy 
dependence
Threshold
Linear 
attenuation 
coefficient
Particles 
released
Atomic 
coefficient 
dependence 
on Z
Mass coefficient
dependence 
on Z
Average energy 
transferred
Subsequent 
effect
Significant 
energy region 
for water
39
(bound electron) electrons electrons Coulomb field
 Photon 
disappears
Photon 
scattered
Photon 
scattered
Photon 
disappears
Decreases 
with energy
Increases with 
energy
No No No 2mec
2
t s
R
s
C
k
Photoelectron None Compton 
(recoil) 
electron
Electron–
positron pair
at µ Z
4
asR µ Z
2
asC µ Z ak µ Z
2
 
Independent
hn – P
K
w
K
E
B
(K) 0 
(see Fig. 1.6)
hn – 2m
e
c2
Characteristic 
X ray, 
Auger effect
None Characteristic 
X ray, 
Auger effect
Annihilation 
radiation
<20 keV <20 keV 20 keV– 
10 MeV
>10 MeV
1
3( )hn
1
2( )hn
t
r
 μ Z 3 s
r
R μ Z k
r
 μ Z
( )EK tr
CE
CHAPTER 1
40
1.4.13. Example of photon attenuation 
For 2 MeV photons in lead (Z = 82; A = 207.2 g/g-atom; r = 11.36 g/cm3) the 
photoelectric effect, coherent scattering, the Compton effect and pair production 
linear attenuation coefficients are: t = 0.055 cm–1, sR = 0.008 cm
–1, sC = 0.395 cm
–1
and k = 0.056 cm–1. The average energy transferred to charged particles (E–K)tr = 
1.13 MeV and the average energy absorbed in lead is (E–K)ab = 1.04 MeV.
Calculate
coefficient m
m
coefficient mtr
fraction g:
m = t + s
or
m m
rm
= =
a m
r= ÊËÁ NA
m
r
tr (= E
h
m
r
m
r
ab e=
g
E= ( )
(
K
 the linear attenuation coefficient m; mass attenuation 
; atomic attenuation coefficient am; mass–energy transfer 
/r; mass–energy absorption coefficient mab/r; and radiative 
R + sC + k = (0.055 + 0.008 + 0.395 + 0.056) cm
–1 = 0.514 cm–1
(1.91)
(1.92)
(1.94)
(1.95)
(1.96)
1
3
2 cm
11.36 g/cm
 cm /g=-0 514 0 0453. .
A
1
3
 g/g-atom 0.514 cm
11.36 g/cm 6.02
mˆ˜¯ = ¥¥- -1 207 2. 22 10 atom/g-atom23¥= ¥ -1 56 10 23. cm /atom2 (1.93)
n
m
r
K tr
2
2) MeV 0.0453 cm /g
2 MeV
 cm /g= ¥ =1 13 0 0256. .
n
m
r
n K ab
2
2( ) MeV 0.0453 cm /g
2 MeV
 cm= = ¥ =E
h
1 04
0 0236
.
. //g
E
E
E
E
- = - = - =( )
)
( )
( )
 MeV
1.13 MeV
tr K ab
K tr
K ab
K tr
1 1
1 04
0
.
.008
BASIC RADIATION PHYSICS
(1.97)
The mass–energy transfer coefficient mtr/r can also be determined using 
Eq. (1.89) with:
hn – PKwKEB = 2 MeV – 0.8 × 0.96 × 0.088 MeV = 1.93 MeV 
(from Fig
(E–K)tr
CE = 
hn – 2mec
to obtain
in good agreem
Thus, as s
average: 
● Transfer 
● 0.87 MeV
Of the 1.
● 1.04 MeV
● 0.09 MeV
The radia
1.4.14. Produ
There ar
transforming t
g = - = - =1 1 0 08m r
m r
ab
tr
2
2
/
/
0.0236 cm /g
0.0256 cm /g
.
m
r
tr = 1
11.
41
. 1.9) (1.98)
0.53 × 2 MeV = 1.06 MeV (from Fig. 1.6) (1.99)
2 = 2 MeV – 1.02 MeV = 0.98 MeV (1.100)
(1.101)
ent with the result obtained in Eq. (1.94).
hown schematically in Fig. 1.10, a 2 MeV photon in lead will on 
1.13 MeV to charged particles (electrons and positrons); and
 will be scattered through Rayleigh and Compton scattering. 
13 MeV of energy transferred: 
 will be absorbed in lead; and 
 will be re-emitted through bremsstrahlung radiative loss. 
tive fraction g for 2 MeV photons in lead is 0.08.
ction of vacancies in atomic shells
e eight main means of producing vacancies in atomic shells and 
he atom from a neutral state into an excited positive ion:
2
 
cm
g
¥ + ¥ + ¥ÊËÁ ˆ˜¯ =36 1 932 0 055 1 062 0 395 0 982 0 056. . . . . . 00 0254. cmg 2
CHAPTER 1
42
● Coulomb
electron.
● Photon in
—Photoe
—Compt
—Triplet
● Nuclear d
—Electro
—Interna
● Positron 
● Auger ef
Electron
track
Bremsstrahlung
photon
hn¢¢ = 0.09 MeV
Incident 
photon
hn = 2 MeV A
B
FIG. 1.10. Schem
2 MeV photon hn
lead atom at poi
scattering, the Co
large number of 2
transferred at poi
to positrons if the
and Compton sca
be absorbed in le
fform of bremsstra
 interaction (1) of an energetic charged particle with an orbital 
teractions: 
lectric effect (2);
on effect (3);
 production (4).
ecay:
n capture (5);
l conversion (6).
annihilation (7).
fect (8).
Scattered
photon
hn¢ = 0.87 MeV
atic diagram of general photon interactions with an atom. In this example a 
 interacts with a lead atom. An individual 2 MeV photon, as it encounters a 
nt A, may interact with the atom through the photoelectric effect, Rayleigh 
mpton effect or pair production, or it may not interact at all. However, for a 
 MeV photons striking lead, we may state that on average: 1.13 MeV will be 
nt A to charged particles (mainly to fast energetic electrons, but possibly also 
 interaction is pair production); 0.87 MeV will be scattered through Rayleigh 
ttering (hn ¢). Of the 1.13 MeV transferred to charged particles: 1.04 MeV will 
ad over the fast charged particle tracks, and 0.09 MeV will be emitted in the 
hlung photons (hn ¢¢). 
BASIC RADIATION PHYSICS
Note that pair production does not produce shell vacancies. Vacancies in 
inner atomic shells are not stable; they are followed by emission of character-
istic photons or Auger electrons and cascade to the outer shell of the ion. The 
ion eventually attracts an electron from its surroundings and reverts to a 
neutral atom.
ATTIX, F.H., In
New York (1986
ATTIX, F.H., R
New York (1968
EVANS, R.D., T
HALE, J., The F
JOHNS, H.E., C
IL (1984).
KASE, K.R., B
Radiation, Acad
KHAN, F., The P
Baltimore, MD 
ROHLF, J.W., M
JAYARAMAN,
Raton, FL (1996
43
BIBLIOGRAPHY
troduction to Radiological Physics and Radiation Dosimetry, Wiley, 
).
OESCH,W.C., TOCHILIN, E., Radiation Dosimetry, Academic Press, 
).
he Atomic Nucleus, McGraw-Hill, New York (1955).
undamentals of Radiological Science, Thomas, Springfield, IL (1974).
UNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, 
JARNGARD, B.E., ATTIX, F.H. (Eds), The Dosimetry of Ionizing 
emic Press, San Diego, CA (1985).
hysics of Radiation Therapy, 3rd edn, Lippincott, Williams and Wilkins, 
(2003).
odern Physics from a to Z0, Wiley, New York (1994).
 S., LANZL, L.H., Clinical Radiotherapy Physics, CRC Press, Boca 
).
BLANK
Chapter 2
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
J.P. SEUNTJENS
Department of Medical Physics,
McGill U
Montrea
W. STRY
Departm
Medical U
Pretoria,
K.R. SHO
Division 
Internati
Vienna
2.1. INTROD
Radiatio
various specifi
dosimetry dea
deposited in a
number of qua
beam, and the
defined below
with calculatin
2.2. PHOTON
The follo
radiation beam
energy fluence
beams and ma
45
niversity Health Centre,
l, Quebec, Canada
DOM
ent of Medical Physics,
niversity of Southern Africa,
 South Africa
RTT
of Human Health,
onal Atomic Energy Agency,
UCTION
n measurements and investigations of radiation effects require 
cations of the radiation field at the point of interest. Radiation 
ls with methods for a quantitative determination of energy 
 given medium by directly or indirectly ionizing radiations. A 
ntities and units have been defined for describing the radiation 
 most commonly used dosimetric quantities and their units are 
. A simplified discussion of cavity theory, the theory that deals 
g the response of a dosimeter in a medium, is also given.
 FLUENCE AND ENERGY FLUENCE
wing quantities are used to describe a monoenergetic ionizing 
: particle fluence, energy fluence, particle fluence rate and 
 rate. These quantities are usually used to describe photon 
y also be used in describing charged particle beams.
CHAPTER 2
46
● The particle fluence F is the quotient dN by dA, where dN is the number 
of particles incident on a sphere of cross-sectional area dA:
(2.1)
The unit of particle fluence is m–2. The use of a sphere of cross-sectional 
area dA expresses in the simplest manner the fact that one considers an 
area dA 
particle f
● Planar pa
area and 
● The ener
energy in
The unit 
particle fluenc
where E is the
with energy E.
Almost a
above defined
particle fluenc
fluence and en
and
where FE(E) 
spectrum and 
tively. 
Figure 2
generated by a
F = d
d
N
A
Y = d
d
E
A
Y = d
d
N
A
FE E( ) ∫
YE E( ) ∫
perpendicular to the direction of each particle and hence that 
luence is independent of the incident angle of the radiation.
rticle fluence is the number of particles crossing a plane per unit 
hence depends on the angle of incidence of the particle beam.
gy fluence Y is the quotient of dE by dA, where dE is the radiant 
cident on a sphere of cross-sectional area dA:
(2.2)
of energy fluence is J/m2. Energy fluence can be calculated from 
e by using the following relation:
(2.3)
 energy of the particle and dN represents the number of particles 
ll realistic photon or particle beams are polyenergetic, and the 
 concepts need to be applied to such beams. The concepts of 
e spectrum and energy fluence spectrum replace the particle 
ergy fluence, respectively. They are defined respectively as:
(2.4)
(2.5)
and YE(E) are shorthand notations for the particle fluence 
the energy fluence spectrum differential in energy E, respec-
.1 shows a photon fluence and an energy fluence spectrum 
n orthovoltage X ray unit with a kVp value of 250 kV and an 
F=E E
F
E
E( )
d
d
Y F
E
E
E
E E( ) ( )=d
d
d
d
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
added filtratio
filtration: 2 m
bremsstrahlun
produced in th
The part
increment of th
with units of m
The ener
dY by dt, wher
dt:
The unit of ene
Particle fluence spectrum
Energy fluence spectrum
0.25 
0.20 
0.15
0.10
0.05
Fl
ue
nc
e 
(a
rb
itr
ar
y 
un
its
)
FIG. 2.1. Photo
machine with a t
(target material:
�F F= d
dt
�Y Y= d
dt
47
n of 1 mm Al and 1.8 mm Cu (target material: W; inherent 
m Be). The two spikes superimposed on the continuous 
g spectrum represent the Ka and the Kb characteristic X ray lines 
e tungsten target.
icle fluence rate F� is the quotient of dF by dt, where dF is the 
e fluence in time interval dt:
(2.6)
–2◊s–1.
gy fluence rate (also referred to as intensity) is the quotient of 
e dY is the increment of the energy fluence in the time interval 
(2.7)
rgy fluence rate is W/m2 or J·m–2·s–1.
50 100 150 200 250
Energy (keV)
 
 
n fluence and energy fluence spectra at 1 m from the target of an X ray 
ube potential of 250 kV and added filtration of 1 mm Al and 1.8 mm Cu 
 W; inherent filtration: 2 mm Be).
CHAPTER 2
48
2.3. KERMA
Kerma is an acronym for kinetic energy released per unit mass. It is a non-
stochastic quantity applicable to indirectly ionizing radiations such as photons 
and neutrons. It quantifies the average amount of energy transferred from 
indirectly ionizing radiation to directly ionizing radiation without concern as to 
what happens after this transfer. In the discussion that follows we will limit 
ourselves to ph
The ener
first stage, the
particles (elec
effect, the Co
charged partic
and ionization
In this co
the indirectly i
per unit m
The unit of ker
is the gray (Gy
2.4. CEMA
Cema is 
stochastic qua
and protons. T
lost by charged
of a material:
The unit of cem
the gray (Gy).
Ed tr
K
E
m
= d
d
tr
C
E
m
= d
d
c
otons.
gy of photons is imparted to matter in a two stage process. In the 
 photon radiation transfers energy to the secondary charged 
trons) through various photon interactions (the photoelectric 
mpton effect, pair production, etc.). In the second stage, the 
le transfers energy to the medium through atomic excitations 
s. 
ntext, the kerma is defined as the mean energy transferred from 
onizing radiation to charged particles (electrons) in the medium 
ass dm: 
(2.8)
ma is joule per kilogram (J/kg). The name for the unit of kerma 
), where 1 Gy = 1 J/kg.
the acronym for converted energy per unit mass. It is a non-
ntity applicable to directly ionizing radiations such as electrons 
he cema C is the quotient of dEc by dm, where dEc is the energy 
 particles, except secondary electrons, in collisions in a mass dm
(2.9)
a is joule per kilogram (J/kg). The name for the unit of cema is 
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
2.5. ABSORBED DOSE
Absorbed dose is a non-stochastic quantity applicable to both indirectly and 
directly ionizing radiations. For indirectly ionizing radiations, energy is imparted 
to matter in a two step process. In the first step (resulting in kerma), the indirectly 
ionizing radiation transfers energy as kinetic energy to secondary charged 
particles. In the second step, these charged particles transfer some of their kinetic 
energy to the m
in the form of r
The abso
The absorbed
radiation to m
The ener
interest minus 
energy conver
the energy by
energy by the s
Note tha
along their tra
location as the
dose is joule pe
gray (Gy).
2.6. STOPPIN
Stopping
rarely measur
positrons the B
The linea
of energy loss 
stopping powe
of the absorbi
almost elimina
except for the 
and mass stopp
D
m
= d
d
e
49
edium (resulting in absorbed dose) and lose some of their energy 
adiative losses (bremsstrahlung, annihilation in flight).
rbed dose is related to the stochastic quantity energy imparted. 
 dose is defined as the mean energy e– imparted by ionizing 
atter of mass m in a finite volume V by: 
(2.10)gy imparted e– is the sum of all the energy entering the volume of 
all the energy leaving the volume, taking into account any mass–
sion within the volume. Pair production, for example, decreases 
 1.022 MeV, while electron–positron annihilation increases the 
ame amount.
t because electrons travel in the medium and deposit energy 
cks, this absorption of energy does not take place at the same 
 transfer of energy described by kerma. The unit of absorbed 
r kilogram (J/kg). The name for the unit of absorbed dose is the 
G POWER
 powers are widely used in radiation dosimetry, but they are 
ed and must be calculated from theory. For electrons and 
ethe theory is used to calculate stopping powers.
r stopping power is defined as the expectation value of the rate 
per unit path length (dE/dx) of the charged particle. The mass 
r is defined as the linear stopping power divided by the density 
ng medium. Division by the density of the absorbing medium 
tes the dependence of the mass stopping power on mass density, 
density effect discussed further below. Typical units for the linear 
ing powers are MeV/cm and MeV·cm2/g, respectively.
CHAPTER 2
50
Two types of stopping power are known: collision (ionization), resulting 
from interactions of charged particles with atomic orbital electrons; and 
radiative, resulting from interactions of charged particles with atomic nuclei.
The unrestricted mass collision stopping power expresses the average rate 
of energy loss by a charged particle in all hard and soft collisions. 
● A soft collision occurs when a charged particle passes an atom at a consid-
erable di
atomic ra
of energy
collision.
● In a hard
a delta el
ejected a
● In the un
transfer t
kinetic en
the full k
The theo
particles, electr
the Bethe the
energy transfe
particle with m
collisions is lim
where 
re is the cla
z is the pro
I is the me
C/Z is the she
The mea
ionization and
binding effect
inadequate to 
Scol
r
p= 4
stance (i.e. b >> a, where b is the impact parameter and a the 
dius). The net effect of the collision is that a very small amount 
 is transferred to an atom of the absorbing medium in a single 
 
 collision where b ª a, a secondary electron (often referred to as 
ectron or historically as a delta ray) with considerable energy is 
nd forms a separate track. 
restricted mass collision stopping power the maximum energy 
o an orbital electron allowed due to a hard collision is half of the 
ergy of the electron (collision of indistinguishable particles) or 
inetic energy of a positron (collision of distinguishable particles).
ry of the mass collision stopping power for heavy charged 
ons and positrons as a result of soft and hard collisions combines 
ory for soft collisions with the stopping power as a result of 
rs due to hard collisions. The result of this, for a heavy charged 
ass M and velocity u, where the energy transfer due to hard 
ited to 2mec
2b2/(1 – b2), where b = u/c, is:
(2.11)
ssical electron radius (2.82 fm);
jectile charge in units of electron charge;
an excitation potential of the medium;
ll correction.
n excitation potential I is a geometric mean value of all 
 excitation potentials of an atom of the absorbing material. Since 
s influence the exact value of I, calculation models are often 
estimate its value accurately. Hence, I values are usually derived 
N Z
A
r m c
z
m
I
C
Z
A e e e
b
u
b b
ÊËÁ ˆ˜¯ - - - -ÈÎÍÍ ˘˚2 12 22 2 2 2 2ln ln( ) ˙˙˙
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
from measurements of stopping powers in heavy charged particle beams, for 
which the effects of scattering in these measurements is minimal.
For elemental materials I varies approximately linearly with Z, with, on 
average, I = 11.5Z. For compounds, I is calculated assuming additivity of the 
collision stopping power, taking into account the fraction by weight of each 
atom constituent in the compound.
The shell correction C/Z accounts for the decrease in mass stopping 
power when th
that of the ato
violation of th
mass collision 
by this, followe
and of the velo
The follo
● The mass
proportio
term 2me
any of th
● The mas
kinetic en
● The lead
stopping 
decrease
● In a give
causes he
times the
For elect
combined with
Bhabba (for p
collisional sto
Report No. 37,
with F – given f
F –(t) = (1
S Ncol
r
=
51
e passing particle’s velocity has ceased to be much greater than 
mic electrons in the stopping medium, an effect that leads to a 
e Born approximation, which underlies the derivation of the 
stopping power. The electrons in the K shell are the first affected 
d by the L shell electrons, etc. C/Z is a function of the medium 
city of the fast charged particle.
wing observations can be made about Eq. (2.11):
 stopping power does not depend on the projectile mass and is 
nal to the inverse square of the projectile velocity. Note that the 
u2 under the logarithm has no relation to the kinetic energy of 
e particles involved in the collision process. 
s stopping power gradually flattens to a broad minimum for 
ergies EK ª 3mec
2. 
ing factor Z/A is responsible for a decrease of about 20% in 
power from carbon to lead. The term –ln I causes a further 
 in stopping power with Z.
n medium, the square dependence on the projectile charge (z2) 
avy charged particles with double the charge to experience four 
 stopping power.
rons and positrons, energy transfers due to soft collisions are 
 those due to hard collisions using the Møller (for electrons) and 
ositrons) cross-sections for free electrons. The complete mass 
pping power for electrons and positrons, according to ICRU 
 is:
(2.12)
or electrons as:
 – b2)[1 + t 2/8 – (2t + 1) ln 2]
Z
A
r m c
E I FA 0 e K/ /
p
b
t t d+ + + -±2 22 22 1 2[ln( ) ln( ) ( ) ]
CHAPTER 2
52
and F+ given for positrons as:
F +(t) = 2 ln 2 – (b2/12)[23 + 14/(t + 2) + 10/(t + 2)2 + 4/(t + 2)3]
In this equation, t = EK/mec
2 and b = u/c. 
The density effect correction d accounts for the fact that the effective 
Coulomb forc
from the partic
caused by the
component of 
ratios of the sto
(such as, for 
developed.
The mass
or positrons t
Heitler theory
power:
where s = a(
structure const
for energies in
This fact
proportional w
energies above
the mass radia
collision stopp
high Z materia
The conc
calculate the e
energy transfe
denoted as D),
region of inter
The restr
power. The ch
For problems i
is 10 keV (the
microdosimetr
value.
Srad
r
s=
e exerted on a fast charged particle by atoms that are distant 
le track is reduced as a result of the polarization of the medium 
 charged particle. The density effect affects the soft collision 
the stopping power. It plays a significant role in the values of 
pping power of a dense material to that of a non-dense material 
example, water to air), and various models for it have been 
 radiative stopping power is the rate of energy loss by electrons 
hat results in the production of bremsstrahlung. The Bethe–
 leads to the following formula for the mass radiative stopping 
(2.13)
e2/(4pe0mec
2))2 = 5.80 × 10–28 cm2/atom, where a is the fine 
ant and B
–
r is a function of Z and EK, varying between 5.33 and 15 
 the range from less than 0.5 MeV to 100 MeV. 
or, together with the increase of the radiative stopping power 
ith EK, is responsible for the increase in total stopping power at 
 2 MeV as depicted in Fig. 2.2. Note that the Z2 dependence of 
tive stopping power in contrast to the Z dependence of the mass 
ing power makes this mode of energy loss more prominent in 
ls.
ept of restricted mass collision stopping power is introduced to 
nergy transferred to a localized region of interest. By limiting the 
r to secondary charged (delta)particles to a threshold (often 
 highly energetic secondary particles are allowed to escape the 
est. 
icted stopping power is lower than the unrestricted stopping 
oice of the energy threshold depends on the problem at hand. 
nvolving ionization chambers a frequently used threshold value 
 range of a 10 keV electron in air is of the order of 2 mm). For 
ic quantities one usually takes 100 eV as a reasonable threshold 
N Z
A
E m c B0
A
K e r+2 2( )
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
The restr
energy transfe
dE
D
 by dl, whe
hard collisions
charged partic
L
D 
= dE
D
The rest
collision stopp
As the th
power increase
mass stopping
secondary elec
mass stopping 
2D. This is indi
Unrestricted total stopping power
Restricted total stopping power (D = 10 keV)
Restricted total stopping power (D = 100 keV)
To
ta
l m
as
s 
st
op
p
in
g 
p
ow
er
 (M
eV
·c
m
2 ·
g–
1 )
0.01 
10 
1
FIG. 2.2. Unres
stopping powers
No. 37. Vertical l
powers begin to 
53
icted linear collision stopping power (also referred to as linear 
r (LET)) L
D
 of a material, for charged particles, is the quotient of 
re dE
D
 is the energy lost by a charged particle due to soft and 
 in traversing a distance dl minus the total kinetic energy of the 
les released with kinetic energies in excess of D:
/dl (2.14)
ricted mass collision stopping power is the restricted linear 
ing power divided by the density of the material.
reshold for maximum energy transfer in the restricted stopping 
s, the restricted mass stopping power tends to the unrestricted 
 power for D Æ EK/2. Note also that since energy transfers to 
trons are limited to EK/2, unrestricted and restricted electron 
powers are identical for kinetic energies lower than or equal to 
cated in Fig. 2.2 by vertical lines at 20 keV and 200 keV.
(S/r)
(L/r)
(L/r)
Kinetic energy (MeV)
0.10 1.00 10.00
tricted S/r and restricted ((L/r)
D
 with D = 10 and 100 keV) total mass 
 for carbon (r = 1.70 g/cm3), based on data published in ICRU Report 
ines indicate the points at which restricted and unrestricted mass stopping 
diverge as the kinetic energy increases.
CHAPTER 2
54
The total mass stopping power is the sum of the collision mass stopping 
power and the radiative mass stopping power. Figure 2.2 shows the total 
unrestricted and restricted (D = 10 keV, 100 keV) electron mass stopping 
powers for carbon, based on data in ICRU Report No. 37.
2.7. RELATIONSHIPS BETWEEN VARIOUS DOSIMETRIC 
QUANT
2.7.1. Energ
The ener
distinct ways:
● Through 
● Through 
annihilat
The tota
collision kerma
● The collis
of electr
electron 
tions wit
value of 
the point
passed fr
● The rad
productio
down an
are brem
charged 
lation in 
The total
K = Kcol +
ITIES
y fluence and kerma (photons)
gy transferred to electrons by photons can be expended in two 
collision interactions (soft collisions and hard collisions); 
radiative interactions (bremsstrahlung and electron–positron 
ion). 
l kerma is therefore usually divided into two components: the 
 Kcol and the radiative kerma Krad.
ion kerma Kcol is that part of kerma that leads to the production 
ons that dissipate their energy as ionization in or near the 
tracks in the medium, and is the result of Coulomb force interac-
h atomic electrons. Thus the collision kerma is the expectation 
the net energy transferred to charged particles per unit mass at 
 of interest, excluding both the radiative energy loss and energy 
om one charged particle to another.
iative kerma Krad is that part of kerma that leads to the 
n of radiative photons as the secondary charged particles slow 
d interact in the medium. These interactions most prominently 
sstrahlung as a result of Coulomb field interactions between the 
particle and the atomic nuclei, but can also result from annihi-
flight.
 kerma K is thus given by the following:
 Krad (2.15)
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
The average fraction of the energy transferred to electrons that is lost 
through radiative processes is represented by a factor referred to as the 
radiative fraction g–. Hence the fraction lost through collisions is (1 – g–). 
A frequently used relation between collision kerma Kcol and total kerma 
K may be written as follows:
Kcol = K(1 – g
–) (2.16)
For mon
medium is rela
following:
where (men/r) i
photons in the
For polye
of spectrum av
present at the 
follows:
In Eq. (2.18):
stands for the t
is a shorthand
medium avera
For mono
related to the e
K col = Y
K
E
col =
Y Y= ÚEmax
0
m
r
enÊËÁ ˆ˜¯ =
55
oenergetic photons the collision kerma Kcol at a point in a 
ted to the energy fluence Y at that point in the medium by the 
(2.17)
s the mass–energy absorption coefficient for the monoenergetic 
 medium. 
nergetic beams a formally similar relation exists, but use is made 
eraged quantities. If a photon energy fluence spectrum YE(E) is 
point of interest, the collision kerma at that point is obtained as 
(2.18)
 
otal (integrated) energy fluence, and:
 notation for the mass–energy absorption coefficient for the 
ged over the energy fluence spectrum. 
energetic photons the total kerma K at a point in a medium is 
nergy fluence Y in the medium by the following:
en 
ÊËÁ ˆ˜¯mr
E EE
en en d
ÊËÁ ˆ˜¯ = ÊËÁ ˆ˜¯Ú Y Y
0
max
( )
m
r
m
r
E E E( )d
m
r
en dÚ1
0
Y YEE E E E( ) ( )max
CHAPTER 2
56
(2.19)
where (mtr/r) is the mass–energy transfer coefficient of the medium for the 
given monoenergetic photon beam. For polyenergetic beams, similarly as 
above, spectrum averaged mass–energy transfer coefficients can be used in 
conjunction wi
Note tha
between collisi
follows:
This equ
(Y)2,1 can be a
scaling theorem
of material 2 is
so as not to dis
tissue in air).
2.7.2. Fluen
Under th
interest and (b
charged partic
to medium D
follows:
where (Scol/r)
medium at the
Owing to
starting electro
spectrum that 
by Fmed,E. 
K tr= ÊËÁ ˆ˜¯Y mr
K
K
col,2
col,1
=
Dmed = F
th total energy fluence to obtain the total kerma.
t, using Eq. (2.17), one can obtain the frequently used relation 
on kerma in two different materials, material 1 and material 2, as 
(2.20)
ation is often used in circumstances in which the fluence ratio 
ssumed to be unity through a proper scaling of dimensions (the 
), for very similar materials or for situations in which the mass 
 sufficient to provide buildup but at the same time small enough 
turb the photon fluence in material 1 (e.g. dose to a small mass of 
ce and dose (electrons)
e conditions that (a) radiative photons escape the volume of 
) secondary electrons are absorbed on the spot (or there is a 
le equilibrium (CPE) of secondary electrons), the absorbed dose 
med is related to the electron fluence Fmed in the medium as 
(2.21)
med is the unrestricted mass collision stopping power of the 
 energy of the electron.
 electron slowdown in a medium, even for a monoenergetic 
n kinetic energy EK, there is always present a primary fluence 
ranges in energy from EK down to zero and is commonly denoted 
en
en
en
ÊËÁ ˆ˜¯ÊËÁ ˆ˜¯ ∫ ( ) ÊËÁ ˆ˜¯YY Y2 21 1 2 1 2
m
r
m
r
m
r, ,11
S
med
col
med
ÊËÁ ˆ˜¯r
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
In this case, the absorbed dose to the medium can be obtained by an 
integration of Eq. (2.20):
(2.22)
The righ
calculated usin
spectrum avera
Based on
med1 and med
where the shor
are being used
electron fluenc
med1, respectiv
The full, 
particles that, 
interacting in 
and result in s
particles that r
knock-on colli
designated del
2.7.3. Kerma
Generallcharged partic
energy by the 
non-zero (finit
interactions. 
D E
S
E E
S
E
E
med med,
col
med
med
col
med
d= ÊËÁ ˆ˜¯ = ÊËÁ ˆ˜¯Ú F F
0
max
( ) ( )
r r
D
D
med
med
2
1
=
( )F med ,m2
57
t hand side of Eq. (2.21) shows that absorbed dose can be 
g a formally similar equation as Eq. (2.20) by making use of 
ged collision stopping power and total fluence.
 Eq. (2.22) and under the same assumptions, for two media, 
2, the ratio of absorbed doses can be calculated as:
(2.23)
thand notations: 
 for the ratio of the electron fluences (often referred to as the 
e ratio) and the collision stopping powers in the media med2 and 
ely.
realistic electron fluence spectrum consists of primary charged 
for example, are the result of a polyenergetic photon beam 
the medium. These primary charged particles are slowed down 
econdary particle fluence. This fluence thus contains charged 
esult from slowing down through soft collisions as well as hard, 
sions. Electrons created as a result of the latter process are 
ta electrons.
 and dose (charged particle equilibrium)
y, the transfer of energy (kerma) from the photon beam to 
les at a particular location does not lead to the absorption of 
medium (absorbed dose) at the same location. This is due to the 
e) range of the secondary electrons released through photon 
S
med ,med
col
med ,med
2 1
2 1
ÊËÁ ˆ˜¯( )F r
ed
col
med ,med
 and 
1
2 1
S
r
ÊËÁ ˆ˜¯
CHAPTER 2
58
Since radiative photons mostly escape from the volume of interest, one 
relates absorbed dose usually to collision kerma. In general, however, the ratio 
of dose and collision kerma is often denoted as:
b = D/Kcol (2.24)
If radiative photons escape the volume of interest, an assumption is made that 
b ª 1.
Figure 2.
dose under bu
conditions of t
As a high
maximal at th
greatest at the
absorbed dose
maximum zmax
If there w
production of 
would occur: th
CPE where D 
In the m
scattering in th
exists an essen
dose. This rela
the average en
change apprec
In the sp
dose in the me
is given by:
D = Kcol 
where g— is the 
higher the ene
material consi
electrons prod
The build
the case of hig
small but does
beam due to p
3 illustrates the relation between collision kerma and absorbed 
ildup conditions; under conditions of CPE in part (a) and under 
ransient charged particle equilibrium (TCPE) in part (b).
 energy photon beam penetrates the medium, collision kerma is 
e surface of the irradiated material because photon fluence is 
 surface. Initially, the charged particle fluence, and hence the 
, increases as a function of depth until the depth of dose 
 is attained.
ere no photon attenuation or scattering in the medium, but yet 
electrons, a hypothetical situation, as illustrated in Fig. 2.3(a), 
e buildup region (with b < 1) is followed by a region of complete 
= Kcol (i.e. b = 1). g
ore realistic situation, however, due to photon attenuation and 
e medium, a region of TCPE occurs (Fig. 2.3(b)) where there 
tially constant relation between collision kerma and absorbed 
tion is practically constant since, in high energy photon beams, 
ergy of the generated electrons and hence their range does not 
iably with depth in the medium.
ecial case in which true CPE exists (at the depth of maximum 
dium), the relation between absorbed dose D and total kerma K
= K(1 – g—) (2.25)
radiative fraction, depending on the electron kinetic energy; the 
rgy, the larger is g—. The radiative fraction also depends on the 
dered, with higher values of g— for higher Z materials. For 
uced by 60Co rays in air the radiative fraction equals 0.0032.
up of absorbed dose is responsible for the skin sparing effect in 
h energy photon beams. However, in practice the surface dose is 
 not equal zero because of the electron contamination in the 
hoton interactions in the media upstream from the phantom or 
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
Bui
reg
Bui
reg
b
b = 1
(a)Kcol
b < 1
D
K
D
R
el
at
iv
e 
en
er
gy
 p
er
 u
ni
t 
m
as
s
R
el
at
iv
e 
en
er
gy
 p
er
 u
ni
t 
m
as
s
FIG. 2.3. Collis
ated by a high en
or scattering and
59
CPEldup
ion
ldup
ion
TCPE
Zmax
b
b
b
col b = 1
b > 1 (b)
Depth in mediumzmax
b < 1
Depth in mediumzmax
ion kerma and absorbed dose as a function of depth in a medium irradi-
ergy photon beam for (a) the hypothetical case of no photon attenuation 
 for (b) the realistic case.
CHAPTER 2
60
due to charged particles generated in the accelerator head and beam modifying 
devices.
2.7.4. Collision kerma and exposure
Exposure X is the quotient of dQ by dm, where dQ is the absolute value 
of the total charge of the ions of one sign produced in air when all the electrons 
and positrons l
stopped in air:
The unit 
exposure is the
units, roentgen
C/kg of air.
The aver
quotient of EK
initial kinetic e
The curre
or 33.97 × 1.60
Multiplyi
charge created
mass of air or e
The relat
Eqs (2.25) and
X
Q
m
= d
d
W
E
Nair
=
W
e
air =
X K= ( co
K Xair =
iberated or created by photons in mass dm of air are completely 
(2.26)
of exposure is coulomb per kilogram (C/kg). The unit used for 
 roentgen R, where 1 R = 2.58 × 10–4 C/kg. In the SI system of 
 is no longer used and the unit of exposure is simply 2.58 × 10–4
age energy expended in air per ion pair formed Wair is the 
 by N, where N is the mean number of ion pairs formed when the 
nergy EK of a charged particle is completely dissipated in air:
(2.27)
nt best estimate for the average value of Wair is 33.97 eV/ion pair 
2 × 1019 J/ion pair:
(2.28)
ng the collision kerma by (e/Wair), the number of coulombs of 
 per joule of energy deposited, gives the charge created per unit 
xposure:
(2.29)
ion between total kerma and exposure is obtained by combining 
 (2.29):
(2.30)
 eV/ion pair J/eV
C/
¥ ¥¥ --33 97 1 602 101 602 10 1919. ( ) . ( ). ( iion pair J/C) .= 33 97
e
W
ÊËÁ ˆ˜¯)l air air 
W
e g
air 
ÊËÁ ˆ˜¯ -11
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
2.8. CAVITY THEORY
In order to measure the absorbed dose in a medium, it is necessary to 
introduce a radiation sensitive device (dosimeter) into the medium. Generally, 
the sensitive medium of the dosimeter will not be of the same material as the 
medium in which it is embedded. Cavity theory relates the absorbed dose in the 
dosimeter’s sensitive medium (cavity) to the absorbed dose in the surrounding 
medium conta
diate or large 
produced by 
charged partic
cavity is regard
developed, wh
Gray and Spen
cavities of inte
2.8.1. Bragg
The Brag
provide a relat
dose in the me
The cond
(a) The cavi
particles 
charged p
(b) The abso
crossing 
and thus 
The resu
the same and 
medium. This 
addition, the p
bation that re
factor. 
Conditio
cavity are pro
secondary elec
stop within the
61
ining the cavity. Cavity sizes are referred to as small, interme-
in comparison with the ranges of secondary charged particles 
photons in the cavity medium. If, for example, the range of 
les (electrons) is much larger than the cavity dimensions, the 
ed as small. Various cavity theories for photon beams have been 
ich depend on the size of the cavity; for example, the Bragg–
cer–Attix theories for small cavities and the Burlin theory for 
rmediate sizes.
–Gray cavity theory
g–Gray cavity theory was the first cavity theory developed to 
ion between the absorbed dose in a dosimeter and the absorbed 
dium containing the dosimeter. 
itions for application of the Bragg–Gray cavity theory are:
ty must be small when compared with the range of charged 
incidenton it, so that its presence does not perturb the fluence of 
articles in the medium;
rbed dose in the cavity is deposited solely by charged particles 
it (i.e. photon interactions in the cavity are assumed negligible 
ignored).
lt of condition (a) is that the electron fluences in Eq. (2.22) are 
equal to the equilibrium fluence established in the surrounding 
condition can only be valid in regions of CPE or TCPE. In 
resence of a cavity always causes some degree of fluence pertur-
quires the introduction of a fluence perturbation correction 
n (b) implies that all electrons depositing the dose inside the 
duced outside the cavity and completely cross the cavity. No 
trons are therefore produced inside the cavity and no electrons 
 cavity. 
CHAPTER 2
62
Under these two conditions, according to the Bragg–Gray cavity theory, 
the dose to the medium Dmed is related to the dose in the cavity Dcav as follows:
(2.31)
where (S
–
/r)med,cav is the ratio of the average unrestricted mass collision 
stopping powe
powers rules 
electrons) in th
Although
Gray cavity t
depend on the
cavity medium
qualifies as a B
may not behav
ray beam. 
2.8.2. Spenc
The Brag
secondary (de
slowing down o
The Spencer–A
for the creatio
further ionizat
gas cavity wou
of their energy
requires modi
theory operat
conditions now
primary partic
The seco
into two comp
electrons with 
deposit their e
equal to D are
electron spectr
and a high ene
kinetic energy
energy loss of 
D D
S
med cav
med,cav
 = ÊËÁ ˆ˜¯r
rs of the medium and the cavity. The use of unrestricted stopping 
out the production of secondary charged particles (or delta 
e cavity and the medium.
 the cavity size is not explicitly taken into account in the Bragg–
heory, the fulfilment of the two Bragg–Gray conditions will 
 cavity size, which is based on the range of the electrons in the 
, the cavity medium and the electron energy. A cavity that 
ragg–Gray cavity for high energy photon beams, for example, 
e as a Bragg–Gray cavity in a medium energy or low energy X 
er–Attix cavity theory
g–Gray cavity theory does not take into account the creation of 
lta) electrons generated as a result of hard collisions in the 
f the primary electrons in the sensitive volume of the dosimeter. 
ttix cavity theory is a more general formulation that accounts 
n of these electrons that have sufficient energy to produce 
ion on their own account. Some of these electrons released in the 
ld have sufficient energy to escape from the cavity, carrying some 
 with them. This reduces the energy absorbed in the cavity and 
fication of the stopping power of the gas. The Spencer–Attix 
es under the two Bragg–Gray conditions; however, these 
 even apply to the secondary particle fluence in addition to the 
le fluence.
ndary electron fluence in the Spencer–Attix theory is divided 
onents based on a user defined energy threshold D. Secondary 
kinetic energies EK less than D are considered slow electrons that 
nergy locally; secondary electrons with energies larger than or 
 considered fast (slowing down) electrons and are part of the 
um. Consequently, this spectrum has a low energy threshold of D
rgy threshold of EK0, where EK0 represents the initial electron 
. Since the lowest energy in the spectrum is D, the maximum 
a fast electron with kinetic energy EK larger than or equal to 2D
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
cannot be larger than D, and the maximum energy loss of a fast electron with 
kinetic energy less than 2D cannot be larger than EK/2 (where D £ EK < 2D).
The energy deposition must be calculated as the product of L
D
(EK)/r, the 
restricted collision stopping power with threshold D, and , the fast 
electron fluence ranging in energy from D to EK0 (e-e stands for the contri-
bution of delta electrons in the slowing down spectrum).
Owing to the Bragg–Gray condition, which stipulates that there must not 
be electron pr
capable of cro
cavity size and
mean chord le
The Spen
in the cavity is
Dmed/Dca
where smed,cav i
of the medium
Using th
expression is:
The term
a part of the en
D and 2D. The
energy to low
deposited on th
track end term
and
Fmede-e K,E
smed,cav =
TEmed =
TEcav =
63
oduction in the cavity, the electrons with energy D must be 
ssing the cavity. The threshold value D is hence related to the 
 is defined as the energy of the electron with a range equal to the 
ngth across the cavity.
cer–Attix relation between the dose to the medium and the dose 
 thus written as:
v = smed,cav (2.32)
s the ratio of the mean restricted mass collision stopping powers 
 to that of the cavity. 
e medium electron fluence spectrum , the full 
(2.33)
s TEmed and TEcav are called the track end terms and account for 
ergy deposited by electrons with initial kinetic energies between 
se electrons can have an energy loss that brings their kinetic 
er than D. Their residual energy after such events should be 
e spot, and these electrons are removed from the spectrum. The 
s are approximated by Nahum as:
(2.34)
(2.35)
Fmed,e-e KKE E( )
E L EE
E
E
med
e-e
K med K med
med,
e-
K
K0
K
( / d TE+Ú FFD D, ,( ) ) ( )ree K cav K cavK0 / d TE( )( ) ( ),E L EED DÚ +r
med,
e-e med
K
F D D DE S( ) ( )r
med
e-e cav
K
F D D D, ( ) ( )E S r
CHAPTER 2
64
Note that the unrestricted collision stopping powers can be used here because 
the maximum energy transfer for an electron with energy less than 2D is less 
than D.
Monte Carlo calculations have shown that the difference between the 
Spencer–Attix and Bragg–Gray cavity theories is non-negligible yet generally 
not very significant. Since collision stopping powers for different media show 
similar trends as a function of particle energy, their ratio for the two media is a 
very slowly var
The valu
chambers is on
Farmer type c
physics a nomi
For a typ
the stopping p
density effect c
2.8.3. Consi
chamb
A dosim
providing a rea
its (the dosime
generally be co
medium, surro
In the co
can be identifi
medium. Gas i
simple electric
medium by rad
The med
the situation in
supplemented 
Bragg–Gray th
dose in the wa
forms the basi
C
l
 based dosim
phantom witho
thinner than th
dose due to e
contribution f
medium and th
ying function with energy. 
e of the stopping power water to air ratio for ionization 
ly weakly dependent on the choice of the cut-off energy. For 
hambers and for parallel-plate chambers used in radiotherapy 
nal value of 10 keV is often used.
ical ionization chamber used in water, the energy dependence of 
ower water to air ratio arises mainly from the difference in the 
orrection between the two materials.
derations in the application of cavity theory to ionization 
er calibration and dosimetry protocols
eter can be defined generally as any device that is capable of 
ding that is a measure of the average absorbed dose deposited in 
ter’s) sensitive volume by ionizing radiation. A dosimeter can 
nsidered as consisting of a sensitive volume filled with a given 
unded by a wall of another medium.
ntext of cavity theories, the sensitive volume of the dosimeter 
ed as the ‘cavity’, which may contain a gaseous, liquid or solid 
s often used as the sensitive medium, since it allows a relatively 
al means for collection of charges released in the sensitive 
iation.
ium surrounding the cavity of an ionization chamber depends on 
 which the device is used. In an older approach, the wall (often 
with a buildup cap) serves as the buildup medium and the 
eory provides a relation between the dose in the gas and the 
ll. This is referred to as a thick walled ionization chamber and 
s of cavity chamber based air kerma in-air standards and of the 
etry protocols of the 1970s. If, however,the chamber is used in a 
ut a buildup material, since typical wall thicknesses are much 
e range of the secondary electrons, the proportion of the cavity 
lectrons generated in the phantom greatly exceeds the dose 
rom the wall, and hence the phantom medium serves as the 
e wall is treated as a perturbation to this concept.
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
In the case of a thick walled ionization chamber in a high energy photon 
beam, the wall thickness must be greater than the range of secondary electrons 
in the wall material to ensure that the electrons that cross the cavity arise in the 
wall and not in the medium. The Bragg–Gray cavity equation then relates the 
dose in the cavity to the dose in the wall of the chamber. The dose in the 
medium is related to the dose in the wall by means of a ratio of the mass–
energy absorption coefficients of the medium and the wall (m–en/r)med,wall by 
assuming that:
(a) The abso
(b) The phot
The dose
cavity as follow
where Q is the
of the gas in th
Spencer–
medium as:
where swall,gas 
cavity wall and
factors associa
above. 
A similar
however, here 
kerma in air. I
the presence o
In the cas
electron beam
Dgas =
D Dmed =
= Q
m
65
rbed dose is the same as the collision kerma;
on fluence is not perturbed by the presence of the chamber. 
 to the cavity gas is related to the ionization produced in the 
s:
(2.36)
 charge (of either sign) produced in the cavity and m is the mass 
e cavity. 
Attix cavity theory can be used to calculate the dose in the 
(2.37)
is the ratio of restricted mass collision stopping powers for a 
 gas with threshold D. In practice, there are additional correction 
ted with Eq. (2.37) to satisfy assumptions (a) and (b) made 
 equation to Eq. (2.37) is used for air kerma in-air calibrations; 
the quantity of interest is not the dose to the medium, but the air 
n this case, a substantial wall correction is introduced to ensure 
f complete CPE in the wall to satisfy assumption (a) above.
e of a thin walled ionization chamber in a high energy photon or 
, the wall, cavity and central electrode are treated as a 
Q
m
W
e
gas 
ÊËÁ ˆ˜¯
D swall
en
med,wall
gas wall,gas
en
med,wa
ÊËÁ ˆ˜¯ = ÊËÁ ˆ˜¯mr mr lll
ÊËÁ ˆ˜¯ ÊËÁ ˆ˜¯We s gas wall,gas en med,wallmr
CHAPTER 2
66
perturbation to the medium fluence, and the equation now involves the ratio of 
restricted collision stopping powers of the medium to that of the gas smed,gas as:
(2.38)
where
pfl is the ele
pdis is the co
point;
pwall is the wa
pcel is the cor
Values fo
photon and ele
details).
2.8.4. Large
A large c
made by elec
outside the ca
electrons creat
For a lar
ratio of the co
to the ratio of t
to that of the m
where the mas
photon fluenc
(denominator)
2.8.5. Burlin
Burlin ex
cavities of inte
logical basis, 
D
Q
m
W
e
s p p p pmed
gas
med,gas fl dis wall cel = ÊËÁ ˆ˜¯
D
D
gas
med
= ÊËÁ
ctron fluence perturbation correction factor;
rrection factor for displacement of the effective measurement 
ll correction factor; 
rection factor for the central electrode. 
r these multiplicative correction factors are summarized for 
ctron beams in typical dosimetry protocols (see Section 9.7 for 
 cavities in photon beams
avity is a cavity with dimensions such that the dose contribution 
trons inside the cavity originating from photon interactions 
vity can be ignored when compared with the contribution of 
ed by photon interactions within the cavity.
ge cavity the ratio of dose cavity to medium is calculated as the 
llision kerma in the cavity to the medium and is therefore equal 
he average mass–energy absorption coefficients of the cavity gas 
edium (m–/r)gas,med:
(2.39)
s–energy absorption coefficients have been averaged over the 
e spectra in the cavity gas (numerator) and in the medium 
.
 cavity theory for photon beams
tended the Bragg–Gray and Spencer–Attix cavity theories to 
rmediate dimensions by introducing, on a purely phenomeno-
a large cavity limit to the Spencer–Attix equation using a 
en
gas,med
ˆ˜¯m
r
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
weighting technique. He provided a formalism to calculate the value of the 
weighting parameter.
The Burlin cavity theory can be written in its simplest form as follows:
(2.40)
where 
d is
ca
sgas,med is
ca
Dgas is
(m–en/r)gas,med is
th
The Burl
● The surro
● A homog
and the c
● CPE exis
the maxim
● The equi
and the c
Burlin pr
theory. It is exp
the medium. C
electron fluenc
value of the w
ratio can be ca
D
D
ds dgas
med
gas,med
en
gas,med
 = + - ÊËÁ ˆ˜¯( )1 mr
d
L
L= Ú ÚFFme0
0
67
 a parameter related to cavity size, approaching unity for small 
vities and zero for large cavities; 
 the mean ratio of the restricted mass stopping powers of the 
vity and the medium; 
 the absorbed dose in the cavity; 
 the mean ratio of the mass–energy absorption coefficients for 
e cavity and the medium. 
in theory effectively requires that:
unding medium and the cavity medium be homogeneous;
eneous photon field exist everywhere throughout the medium 
avity;
t at all points in the medium and the cavity that are further than 
um electron range from the cavity boundary;
librium spectra of secondary electrons generated in the medium 
avity be the same.
ovided a method for estimating the weighting parameter d in his 
ressed as the average value of the electron fluence reduction in 
onsistent with experiments with b sources he proposed that the 
e in the medium decays, on average, exponentially. The 
eighting parameter d in conjunction with the stopping power 
lculated as:
(2.41)
Fmede-e
e l
l
e
L
l
L= -- -ed-e
med
e-e
d
d
b
b
b
1
CHAPTER 2
68
where b is an effective electron fluence attenuation coefficient that quantifies 
the reduction in particle fluence from its initial medium fluence value through 
a cavity of average length L. For convex cavities and isotropic electron fluence 
distributions, L can be calculated as 4V/S, where V is the cavity volume and S its 
surface area. Burlin described the buildup of the electron fluence inside 
the cavity using a similar, complementary equation:
Burlin’s 
theory: that th
d). It had relat
of intermediat
show that, wh
cavity to abso
weighting met
calculate dose 
the Burlin cavi
2.8.6. Stopp
Although
doses, the prac
required addit
Spencer–Attix
Attix dose rati
In photo
stopping powe
depth. Stoppin
are shown in T
Stopping
of absorbed d
measurements
secondary elec
another. An im
restricted stop
as a function o
Fgase-e
1 0- = Úd L
 (2.42)
theory is consistent with the fundamental constraint of cavity 
e weighting factors of both terms add up to unity (i.e. d and 1 – 
ive success in calculating ratios of absorbed dose for some types 
e cavities. More generally, however, Monte Carlo calculations 
en studying ratios of directly calculated absorbed doses in the 
rbed dose in the medium as a function of cavity size, the 
hod is too simplistic and additional terms are necessary to 
ratios for intermediate cavity sizes. For these and other reasons, 
ty theory is no longer used in practice.
ing power ratios
 cavity theory was designed to calculate ratios of absorbed 
tical application of the Spencer–Attix cavity theory has always 
ional correction factors. Since the central component of the 
 cavity theory results in averaging stopping powers, Spencer–
os are often referred to as ‘stopping power ratios’. 
n beams, except at or near the surface, average restricted 
r ratios of water to air do not vary significantly as a function of 
g power ratios (with D = 10 keV) under full buildup conditions 
able 2.1. 
 power ratiosnot only play a role in the absolute measurement 
ose, they are also relevant in performing accurate relative 
 of absorbed dose in regimes in which the energy of the 
trons changes significantly from one point in a phantom to 
portant example of this is apparent from Fig. 2.4, which shows 
ping power ratios (D = 10 keV) of water to air for electron beams 
f depth in water. Note that these curves are for monoenergetic
1
1
0
- = - +- -Ú e ll L eLlL LF Fgase-e gase-e dd( )b bb b
DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS
TABLE 2.1. AVERAGE RESTRICTED STOPPING 
POWER RATIO OF WATER TO AIR, swater,air, FOR 
DIFFERENT PHOTON SPECTRA IN THE RANGE 
FROM 60Co g RAYS TO 35 MV X RAYS
Photon spectrum swater,air
60Co 1.134
 4 M
 6 M
 8 M
10 M
15 M
20 M
25 M
35 M
s w
at
er
,a
ir
FIG. 2.4. Restric
of depth for diffe
69
V 1.131
V 1.127
V 1.121
V 1.117
V 1.106
V 1.096
V 1.093
V 1.084
1.10 
1.05 
1.00 
0.95
5 10 15
Depth in water (cm)
5 MeV
10 MeV
20 MeV
30 MeV
40 MeV
ted collision stopping power water to air ratio (D = 10 keV) as a function 
rent monoenergetic electron energies.
CHAPTER 2
70
electrons; protocols or codes of practice for electron dosimetry provide fits of 
stopping power ratios for realistic accelerator beams. However, Fig. 2.4 shows 
clearly that the accurate measurement of electron beam depth dose curves 
requires depth dependent correction factors.
More detailed information on stopping power ratios is given in 
Section 9.5.
ATTIX, F.H., In
New York (1986
GREENING, J.R
INTERNATION
MEASUREME
Bethesda, MD (
— Fundamental
MD (1998).
JOHNS, H.E., C
IL (1985).
KHAN, F.M., T
Baltimore, MD 
BIBLIOGRAPHY
troduction to Radiological Physics and Radiation Dosimetry, Wiley, 
).
., Fundamentals of Radiation Dosimetry, Adam Hilger, Bristol (1981).
AL COMMISSION ON RADIATION UNITS AND 
NTS, Stopping Powers for Electrons and Positrons, Rep. 37, ICRU, 
1984).
 Quantities and Units for Ionizing Radiation, Rep. 60, ICRU, Bethesda, 
UNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, 
he Physics of Radiation Therapy, Lippincott, Williams and Wilkins, 
(2003).
Chapter 3
RADIATION DOSIMETERS
J. IZEWSKA
Division of Human Health,
Internati
Vienna
G. RAJA
Medical P
Bhabha A
Mumbai,
3.1. INTROD
A radiati
evaluates, eith
absorbed dose
quantities of io
as a dosimetry
Measure
of the quanti
measurement 
a numerical va
To functi
one physical p
and that can b
to be useful, ra
For example, i
water at a spec
as the possibili
this context, 
accuracy and 
response, direc
Obviousl
a radiation dos
into account th
radiotherapy i
71
onal Atomic Energy Agency,
N
hysics and Safety Section,
tomic Research Centre,
 Maharashtra, India
UCTION
on dosimeter is a device, instrument or system that measures or 
er directly or indirectly, the quantities exposure, kerma, 
 or equivalent dose, or their time derivatives (rates), or related 
nizing radiation. A dosimeter along with its reader is referred to 
 system.
ment of a dosimetric quantity is the process of finding the value 
ty experimentally using dosimetry systems. The result of a 
is the value of a dosimetric quantity expressed as the product of 
lue and an appropriate unit.
on as a radiation dosimeter, the dosimeter must possess at least 
roperty that is a function of the measured dosimetric quantity 
e used for radiation dosimetry with proper calibration. In order 
diation dosimeters must exhibit several desirable characteristics. 
n radiotherapy exact knowledge of both the absorbed dose to 
ified point and its spatial distribution are of importance, as well 
ty of deriving the dose to an organ of interest in the patient. In 
the desirable dosimeter properties will be characterized by 
precision, linearity, dose or dose rate dependence, energy 
tional dependence and spatial resolution. 
y, not all dosimeters can satisfy all characteristics. The choice of 
imeter and its reader must therefore be made judiciously, taking 
e requirements of the measurement situation; for example, in 
onization chambers are recommended for beam calibrations 
CHAPTER 3
72
(reference dosimetry: see Chapter 9) and other dosimeters, such as those 
discussed below, are suitable for the evaluation of the dose distribution 
(relative dosimetry) or dose verification.
3.2. PROPERTIES OF DOSIMETERS
3.2.1. Accur
In radio
measurement 
precision of d
measurements
obtained in re
standard devia
of dosimetry m
‘true value’ o
absolutely acc
terized as ‘unc
The unc
measured valu
by other meth
symmetrical. 
The erro
of a quantity a
● An error
● Typically
estimated
correctio
● After ap
errors sh
tainties.
3.2.1.1. Type A
If a meas
best estimate f
acy and precision
therapy dosimetry the uncertainty associated with the 
is often expressed in terms of accuracy and precision. The 
osimetry measurements specifies the reproducibility of the 
 under similar conditions and can be estimated from the data 
peated measurements. High precision is associated with a small 
tion of the distribution of the measurement results. The accuracy 
easurements is the proximity of their expectation value to the 
f the measured quantity. Results of measurements cannot be 
urate and the inaccuracy of a measurement result is charac-
ertainty’. 
ertainty is a parameter that describes the dispersion of the 
es of a quantity; it is evaluated by statistical methods (type A) or 
ods (type B), has no known sign and is usually assumed to be 
r of measurement is the difference between the measured value 
nd the true value of that quantity. 
 has both a numerical value and a sign.
, the measurement errors are not known exactly, but they are 
 in the best possible way, and, where possible, compensating 
ns are introduced.
plication of all known corrections, the expectation value for 
ould be zero and the only quantities of concern are the uncer-
 standard uncertainties
urement of a dosimetric quantity x is repeated N times, then the 
or x is the arithmetic mean value of all measurements xi:x,
RADIATION DOSIMETERS
(3.1)
The standard deviation sx characterizes the average uncertainty for an 
individual result xi and is given by:
The stand
● The stan
standard
● The stand
repeated
the numb
3.2.1.2. Type B
Type B 
measurements
non-statistical 
influences on 
physical data t
It is ofte
distribution, su
probability an
can be derived
not going to lie
according to th
3.2.1.3. Comb
The equa
the type:
x
N
xi
i
N= =Â1 1
s x N
=
s x N
= 1
73
(3.2)
ard deviation of the mean value is given by:
(3.3)
dard uncertainty of type A, denoted uA, is defined as the 
 deviation of the mean value, uA = .
ard uncertainty of type A is obtained by a statistical analysis of 
 measurements and, in principle, can be reduced by increasing 
er of measurements.
 standard uncertainties
standard uncertainties uB cannot be estimated by repeated 
; rather, they are intelligent guesses or scientific judgements of 
uncertainties associated with the measurement. They include 
the measuring process, application of correction factors or 
aken from the literature. 
n assumed that type B standard uncertainties have a probability 
ch as a normal (Gaussian) or a rectangular distribution (equal 
ywhere within the given limits). Type B standard uncertainties 
 by estimating the limit beyond which the value of the factor is 
, and a fraction of this limit is taken as uB. The fraction is chosen 
e distribution assumed.
ined and expanded uncertainties
tion that determines a dosimetric quantity Q at a point P is of 
i
i
N
x x- -=Â1 21 1 ( )
s x i
i
N
N N
x x= - -=Â11 2( ) ( )1
s x
CHAPTER 3
74
(3.4)
where M is the reading provided by the dosimetry system and Fi is the 
correction or conversion coefficient.
● The comb
quadratic
● The comb
is multip
uncertain
then expr
● The exp
sponding
overall u
the quan
3.2.2. Linea
Ideally, t
dosimetric qua
sets in. The lin
of dosimeter a
Two typic
shown in Fig. 3
behaviour, and
saturation at h
In genera
and its reader 
effect could pr
3.2.3. Dose 
Integrati
system. For s
independent o
Q M F
i
N
iP =1
= P
u uC A= 2
ined standard uncertainty uC associated with the quantity Q is a 
 summation of type A (uA) and type B (uB) uncertainties:
(3.5)
ined uncertainty is assumed to exhibit a normal distribution and 
lied by a coverage factor, denoted by k, to obtain the expanded 
ty U = kuC. The result of the measurement of the quantity Q is 
essed by QP ± U. 
anded uncertainty U with the coverage factor k = 2, corre-
 to the 95% confidence level, is often used to represent the 
ncertainty, which relates to the accuracy of the measurement of 
tity Q. 
rity
he dosimeter reading M should be linearly proportional to the 
ntity Q. However, beyond a certain dose range a non-linearity 
earity range and the non-linearity behaviour depend on the type 
nd its physical characteristics. 
al examples of response characteristics of dosimetry systems are 
.1. Curve A first exhibits linearity with dose, then a supralinear 
 finally saturation. Curve B first exhibits linearity and then 
igh doses.
l, a non-linear behaviour should be corrected for. A dosimeter 
may both exhibit non-linear characteristics, but their combined 
oduce linearity over a wider range. 
rate dependence
ng systems measure the integrated response of a dosimetry 
uch systems the measured dosimetric quantity should be 
f the rate of that quantity.
uB+ 2
RADIATION DOSIMETERS
Ideally, t
rates ((dQ/dt)1
may influence
necessary, for 
pulsed beams.
3.2.4. Energ
The resp
radiation beam
a specified rad
energy range,
radiation quali
Ideally, t
should be inde
reality, the ene
quantity Q for
interest is the 
equivalent for
important char
A
B
D
os
im
et
er
 r
ea
d
in
g 
FIG. 3.1. Resp
linearity with d
exhibits linearity
75
he response of a dosimetry system M/Q at two different dose 
 and (dQ/dt)2) should remain constant. In reality, the dose rate 
 the dosimeter readings and appropriate corrections are 
example recombination corrections for ionization chambers in 
y dependence
onse of a dosimetry system M/Q is generally a function of 
 quality (energy). Since the dosimetry systems are calibrated at 
iation beam quality (or qualities) and used over a much wider 
 the variation of the response of a dosimetry system with 
ty (called energy dependence) requires correction.
he energy response should be flat (i.e. the system calibration 
pendent of energy over a certain range of radiation qualities). In 
rgy correction has to be included in the determination of the 
 most measurement situations. Ιn radiotherapy, the quantity of 
dose to water (or to tissue). As no dosimeter is water or tissue 
 all radiation beam qualities, the energy dependence is an 
acteristic of a dosimetry system.
Dose
onse characteristics of two dosimetry systems. Curve A first exhibits 
ose, then supralinear behaviour and finally saturation. Curve B first 
 and then saturation at high doses.
CHAPTER 3
76
3.2.5. Directional dependence
The variation in response of a dosimeter with the angle of incidence of 
radiation is known as the directional, or angular, dependence of the dosimeter. 
Dosimeters usually exhibit directional dependence, due to their constructional 
details, physical size and the energy of the incident radiation. Directional 
dependence is important in certain applications, for example in in vivo 
dosimetry wh
generally used
3.2.6. Spatia
Since the
nation of the d
to characterize
determined (i.
coordinate sys
Thermolu
and their use,
dosimeters ha
measurement 
Ionization cha
required sensit
overcomes the
3.2.7. Reado
Direct re
convenient th
processing foll
dosimeters are
can measure in
3.2.8. Conve
Ionizatio
within their l
gradual loss of
not reusable (
distribution in
ile using semiconductor dosimeters. Therapy dosimeters are 
 in the same geometry as that in which they are calibrated.
l resolution and physical size
 dose is a point quantity, the dosimeter should allow the determi-
ose from a very small volume (i.e. one needs a ‘point dosimeter’ 
 the dose at a point). Τhe position of the point where the dose is 
e. its spatial location) should be well defined in a reference 
tem.
minescent dosimeters (TLDs) come in very small dimensions 
 to a great extent, approximates a point measurement. Film 
ve excellent 2-D and gels 3-D resolution, where the point 
is limited only by the resolution of the evaluation system. 
mber type dosimeters, however, are of finite size to give the 
ivity, although the new type of pinpoint microchambers partially 
 problem.
ut convenience
ading dosimeters (e.g. ionization chambers) are generally more 
an passive dosimeters (i.e. those that are read after due 
owing the exposure, for example TLDs and films). While some 
 inherently of the integrating type (e.g. TLDs and gels), others 
 both integral and differential modes (ionization chambers).
nience of use
n chambers are reusable, with no or little change in sensitivity 
ifespan. Semiconductor dosimeters are reusable, but with a 
 sensitivity within their lifespan; however, some dosimeters are 
e.g. films, gels and alanine). Some dosimeters measure dose 
 a single exposure (e.g. films and gels) and some dosimeters are 
RADIATION DOSIMETERS
quite rugged (i.e. handling will not influence sensitivity, for example ionization 
chambers), while others are sensitive to handling (e.g. TLDs).
3.3. IONIZATION CHAMBER DOSIMETRY SYSTEMS
3.3.1. Chambers and electrometers
Ionizatio
for the determ
irradiation co
details). Ioniza
the specific req
● An ioniz
conductiv
Fig. 3.2). 
quality in
is applied
● A guard 
chamber
allows it
ensures i
chamber,
● Measure
and press
chamber
pressure.
 
PTCFE
FIG. 3.2
77
n chambers are used in radiotherapy and in diagnostic radiology 
ination of radiation dose. The dose determination in reference 
nditions is also called beam calibration (see Chapter 9 for 
tion chambers come in various shapes and sizes, depending upon 
uirements, but generally they all have the following properties: 
ation chamber is basically a gas filled cavity surrounded by a 
e outer wall and having a central collecting electrode (see 
The wall and the collecting electrode are separated with a high 
sulator to reduce the leakage current when a polarizing voltage 
 to the chamber. 
electrode is usually provided in the chamber to further reduce 
 leakage. The guard electrode intercepts the leakage current and 
 to flow to ground, bypassing the collecting electrode. It also 
mproved field uniformity in the active or sensitive volume of the 
 with resulting advantages in charge collection.
ments with open air ionization chambers require temperature 
ure correction to account for the change in the mass of air in the 
 volume, which changes with the ambient temperature and 
 
Outer electrode 
Central electrode 
Insulator 
Aluminium 
Graphite
Dural
. Basic design of a cylindrical Farmer type ionization chamber.
CHAPTER 3
78
Electrometers are devices for measuring small currents, of the order of 10–9 A 
or less. An electrometer used in conjunction with an ionization chamber is a 
high gain, negative feedback, operational amplifier with a standard resistor or a 
standard capacitor in the feedback path tomeasure the chamber current or 
charge collected over a fixed time interval, as shown schematically in Fig. 3.3.
3.3.2. Cylindrical (thimble type) ionization chambers
The mos
designed by Fa
from several 
chamber sensi
chamber is also
type thimble io
dosimetry syst
Cylindric
volumes betw
greater than 2
material is of 
thickness less t
thickness of ab
The cha
although an alu
 
 
 
 
 
 
 
 
Rf = fee
 (va
Cf = fee
 (va
t popular cylindrical ionization chamber is the 0.6 cm3 chamber 
rmer and originally manufactured by Baldwin, but now available 
vendors, for beam calibration in radiotherapy dosimetry. Its 
tive volume resembles a thimble, and hence the Farmer type 
 known as a thimble chamber. A schematic diagram of a Farmer 
nization chamber is shown in Fig. 3.2; ionization chamber based 
ems are discussed in Section 9.2.
al chambers are produced by various manufacturers, with active 
een 0.1 and 1 cm3. They typically have an internal length no 
5 mm and an internal diameter no greater than 7 mm. The wall 
low atomic number Z (i.e. tissue or air equivalent), with the 
han 0.1 g/cm2. A chamber is equipped with a buildup cap with a 
out 0.5 g/cm2 for calibration free in air using 60Co radiation.
mber construction should be as homogeneous as possible, 
minium central electrode of about 1 mm in diameter is typically 
 
 
 
 
 - 
I
 
 + 
 
 
 
 
V = (II � t)/Cf
(integrated mode)
V = II Rf (rate mode) 
dback resistor
riable to vary sensitivity)
dback capacitor
riable to vary sensitivity) 
Rf
Cf
FIG. 3.3. Electrometer in feedback mode of operation.
RADIATION DOSIMETERS
used to ensure flat energy dependence. Construction details of various 
commercially available cylindrical chambers are given in the IAEA Technical 
Reports Series (TRS) 277 and TRS 398 codes of practice. The use of the 
cylindrical chamber in electron and photon beam dosimetry is discussed in 
Chapter 9.
3.3.3. Parallel-plate (plane-parallel) ionization chambers
A parall
serving as an e
wall and collec
usually a bloc
Perspex or po
collecting elec
a parallel-plate
The para
beams with en
dose measurem
measurements
Section 6.13. 
chambers and
explained in d
parallel-plate 
because they a
3.3.4. Brach
Sources u
chambers of su
Well type cham
and standardiz
diagram of a w
Well type
typical sizes an
calibrated in te
3.3.5. Extrap
Extrapol
sensitive volum
79
el-plate ionization chamber consists of two plane walls, one 
ntry window and polarizing electrode and the other as the back 
ting electrode, as well as a guard ring system. The back wall is 
k of conducting plastic or a non-conducting material (usually 
lystyrene) with a thin conducting layer of graphite forming the 
trode and the guard ring system on top. A schematic diagram of 
 ionization chamber is shown in Fig. 3.4.
llel-plate chamber is recommended for dosimetry of electron 
ergies below 10 MeV. It is also used for surface dose and depth 
ents in the buildup region of megavoltage photon beams. Dose 
 in the buildup region of photon beams are discussed in 
The characteristics of commercially available parallel-plate 
 the use of these chambers in electron beam dosimetry are 
etail in the TRS 381 and TRS 398 codes of practice. Some 
chambers require significant fluence perturbation correction 
re provided with an inadequate guard width.
ytherapy chambers
sed in brachytherapy are low air kerma rate sources that require 
fficient volume (about 250 cm3 or more) for adequate sensitivity. 
bers or re-entrant chambers are ideally suited for calibration 
ation of brachytherapy sources. Figure 3.5 shows a schematic 
ell type chamber.
 chambers should be designed to accommodate sources of the 
d shapes that are in clinical use in brachytherapy and are usually 
rms of the reference air kerma rate.
olation chambers
ation chambers are parallel-plate chambers with a variable 
e. They are used in the measurement of surface doses in ortho-
CHAPTER 3
80
voltage and m
energy X rays
directly embed
for electrons c
cavity thicknes
the cavity pert
estimated. 
a
A
FIG. 3.4. Parall
electrode. 3: the 
diameter of the 
width of the gua
egavoltage X ray beams and in the dosimetry of b rays, and low 
. They can also be used in absolute radiation dosimetry when 
ded into a tissue equivalent phantom. The cavity perturbation 
an be eliminated by making measurements as a function of the 
s and then extrapolating to zero thickness. Using this chamber, 
urbation for parallel-plate chambers of finite thickness can be 
Schnitt A–B
B
g
d
3 1 2 3
m
el-plate ionization chamber. 1: the polarizing electrode. 2: the measuring 
guard ring. a: the height (electrode separation) of the air cavity. d: the 
polarizing electrode. m: the diameter of the collecting electrode. g: the 
rd ring.
RADIATION DOSIMETERS
3.4. FILM DO
3.4.1. Radio
Radiogra
diagnostic rad
radiation dete
medium.
Unexpos
sensitive emul
uniformly on o
● Ionizatio
latent im
blackenin
● Light tra
in terms 
● The OD 
initial lig
● Film give
provides 
area of in
Source holder
Collecting electrode 
Outer electrode (HV)
FI
81
SIMETRY
graphic film
phic X ray film performs several important functions in 
iology, radiotherapy and radiation protection. It can serve as a 
ctor, a relative dosimeter, a display device and an archival 
ed X ray film consists of a base of thin plastic with a radiation 
sion (silver bromide (AgBr) grains suspended in gelatin) coated 
ne or both sides of the base.
n of AgBr grains, as a result of radiation interaction, forms a 
age in the film. This image only becomes visible (film 
g) and permanent subsequently to processing.
nsmission is a function of the film opacity and can be measured 
of optical density (OD) with devices called densitometers.
is defined as OD = log10 (I0/I) and is a function of dose. I0 is the 
ht intensity and I is the intensity transmitted through the film.
s excellent 2-D spatial resolution and, in a single exposure, 
information about the spatial distribution of radiation in the 
terest or the attenuation of radiation by intervening objects.
Insulator 
To electrometer 
G. 3.5. Basic design of a brachytherapy well type chamber.
CHAPTER 3
82
● Τhe useful dose range of film is limited and the energy dependence is 
pronounced for lower energy photons. The response of the film depends 
on several parameters, which are difficult to control. Consistent 
processing of the film is a particular challenge in this regard.
● Typically, film is used for qualitative dosimetry, but with proper 
calibration, careful use and analysis film can also be used for dose 
evaluation.
● Various 
exposure
films use
imaging)
● Unexpos
(ODf). T
obtained
● OD rea
automati
tometer i
Ideally, t
this is not alwa
limited dose r
known as the 
curve, in hon
relationship) m
dosimetry wor
A typica
four regions: (
Film 
types of film are available for radiotherapy work (e.g. direct 
 non-screen films for field size verification, phosphor screen 
d with simulators and metallic screen films used in portal 
.
ed film would exhibit a background OD called the fog density 
he density due to radiation exposure, called the net OD, can be 
 from the measured density by subtracting the fogdensity.
ders include film densitometers, laser densitometers and 
c film scanners. The principle of operation of a simple film densi-
s shown in Fig. 3.6.
he relationship between the dose and OD should be linear, but 
ys the case. Some emulsions are linear, some are linear over a 
ange and others are non-linear. The dose versus OD curve, 
sensitometric curve (also known as the characteristic or H&D 
our of Hurter and Driffield, who first investigated the 
ust therefore be established for each film before using it for 
k.
l H&D curve for a radiographic film is shown in Fig. 3.7. It has 
1) fog, at low or zero exposures; (2) toe; (3) a linear portion at 
2.99 
_
+
Log ratio amplifier
I0 
Isig 
(3½ digits DPM) 
OD = log10 (I0/Isig)
FIG. 3.6. Basic film densitometer.
RADIATION DOSIMETERS
intermediate exposures; and (4) shoulder and saturation at high exposures. The 
linear portion is referred to as optimum measurement conditions, the toe is the 
region of underexposure and the shoulder is the region of overexposure.
Important parameters of film response to radiation are gamma, latitude 
and speed:
● The slope of the straight line portion of the H&D curve is called the 
gamma o
● The expo
the linea
ODs.
● The latitu
lie in the
● The spee
produce 
Typical a
and quantitati
control of radi
and the determ
0
1
2
3
4
O
D
FIG. 3.7. Typ
83
f the film.
sure should be chosen to make all parts of the radiograph lie on 
r portion of the H&D curve, to ensure the same contrast for all 
de is defined as the range of exposures over which the ODs will 
 linear region.
d of a film is determined by giving the exposure required to 
an OD of 1.0 greater than the OD of fog.
pplications of a radiographic film in radiotherapy are qualitative 
ve measurements, including electron beam dosimetry, quality 
otherapy machines (e.g. congruence of light and radiation fields 
ination of the position of a collimator axis, the so called star 
1 10 100 1000
(1) Fog (2) Toe
(3) Linear portion
(4) Shoulder
 
Exposure (arbitrary units) 
ical sensitometric (characteristic H&D) curve for a radiographic film.
CHAPTER 3
84
test), verification of treatment techniques in various phantoms and portal 
imaging.
3.4.2. Radiochromic film
Radiochromic film is a new type of film in radiotherapy dosimetry. The 
most commonly used is a GafChromic film. It is a colourless film with a nearly 
tissue equivale
and 19.2% oxy
Radiochr
exposure to ra
through the fil
film is self-de
chromic film is
dose gradient r
stereotactic fie
Dosimetr
graphic films, 
facilities, film 
energy charac
insensitivity to
avoided). Rad
films and are u
should be corr
● Radiochr
calibratio
is achieva
● Data on 
linearity,
available
3.5. LUMINE
Some ma
energy in meta
form of ultravi
cence. Two ty
known, which 
of light. Fluor
nt composition (9.0% hydrogen, 60.6% carbon, 11.2% nitrogen 
gen) that develops a blue colour upon radiation exposure.
omic film contains a special dye that is polymerized upon 
diation. The polymer absorbs light, and the transmission of light 
m can be measured with a suitable densitometer. Radiochromic 
veloping, requiring neither developer nor fixer. Since radio-
 grainless, it has a very high resolution and can be used in high 
egions for dosimetry (e.g. measurements of dose distributions in 
lds and in the vicinity of brachytherapy sources).
y with radiochromic films has a few advantages over radio-
such as ease of use; elimination of the need for darkroom 
cassettes or film processing; dose rate independence; better 
teristics (except for low energy X rays of 25 kV or less); and 
 ambient conditions (although excessive humidity should be 
iochromic films are generally less sensitive than radiographic 
seful at higher doses, although the dose response non-linearity 
ected for in the upper dose region.
omic film is a relative dosimeter. If proper care is taken with 
n and the environmental conditions, a precision better than 3% 
ble.
the various characteristics of radiochromic films (e.g. sensitivity, 
 uniformity, reproducibility and post-irradiation stability) are 
 in the literature.
SCENCE DOSIMETRY
terials, upon absorption of radiation, retain part of the absorbed 
stable states. When this energy is subsequently released in the 
olet, visible or infrared light, the phenomenon is called lumines-
pes of luminescence, fluorescence and phosphorescence, are 
depend on the time delay between stimulation and the emission 
escence occurs with a time delay of between 10–10 and 10–8 s; 
RADIATION DOSIMETERS
phosphorescence occurs with a time delay exceeding 10–8 s. The process of 
phosphorescence can be accelerated with a suitable excitation in the form of 
heat or light.
● If the exciting agent is heat, the phenomenon is known as thermolumines-
cence and the material is called a thermoluminescent material, or a TLD 
when used for purposes of dosimetry.
● If the ex
stimulate
As discu
particles, usua
photons with m
matter. In a 
numerous low 
ions. The free
become trappe
crystal.
The traps
lattice imperfe
known in gene
● A storage
the subse
or (b) irr
● A charge
trapped 
(lumines
emitted i
measured
3.5.1. Therm
Thermolu
most spectacul
induced therm
archaeological
Suntharalingam
process that is
the thermolum
the thermolum
85
citing agent is light, the phenomenon is referred to as optically 
d luminescence (OSL). 
ssed in Section 1.4, the highly energetic secondary charged 
lly electrons, that are produced in the primary interactions of 
atter are mainly responsible for the photon energy deposition in 
crystalline solid these secondary charged particles release 
energy free electrons and holes through ionizations of atoms and 
 electrons and holes thus produced will either recombine or 
d in an electron or hole trap, respectively, somewhere in the 
 can be intrinsic or can be introduced in the crystal in the form of 
ctions consisting of vacancies or impurities. Two types of trap are 
ral: storage traps and recombination centres.
 trap merely traps free charge carriers and releases them during 
quent (a) heating, resulting in the thermoluminescence process, 
adiation with light, resulting in the OSL process.
 carrier released from a storage trap may recombine with a 
charge carrier of opposite sign in a recombination centre 
cence centre). The recombination energy is at least partially 
n the form of ultraviolet, visible or infrared light that can be 
 with photodiodes or photomultiplier tubes (PMTs).
oluminescence
minescence is thermally activated phosphorescence; it is the 
ar and widely known of a number of different ionizing radiation 
ally activated phenomena. Its practical applications range from 
 pottery dating to radiation dosimetry. In 1968 Cameron, 
 and Kenney published a book on the thermoluminescence 
 still considered an excellent treatise on the practical aspects of 
inescence phenomenon. A useful phenomenological model of 
inescence mechanism is provided in terms of the band model for 
CHAPTER 3
86
solids. The storage traps and recombination centres, each type characterized 
with an activation energy (trap depth) that depends on the crystalline solid and 
the nature of the trap, are located in the energy gap between the valence band 
and the conduction band. The states just below the conduction band represent 
electron traps, the states just above the valence band are hole traps. The 
trapping levels are empty before irradiation (i.e. the hole traps contain 
electrons and the electron traps do not).
During ir
conduction ba
valence band) 
The syste
● Free char
into heat
● A free ch
trapped 
emitted a
● The free 
is then re
OSL pro
3.5.2. Therm
The TLDLiF:Mg,Cu,P 
TLDs, used b
CaF2:Mn.
● TLDs ar
ribbons).
● Before th
signal. W
heating a
A basic T
the TLD, a PM
it into an elect
and an electro
basic schemati
radiation the secondary charged particles lift electrons into the 
nd either from the valence band (leaving a free hole in the 
or from an empty hole trap (filling the hole trap).
m may approach thermal equilibrium through several means:
ge carriers recombine with the recombination energy converted 
;
arge carrier recombines with a charge carrier of opposite sign 
at a luminescence centre, the recombination energy being 
s optical fluorescence;
charge carrier becomes trapped at a storage trap, and this event 
sponsible for phosphorescence or the thermoluminescence and 
cesses.
oluminescent dosimeter systems
s most commonly used in medical applications are LiF:Mg,Ti, 
and Li2B4O7:Mn, because of their tissue equivalence. Other 
ecause of their high sensitivity, are CaSO4:Dy, Al2O3:C and 
e available in various forms (e.g. powder, chips, rods and 
 
ey are used, TLDs need to be annealed to erase the residual 
ell established and reproducible annealing cycles, including the 
nd cooling rates, should be used. 
LD reader system consists of a planchet for placing and heating 
T to detect the thermoluminescence light emission and convert 
rical signal linearly proportional to the detected photon fluence 
meter for recording the PMT signal as a charge or current. A 
c diagram of a TLD reader is shown in Fig. 3.8.
RADIATION DOSIMETERS
● The ther
temperat
T propor
plotted a
measurin
general, i
obtains a
● The pea
responsib
● The main
and 260ºC
as not to
to interfe
● The tota
appropri
proper ca
● Good rep
accurate 
● The ther
due to sp
called fad
does not 
● The ther
doses us
region, ex
doses.
 
 
Electrometer 
Thermoluminescence ~ chargeHV 
PMT 
TLD 
87
moluminescence intensity emission is a function of the TLD 
ure T. Keeping the heating rate constant makes the temperature 
tional to time t, and so the thermoluminescence intensity can be 
s a function of t if a recorder output is available with the TLD 
g system. The resulting curve is called the TLD glow curve. In 
f the emitted light is plotted against the crystal temperature one 
 thermoluminescence thermogram (Fig. 3.9).
ks in the glow curve may be correlated with trap depths 
le for thermoluminescence emission.
 dosimetric peak of the LiF:Mg,Ti glow curve between 180ºC 
 is used for dosimetry. The peak temperature is high enough so 
 be affected by room temperature and still low enough so as not 
re with black body emission from the heating planchet.
l thermoluminescence signal emitted (i.e. the area under the 
ate portion of the glow curve) can be correlated to dose through 
libration.
roducibility of heating cycles during the readout is important for 
dosimetry.
moluminescence signal decreases in time after the irradiation 
ontaneous emission of light at room temperature. This process is 
ing. Typically, for LiF:Mg,Ti, the fading of the dosimetric peak 
exceed a few per cent in the months after irradiation.
moluminescence dose response is linear over a wide range of 
ed in radiotherapy, although it increases in the higher dose 
hibiting supralinear behaviour before it saturates at even higher 
Heater 
FIG. 3.8. TLD reader.
CHAPTER 3
88
● TLDs ne
relative d
nescence
those for
● Typical a
patients 
monitori
critical o
of treatm
phantom
zation (W
among ho
3.5.3. Optica
OSL is 
dosimetry. Ins
energy in the
0
0.0
0.2
0.4
0.6
0.8
1.0
 1 h
 4 d
 20 d
N
o
rm
al
iz
ed
 t
he
rm
o
lu
m
es
ce
nc
e 
si
g
na
l
Time after irradiation
FIG. 3.9. A typi
at a low heating 
ed to be calibrated before they are used (thus they serve as 
osimeters). To derive the absorbed dose from the thermolumi-
 reading a few correction factors have to be applied, such as 
 energy, fading and dose response non-linearity.
pplications of TLDs in radiotherapy are: in vivo dosimetry on 
(either as a routine quality assurance procedure or for dose 
ng in special cases, for example complicated geometries, dose to 
rgans, total body irradiation (TBI), brachytherapy); verification 
ent techniques in various phantoms (e.g. anthropomorphic 
s); dosimetry audits (such as the IAEA–World Health Organi-
HO) TLD postal dose audit programme); and comparisons 
spitals.
lly stimulated luminescence systems
based on a principle similar to that of thermoluminescence 
tead of heat, light (from a laser) is used to release the trapped 
 form of luminescence. OSL is a novel technique offering a 
50 100 150 200 250 300 350 400
Temperature (˚C)
cal thermogram (glow curve) of LiF:Mg,Ti measured with a TLD reader 
rate.
RADIATION DOSIMETERS
potential for in vivo dosimetry in radiotherapy. The integrated dose measured 
during irradiation can be evaluated using OSL directly afterwards.
The optical fibre optically stimulated thermoluminescent dosimeter 
consists of a small (~1 mm3) chip of carbon doped aluminium oxide (Al2O3:C) 
coupled with a long optical fibre, a laser, a beam splitter and a collimator, a 
PMT, electronics and software. To produce OSL, the chip is excited with laser 
light through an optical fibre, and the resulting luminescence (blue light) is 
carried back in
measured in a 
The optic
of dose rates a
linear and inde
response requi
Various e
conjunction w
at the time of 
during irradia
technique, alth
valuable tool f
3.6. SEMICO
3.6.1. Silicon
A silicon
produced by ta
produce the op
Si dosimeters,
commercially 
dosimetry, sinc
dark current.
Radiatio
dosimeter, incl
produced in th
the depleted r
action of the e
generated in th
89
 the same fibre, reflected through 90º by the beam splitter and 
PMT.
al fibre dosimeter exhibits high sensitivity over the wide range 
nd doses used in radiotherapy. The OSL response is generally 
pendent of energy as well as the dose rate, although the angular 
res correction.
xperimental set-ups exist, such as pulsed OSL or OSL used in 
ith radioluminescence. Radioluminescence is emitted promptly 
dosimeter irradiation and provides information on the dose rate 
tion, while OSL provides the integrated dose thereafter. This 
ough not yet used routinely in radiotherapy, may prove to be a 
or in vivo dosimetry in the future.
NDUCTOR DOSIMETRY
 diode dosimetry systems
 diode dosimeter is a p–n junction diode. The diodes are 
king n type or p type silicon and counter-doping the surface to 
posite type material. These diodes are referred to as n–Si or p–
 depending upon the base material. Both types of diode are 
available, but only the p–Si type is suitable for radiotherapy 
e it is less affected by radiation damage and has a much smaller 
n produces electron–hole (e–h) pairs in the body of the 
uding the depletion layer. The charges (minority charge carriers) 
e body of the dosimeter, within the diffusion length, diffuse into 
egion. They are swept across the depletion region under the 
lectric field due to the intrinsic potential. In this way a current is 
e reverse direction in the diode.
CHAPTER 3
90
● Diodes are used in the short circuit mode, since this mode exhibits a 
linear relationship between the measured charge and dose. They are 
usually operated without an external bias to reduce leakage current.
● Diodes are more sensitive and smaller in size than typical ionization 
chambers. They are relative dosimeters and should not be used for beam 
calibration, since their sensitivity changes with repeated use due to 
radiation damage.
● Diodes a
of small 
areas suc
ments of
devices i
lation. W
measure 
measured● Diodes a
bladder o
provided
chosen, d
encapsul
● Diodes n
and sever
sensitivit
calibratio
● Diodes sh
ularly im
on the d
distances
even for 
(importa
3.6.2. MOSF
A metal
miniature silic
very little atte
useful for in
measurement 
dose. Ionizing
permanently 
integrated dos
re particularly useful for measurement in phantoms, for example 
fields used in stereotactic radiosurgery or high dose gradient 
h as the penumbra region. They are also often used for measure-
 depth doses in electron beams. For use with beam scanning 
n water phantoms, they are packaged in a waterproof encapsu-
hen used in electron beam depth dose measurements, diodes 
directly the dose distribution (in contrast to the ionization 
 by ionization chambers).
re widely used in routine in vivo dosimetry on patients or for 
r rectum dose measurements. Diodes for in vivo dosimetry are 
 with buildup encapsulation and hence must be appropriately 
epending on the type and quality of the clinical beams. The 
ation also protects the fragile diode from physical damage.
eed to be calibrated when they are used for in vivo dosimetry, 
al correction factors have to be applied for dose calculation. The 
y of diodes depends on their radiation history, and hence the 
n has to be repeated periodically. 
ow a variation in dose response with temperature (this is partic-
portant for long radiotherapy treatments), dependence of signal 
ose rate (care should be taken for different source to skin 
), angular (directional) dependence and energy dependence 
small variations in the spectral composition of radiation beams 
nt for the measurement of entrance and exit doses). 
ET dosimetry systems
-oxide semiconductor field effect transistor (MOSFET), a 
on transistor, possesses excellent spatial resolution and offers 
nuation of the beam due to its small size, which is particularly 
 vivo dosimetry. MOSFET dosimeters are based on the 
of the threshold voltage, which is a linear function of absorbed 
 radiation penetrating the oxide generates charge that is 
trapped, thus causing a change in threshold voltage. The 
e may be measured during or after irradiation. MOSFETs 
RADIATION DOSIMETERS
require a connection to a bias voltage during irradiation. They have a limited 
lifespan.
● A single MOSFET dosimeter can cover the full energy range of photons 
and electrons, although the energy response should be examined, since it 
varies with radiation quality. For megavoltage beams, however, 
MOSFETs do not require energy correction, and a single calibration 
factor can
● MOSFET
require d
● Similarly
but this e
MOSFET
the tota
MOSFET
changes i
response
a specifie
● MOSFET
therapy 
including
modulate
surgery. T
the appli
3.7. OTHER
3.7.1. Alanin
Alanine, 
with an inert b
dosimeter can
precision for r
formation of a
using an elec
resonance) spe
of the central l
● Alanine 
quality ra
91
 be used.
s exhibit small axial anisotropy (±2% for 360º) and do not 
ose rate corrections.
 to diodes, single MOSFETs exhibit a temperature dependence, 
ffect has been overcome by specially designed double detector 
 systems. In general, they show non-linearity of response with 
l absorbed dose; however, during their specified lifespan, 
s retain adequate linearity. MOSFETs are also sensitive to 
n the bias voltage during irradiation (it must be stable), and their 
 drifts slightly after the irradiation (the reading must be taken in 
d time after exposure). 
s have been in use for the past few years in a variety of radio-
applications for in vivo and phantom dose measurements, 
 routine patient dose verification, brachytherapy, TBI, intensity 
d radiotherapy (IMRT), intraoperative radiotherapy and radio-
hey are used with or without additional buildup, depending on 
cation.
 DOSIMETRY SYSTEMS
e/electron paramagnetic resonance dosimetry system
one of the amino acids, pressed in the form of rods or pellets 
inding material, is typically used for high dose dosimetry. The 
 be used at a level of about 10 Gy or more with sufficient 
adiotherapy dosimetry. The radiation interaction results in the 
lanine radicals, the concentration of which can be measured 
tron paramagnetic resonance (known also as electron spin 
ctrometer. The intensity is measured as the peak to peak height 
ine in the spectrum. The readout is non-destructive.
is tissue equivalent and requires no energy correction within the 
nge of typical therapeutic beams. It exhibits very little fading for 
CHAPTER 3
92
many months after irradiation. The response depends on environmental 
conditions during irradiation (temperature) and storage (humidity).
● At present, alanine’s potential application for radiotherapy is in 
dosimetry comparisons among hospitals. 
3.7.2. Plastic scintillator dosimetry system
Plastic sc
dosimetry. The
away by an op
typical set-up 
different PMT
from the meas
in the dose ran
Plastic sc
density and ato
power and ma
beam energies
nearly energy 
measurements
● Plastic sc
less) and
can be u
dose gra
dosimetr
energy d
dosimete
● Dosimetr
ducibility
radiation
monitore
● Plastic sc
10 mGy/m
beam do
need no a
3.7.3. Diamo
Diamond
applying a bias
intillators are a relatively new development in radiotherapy 
 light generated in the scintillator during its irradiation is carried 
tical fibre to a PMT located outside the irradiation room. A 
requires two sets of optical fibres, which are coupled to two 
s, allowing subtraction of the background Cerenkov radiation 
ured signal. The response of the scintillation dosimeter is linear 
ge of therapeutic interest.
intillators are almost water equivalent in terms of electron 
mic composition. Typically, they match the water mass stopping 
ss energy absorption coefficient to within ±2% for the range of 
 in clinical use, including the kilovoltage region. Scintillators are 
independent and can thus be used directly for relative dose 
.
intillation dosimeters can be made very small (about 1 mm3 or 
 yet give adequate sensitivity for clinical dosimetry. Hence they 
sed in cases where high spatial resolution is required (e.g. high 
dient regions, buildup regions, interface regions, small field 
y and doses very close to brachytherapy sources). Due to flat 
ependence and small size, plastic scintillators are ideal 
rs for brachytherapy applications.
y based on plastic scintillators is characterized by good repro-
 and long term stability. Scintillators suffer no significant 
 damage (up to about 10 kGy), although the light yield should be 
d when used clinically.
intillators are independent of dose rate and can be used from 
in (ophthalmic plaque dosimetry) to about 10 Gy/min (external 
simetry). They have no significant directional dependence and 
mbient temperature or pressure corrections.
nd dosimeters
s change their resistance upon radiation exposure. When 
 voltage, the resulting current is proportional to the dose rate of 
RADIATION DOSIMETERS
radiation. Commercially available diamond dosimeters are designed to 
measure relative dose distributions in high energy photon and electron beams. 
The dosimeter is based on a natural diamond crystal sealed in a polystyrene 
housing with a bias applied through thin golden contacts. 
● Diamonds have a small sensitive volume, of the order of a few cubic milli-
metres, which allows the measurement of dose distributions with an 
excellent
● Diamond
correctio
negligible
high dose
● In order 
prior to 
dependen
when me
an insign
● High sen
features o
measurem
3.7.4. Gel do
Gel dosi
relative dose m
can measure a
tissue equivale
Gel dosim
● Fricke ge
● Polymer 
In Fricke
throughout ge
either due to 
radicals. Upon
ions Fe3+ with 
measured usin
techniques. A 
of Fricke gel sy
in ablurred do
93
 spatial resolution.
 dosimeters are tissue equivalent and require nearly no energy 
n. Owing to their flat energy response, small physical size and 
 directional dependence, diamonds are well suited for use in 
 gradient regions, for example for stereotactic radiosurgery.
to stabilize their dose response, diamonds should be irradiated 
each use to reduce the polarization effect. They exhibit some 
ce of the signal on the dose rate, which has to be corrected for 
asuring a given physical quality (e.g. depth dose). Also, they have 
ificant temperature dependence, of the order of 0.1%/ºC or less.
sitivity and resistance to radiation damage are other important 
f diamond dosimeters. They are waterproof and can be used for 
ents in a water phantom.
simetry systems
metry systems are the only true 3-D dosimeters suitable for 
easurements. The dosimeter is at the same time a phantom that 
bsorbed dose distribution in a full 3-D geometry. Gels are nearly 
nt and can be moulded to any desired shape or form. 
etry can be divided into two types: 
ls based on the well established Fricke dosimetry; 
gels.
 gels, Fe2+ ions in ferrous sulphate solutions are dispersed 
latin, agarose or PVA matrix. Radiation induced changes are 
direct absorption of radiation or via intermediate water free 
 radiation exposure, ferrous ions Fe2+ are converted into ferric 
a corresponding change in paramagnetic properties that may be 
g nuclear magnetic resonance (NMR) relaxation rates or optical 
3-D image of the dose distribution is created. A major limitation 
stems is the continual post-irradiation diffusion of ions, resulting 
se distribution.
CHAPTER 3
94
In polymer gel, monomers such as acrylamid are dispersed in a gelatin or 
agarose matrix. Upon radiation exposure, monomers undergo a polymerization 
reaction, resulting in a 3-D polymer gel matrix that is a function of absorbed 
dose that can be evaluated using NMR, X ray computed tomography (CT), 
optical tomography, vibrational spectroscopy or ultrasound.
● A number of polymer gel formulations are available, including polyacryl-
amide ge
new norm
presence
● There is 
the absor
relaxatio
computa
● Due to t
equivalen
electron 
● No signif
NMR ev
which th
during ev
taken of
gelation 
distortion
● Gel dosi
may pro
situation
evaluatio
therapy.
3.8. PRIMAR
Primary 
that permit de
accuracy of w
institutions of 
standards dosi
Regular intern
international d
the dosimetry 
ls, generally referred to as PAG gels (e.g. BANG gel), and the 
oxic gels (e.g. MAGIC gel); the latter are not sensitive to the 
 of atmospheric oxygen.
a semilinear relationship between the NMR relaxation rate and 
bed dose at a point in the gel dosimeter. Hence, by mapping the 
n rates using an NMR scanner, the dose map can be derived by 
tion and by proper calibration.
he large proportion of water, polymer gels are nearly water 
t and no energy corrections are required for photon and 
beams used in radiotherapy.
icant dose rate effects in polymer gels have been observed using 
aluation, although dose response depends on the temperature at 
e dosimeter is evaluated. The strength of the magnetic field 
aluation may also influence the dose response. Care should be 
 post-irradiation effects such as continual polymerization, 
and strengthening of the gel matrix, which may lead to image 
.
metry is a highly promising relative dosimetry technique that 
ve particularly useful for dose verification in complex clinical 
s (e.g. IMRT), in anatomically shaped phantoms, and for 
n of doses in brachytherapy, including cardiovascular brachy-
Y STANDARDS
standards are instruments of the highest metrological quality 
termination of the unit of a quantity from its definition, the 
hich has been verified by comparison with standards of other 
the same level. Primary standards are realized by the primary 
metry laboratories (PSDLs) in about 20 countries worldwide. 
ational comparisons between the PSDLs, and with the Bureau 
es poids et mesures (BIPM), ensure international consistency of 
standards.
RADIATION DOSIMETERS
Ionization chambers used in hospitals for calibration of radiotherapy 
beams must have a calibration traceable (directly or indirectly) to a primary 
standard. Primary standards are not used for routine calibrations, since they 
represent the unit for the quantity at all times. Instead, the PSDLs calibrate 
secondary standard dosimeters for secondary standards dosimetry laboratories 
(SSDLs) that in turn are used for calibrating the reference instruments of users, 
such as therapy level ionization chambers used in hospitals.
3.8.1. Prima
Free-air i
for superficial 
a primary sta
sensitive volum
would become
various requ
problematic.
● At 60Co 
known ch
● The use o
theory.
3.8.2. Prima
The stand
chambers to be
air kerma in 
hospital level 
formalism. Sta
for 60Co beam
calibration ser
ators.
Ideally, t
water calorime
measure the d
establishment 
standard of ab
At prese
absorbed dose
method; (2) th
95
ry standard for air kerma in air 
onization chambers are the primary standard for air kerma in air 
and orthovoltage X rays (up to 300 kV); they cannot function as 
ndard for 60Co beams, since the air column surrounding the 
e (for establishing the electronic equilibrium condition in air) 
 very long. This would make the chamber very bulky and the 
ired corrections and their uncertainties would become 
energy, graphite cavity ionization chambers with an accurately 
amber volume are used as the primary standard.
f the graphite cavity chamber is based on the Bragg–Gray cavity 
ry standards for absorbed dose to water
ards for absorbed dose to water enable therapy level ionization 
 calibrated directly in terms of absorbed dose to water instead of 
air. This simplifies the dose determination procedure at the 
and improves the accuracy compared with the air kerma based 
ndards for absorbed dose to water calibration are now available 
s in several PSDLs, some of which have extended their 
vices to high energy photon and electron beams from acceler-
he primary standard for absorbed dose to water should be a 
ter that would be an integral part of a water phantom and would 
ose under reference conditions. However, difficulties in the 
of this standard have led to the development of a primary 
sorbed dose in various different ways.
nt there are three basic methods used for the determination of 
 to water at the primary standard level: (1) the ionometric 
e total absorption method based on chemical dosimetry; and 
CHAPTER 3
96
(3) calorimetry. The three methods are discussed below and in more detail in 
Chapter 9.
3.8.3. Ionometric standard for absorbed dose to water
A graphite cavity ionization chamber with an accurately known active 
volume, constructed as a close approximation to a Bragg–Gray cavity, is used in 
a water phanto
point is derived
to the air in t
material to th
absorbed dose
3.8.4. Chem
In chemi
chemical chan
dosimeter) usi
● The mo
dosimete
● The Fric
Fe(NH4)
● Irradiatio
Fe3+; the
ferrous io
● Radiation
photomet
● The Fric
known a
number o
in the sol
● The chem
transfer d
applicatio
condition
● The resp
absorptio
response
energy, t
absorbed
m at a reference depth. Absorbed dose to water at the reference 
 from the cavity theory using the mean specific energy imparted 
he cavity and the restricted stopping power ratio of the wall 
e cavity gas. The BIPM maintains an ionometric standard of 
 to water.
ical dosimetry standard for absorbed dose to water
cal dosimetry systems the dose is determined by measuring the 
ge produced in the medium (the sensitive volume of the 
ng a suitable measuring system.
st widely used chemical dosimetry standard is the Fricker.
ke solution has the following composition: 1mM FeSO4 or 
2(SO4)2 + 0.8N H2SO4 air saturated + 1mM NaCl.
n of a Fricke solution oxidizes ferrous ions Fe2+ into ferric ions 
 latter exhibit a strong absorption peak at l = 304 nm, whereas 
ns do not show any absorption at this wavelength. 
 induced ferric ion concentration can be determined using spectro-
ry, which measures the absorbance (in OD units) of the solution.
ke dosimeter response is expressed in terms of its sensitivity, 
s the radiation chemical yield, G value, and defined as the 
f moles of ferric ions produced per joule of the energy absorbed 
ution.
ical dosimetry standard is realized by the calibration of a 
osimeter in a total absorption experiment and the subsequent 
n of the transfer dosimeter in a water phantom, in reference 
s.
onse of the Fricke solution is determined first using the total 
n of an electron beam. An accurate determination of the energy 
 of the transfer instrument is necessary (i.e. knowing the electron 
he beam current and the absorbing mass accurately, the total 
 energy can be determined and related to the change in 
RADIATION DOSIMETERS
absorbance of the Fricke solution). Next, the absorbed dose to water at 
the reference point in a water phantom is obtained using the Fricke 
dosimeter as the transfer dosimeter. 
3.8.5. Calorimetric standard for absorbed dose to water 
Calorimetry is the most fundamental method of realizing the primary 
standard for 
consequence o
material for ca
energy reappe
the heat defe
determine the
conversion to a
may be perfor
by measureme
● Graphite
amount o
● Water ca
dose to w
dose to w
water, re
scaling la
there are
technical
and heat 
● Water c
thermisto
through e
3.9. SUMMA
SYSTEM
Radiatio
forms, and the
the dosimetric
● Ionizatio
● Radiogra
97
absorbed dose, since temperature rise is the most direct 
f energy absorption in a medium. Graphite is in general an ideal 
lorimetry, since it is of low atomic number Z and all the absorbed 
ars as heat, without any loss of heat in other mechanisms (such as 
ct). The graphite calorimeter is used by several PSDLs to 
 absorbed dose to graphite in a graphite phantom. The 
bsorbed dose to water at the reference point in a water phantom 
med by an application of the photon fluence scaling theorem or 
nts based on cavity ionization theory.
 calorimeters are electrically calibrated by depositing a known 
f electrical energy into the core.
lorimeters offer a more direct determination of the absorbed 
ater at the reference point in a water phantom. The absorbed 
ater is derived from the measured temperature rise at a point in 
lying on an accurate knowledge of the specific heat capacity. No 
ws are required, as in the case of graphite calorimetry; however, 
 corrections that need to be introduced to compensate for 
 complications related to a heat defect due to water radiolysis 
transport.
alorimeters are calibrated through the calibration of their 
rs in terms of the absolute temperature difference rather than 
nergy deposition, as is the case for graphite calorimeters. 
RY OF SOME COMMONLY USED DOSIMETRIC 
S
n dosimeters and dosimetry systems come in many shapes and 
y rely on numerous physical effects for storage and readout of 
 signal. The four most commonly used radiation dosimeters are:
n chambers;
phic films;
CHAPTER 3
98
● TLDs;
● Diodes.
The strengths and weaknesses of these four dosimeters are summarized in 
Table 3.1.
TABLE 3.1. 
FOUR COMM
Ionization 
chamber
Film
TLD
Diode
MAIN ADVANTAGES AND DISADVANTAGES OF THE 
ONLY USED DOSIMETRIC SYSTEMS
 Advantage Disadvantage
Accurate and precise
Recommended for beam 
calibration
Necessary corrections well 
 understood 
Instant readout
Connecting cables required
High voltage supply required
Many corrections required for 
high energy beam dosimetry
2-D spatial resolution
Very thin: does not perturb 
the beam
Darkroom and processing 
facilities required
Processing difficult to control
Variation between films and batches
Needs proper calibration against 
ionization chamber measurements
Energy dependence problems
Cannot be used for beam calibration
Small in size: point dose 
measurements possible
Many TLDs can be exposed 
in a single exposure
Available in various forms
Some are reasonably tissue 
equivalent
Not expensive
Signal erased during readout
Easy to lose reading
No instant readout
Accurate results require care
Readout and calibration time 
consuming
Not recommended for beam 
 calibration
Small size
High sensitivity
Instant readout
No external bias voltage
Simple instrumentation
Requires connecting cables
Variability of calibration with 
temperature
Change in sensitivity with 
 accumulated dose
Special care needed to ensure 
constancy of response
Cannot be used for beam calibration
RADIATION DOSIMETERS
BIBLIOGRAPHY
ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, 
New York (1986).
CAMERON, J.R., SUNTHARALINGAM, N., KENNEY, G.K., Thermoluminescent 
Dosimetry, Univ
HORTON, J., H
INTERNATION
in Photon and E
— Calibration o
IAEA, Vienna (
— The Use of P
Beams, Technica
— Absorbed Do
Series No. 398, I
INTERNATION
Expression of U
KHAN, F.M., T
Baltimore, MD 
KLEVENHAG
Physics Publishi
VAN DYK, J. (
Medical Physicis
(1999).
99
ersity of Wisconsin Press, Madison, WI (1968).
andbook of Radiation Therapy Physics, Prentice Hall, New York (1987).
AL ATOMIC ENERGY AGENCY, Absorbed Dose Determination 
lectron Beams, Technical Reports Series No. 277, IAEA, Vienna (1987).
f Dosimeters Used in Radiotherapy, Technical Reports Series No. 374, 
1994).
lane Parallel Ionization Chambers in High Energy Electron and Photon 
l Reports Series No. 381, IAEA, Vienna (1997).
se Determination in External Beam Radiotherapy, Technical Reports 
AEA, Vienna (2000).
AL ORGANIZATION FOR STANDARDIZATION, Guide to 
ncertainty in Measurement, ISO, Geneva (1992).
he Physics of Radiation Therapy, Lippincott, Williams and Wilkins, 
(2003).
EN, S.C., Physics and Dosimetry of Therapy Electron Beams, Medical 
ng, Madison, WI (1993).
Ed.), Modern Technology of Radiation Oncology: A Compendium for 
ts and Radiation Oncologists, Medical Physics Publishing, Madison, WI 
BLANK
Chapter 4
RADIATION MONITORING INSTRUMENTS
G. RAJAN
Medical Physics and Safety Section,
Bhabha A
Mumbai,
J. IZEWS
Division 
Internati
Vienna 
4.1. INTROD
Radiatio
external expo
exposure, are 
the monitoring
● External
— Radia
— Radia
— Equiv
● Radiatio
— To ass
— To en
the wo
— To ke
purpo
● Radiatio
for indivi
levels are
instrume
individua
(or indivi
the appro
101
tomic Research Centre,
 Maharashtra, India
KA
of Human Health,
onal Atomic Energy Agency,
UCTION
n exposure to humans can be broadly classified as internal and 
sure. Sealed sources, which are unlikely to cause internal 
used almost exclusively in radiotherapy. This chapter deals with 
 of external exposures.
 exposure monitoring refers to measuring:
tion levels in and around work areas;
tion levels around radiotherapy equipment or source containers;
alent doses received by individuals working with radiation.
n monitoring is carried out:
ess workplace conditions and individual exposures; 
sure acceptably safe and satisfactory radiological conditions in 
rkplace;
ep records of monitoring, over a long period of time, for the 
ses of regulation or good practice.
n monitoring instruments are used both for area monitoring and 
dual monitoring. The instruments used for measuring radiation 
 referred to as area survey meters (or area monitors) and the 
nts used for recording the equivalent doses received byls working with radiation are referred to as personal dosimeters 
dual dosimeters). All instruments must be calibrated in terms of 
priate quantities used in radiation protection.
CHAPTER 4 
102
4.2. OPERATIONAL QUANTITIES FOR RADIATION MONITORING
Recommendations regarding dosimetric quantities and units in radiation 
protection dosimetry are set forth by the International Commission on 
Radiation Units and Measurements (ICRU). The recommendations on the 
practical application of these quantities in radiation protection are established 
by the International Commission on Radiological Protection (ICRP).
The oper
for area and in
terized as eith
equivalent is 
penetrating’ r
radiation.
For the p
and directiona
radiation field
(see Chapter 1
● For stron
ambient 
equivalen
● For wea
equivalen
relevant,
relevant.
For indiv
which is the do
depth d (see al
● For stron
personal 
● For weak
at d = 0.0
used.
● Hp(d) can
body and
ational quantities are defined for practical measurements both 
dividual monitoring. In radiation protection radiation is charac-
er weakly or strongly penetrating, depending on which dose 
closer to its limiting value. In practice, the term ‘weakly 
adiation usually applies to photons below 15 keV and to b
urpose of area monitoring, the ambient dose equivalent H*(d) 
l dose equivalent H¢(d,W) are defined. They link the external 
 to the effective dose equivalent in the ICRU sphere phantom 
6), at depth d, on a radius in a specified direction W.
gly penetrating radiation the depth d = 10 mm is used; the 
dose equivalent is denoted as H*(10) and the directional dose 
t as H¢(10,W). 
kly penetrating radiation the ambient and directional dose 
ts in the skin at d = 0.07 mm, H*(0.07) and H¢(0.07,W), are 
 and in the lens of the eye at d = 3 mm, H*(3) and H¢(3,W), are 
 
idual monitoring the personal dose equivalent Hp(d) is defined, 
se equivalent in soft tissue below a specified point on the body at 
so Chapter 16).
gly penetrating radiation the depth d = 10 mm is used and the 
dose equivalent is denoted as Hp(10). 
ly penetrating radiation the personal dose equivalent in the skin 
7 mm, Hp(0.07), and in the lens of the eye at d = 3 mm, Hp(3), are 
 be measured with a dosimeter that is worn at the surface of the 
 covered with an appropriate layer of tissue equivalent material.
RADIATION MONITORING INSTRUMENTS
4.3. AREA SURVEY METERS
Radiation instruments used as survey monitors are either gas filled 
detectors or solid state detectors (e.g. scintillator or semiconductor detectors). 
A gas filled detector is usually cylindrical in shape, with an outer wall and a 
central electrode well insulated from each other. The wall is usually made of 
tissue equivalent material for ionization chamber detectors and of brass or 
copper for oth
Dependi
applied betwe
regions, shown
Geiger–Müller
proportionality
respectively, in
101
101
10
10
10
10
10
N
um
b
er
 o
f i
on
 p
ai
rs
 c
ol
le
ct
ed
FIG. 4.1. Vario
recombination re
region D the reg
for 1 MeV b par
103
er types of detector.
ng upon the design of the gas filled detector and the voltage 
en the two electrodes, the detector can operate in one of three 
 in Fig. 4.1 (i.e. the ionization region B, proportional region C or 
 (GM) region E). Regions of recombination and of limited 
 in the ‘signal versus applied voltage’ plot (regions A and D, 
 Fig. 4.1) are not used for survey meters.
A D ECB F
Region of 
limited 
proportionality
GM 
counter region
Region of 
continuous 
discharge
2 
0 
8 
6 
4 
2 
0
(a)
(b)
Proportional
region
Recombination 
region
Ionization 
chamber region
Applied voltage
us regions of operation of a gas filled detector. Region A represents the 
gion, region B the ionization region, region C the proportionality region, 
ion of limited proportionality and region E the GM region. Curve (a) is 
ticles, curve (b) for 100 keV b particles.
CHAPTER 4 
104
● Survey m
specific a
● The gas i
formatio
time in t
The incr
mobility 
that of el
● b–g surv
radiation
determin
b particle
● Owing to
smaller in
Ionization chambers
FIG. 4.2. Area
ments: ionization
eters come in different shapes and sizes, depending upon the 
pplication (see Fig. 4.2).
s usually a non-electronegative gas in order to avoid negative ion 
n by electron attachment, which would increase the collection 
he detector, thus limiting the dose rate that can be monitored. 
ease in charge collection time results from the relatively slow 
of ions, which is about three orders of magnitude smaller than 
ectrons. Noble gases are generally used in these detectors.
ey meters have a thin end window to register weakly penetrating 
. The g efficiency of these detectors is only a few per cent (as 
ed by the wall absorption), while the b response is near 100% for 
s entering the detector.
 their high sensitivity, the tubes of GM based g monitors are 
 size than ionization chamber type detectors. 
GM counters
Proportional
counter
 survey meters commonly used for radiation protection level measure-
 chambers, a proportional counter and GM counters.
RADIATION MONITORING INSTRUMENTS
● Depending upon the electronics used, detectors can operate in a ‘pulse’ 
mode or in the ‘mean level’ or current mode. Proportional and GM 
counters are normally operated in the pulse mode.
● Owing to the finite resolving time (the time required by the detector to 
regain its normal state after registering a pulse), these detectors will 
saturate at high intensity radiation fields. Ionization chambers operating 
in the current mode are more suitable for higher dose rate measurements.
4.3.1. Ioniza
In the io
collected is pro
in the detector
the particle dis
required to im
radiation, but 
(10–100 keV) a
4.3.2. Propo
In the pr
signal due to i
multiplication)
ions gain suffic
cause further i
Proportio
are suitable fo
charge collecte
deposited in th
4.3.3. Neutr
Neutron 
photon backgr
● Thermal 
on the in
● A therma
and the a
● To detec
made of h
105
tion chambers 
nization region the number of primary ions of either sign 
portional to the energy deposited by the charged particle tracks 
 volume. Owing to the linear energy transfer (LET) differences, 
crimination function can be used (see Fig. 4.1). Buildup caps are 
prove detection efficiency when measuring high energy photon 
they should be removed when measuring lower energy photons 
nd b particles.
rtional counters
oportional region there is an amplification of the primary ion 
onization by collision between ions and gas molecules (charge 
. This occurs when, between successive collisions, the primary 
ient energy in the neighbourhood of the thin central electrode to 
onization in the detector. The amplification is about 103–104-fold.
nal counters are more sensitive than ionization chambers and 
r measurements in low intensity radiation fields. The amount of 
d from each interaction is proportional to the amount of energy 
e gas of the counter by the interaction.
on area survey meters
area survey meters operate in the proportional region so that the 
ound can be easily discriminated against.
neutron detectors usually have a coating of a boron compound 
side of the wall, or the counter is filled with BF3 gas.
l neutron interacts with a 10B nucleus causing an (n,a) reaction, 
 particles can easily be detected by their ionizing interactions.
t fast neutrons the same counter is surrounded by a moderator 
ydrogenous material (Fig. 4.3); the whole assembly is then a fast 
CHAPTER 4 
106
neutron 
thermaliz
inside the
● Filter com
that the 
Chapter 
equivalen
spectra.
● Other ne
same prin
4.3.4. GeigeThe disch
detector and t
or the energy 
FIG. 4.3. Neutr
with a diameter o
counter. The fast neutrons interacting with the moderator are 
ed and are subsequently detected by a BF3 counter placed 
 moderator.
pensation is applied to reduce thermal range over-response so 
response follows the ICRP radiation weighting factors wR (see 
16). The output is approximately proportional to the dose 
t in soft tissue over a wide range (10 decades) of neutron energy 
utron detectors (e.g. those based on 3He) also function on the 
ciples.
r–Müller counters
arge spreads in the GM region throughout the volume of the 
he pulse height becomes independent of the primary ionization 
of the interacting particles. In a GM counter detector the gas 
on dose equivalent rate meter with a thermalizing polyethylene sphere 
f 20 cm.
RADIATION MONITORING INSTRUMENTS
multiplication spreads along the entire length of the anode. Gas filled detectors 
cannot be operated at voltages beyond the GM region because they continu-
ously discharge.
Owing to the large charge amplification (nine to ten orders of 
magnitude), GM survey meters are widely used at very low radiation levels 
(e.g. in areas of public occupancy around radiotherapy treatment rooms). They 
are particularly applicable for leak testing and detection of radioactive 
contamination
GM coun
and are not su
indicators of ra
measurements
GM dete
hundreds of m
accurate measu
counts per sec
very high radia
therefore be u
4.3.5. Scintil
Detector
lation detector
and inorganic
absorption of r
phosphors are 
lators are most
● Scintillat
anthrace
inorganic
● A photom
convert t
photodio
4.3.6. Semic
Bulk con
very high bulk
chambers on e
the class of sol
107
.
ters exhibit strong energy dependence at low photon energies 
itable for use in pulsed radiation fields. They are considered 
diation, whereas ionization chambers are used for more precise 
.
ctors suffer from very long dead times, ranging from tens to 
illiseconds. For this reason, GM counters are not used when 
rements are required of count rates of more than a few hundred 
ond. A portable GM survey meter may become paralysed in a 
tion field and yield a zero reading. Ionization chambers should 
sed in areas where radiation rates are high.
lator detectors
s based on scintillation (light emission) are known as scintil-
s and belong to the class of solid state detectors. Certain organic 
 crystals contain activator atoms, emit scintillations upon 
adiation and are referred to as phosphors. High atomic number 
mostly used for the measurement of g rays, while plastic scintil-
ly used with b particles.
ing phosphors include solid organic materials such as 
ne, stilbene and plastic scintillators as well as thallium activated 
 phosphors such as NaI(Tl) or CsI(Tl).
ultiplier tube (PMT) is optically coupled to the scintillator to 
he light pulse into an electric pulse. Some survey meters use 
des in place of PMTs.
onductor detectors
ductivity detectors are formed from intrinsic semiconductors of 
 resistivity (e.g. CdS or CdSe). They act like solid state ionization 
xposure to radiation and, like scintillation detectors, belong to 
id state detectors.
CHAPTER 4 
108
Extrinsic (i.e. doped with trace quantities of impurities such as 
phosphorus or lithium) semiconductors such as silicon or germanium are used 
to form junction detectors. They too act as solid state ionization chambers on 
application of a reverse bias to the detectors and on exposure to radiation. 
The sensitivity of solid state detectors is about 104 times higher than that 
of gas filled detectors, owing to the lower average energy required to produce 
an ion pair in s
magnitude low
compared wit
properties fac
instruments. 
4.3.7. Comm
The com
● A ‘low ba
● Automat
facilities;
● A variab
● The optio
● An anal
kerma) o
● An audio
● A resetta
● A visual 
● Remote o
4.3.8. Calibr
Protectio
instrument tha
laboratory.
A referen
(Fig. 4.4) with
directly the do
monitoring ins
as the air kerm
determined by
H = hNR
olid detector materials compared with air (typically one order of 
er) and the higher density of the solid detector materials 
h air (typically three orders of magnitude higher). These 
ilitate the miniaturization of solid state radiation monitoring 
only available features of area survey meters
monly available features of area survey meters are:
ttery’ visual indication; 
ic zeroing, automatic ranging and automatic back-illumination 
le response time and memory to store the data;
n of both ‘rate’ and ‘integrate’ modes of operation;
og or digital display, marked in conventional (exposure/air 
r ‘ambient dose equivalent’ or ‘personal dose equivalent’ units;
 indication of radiation levels (through the ‘chirp’ rate);
ble/non-resettable alarm facility with adjustable alarm levels;
indication of radiation with flashing LEDs;
peration and display of readings.
ation of survey meters
n level area survey meters must be calibrated against a reference 
t is traceable (directly or indirectly) to a national standards 
ce instrument for g radiation is generally an ionization chamber 
 a measuring assembly. Reference instruments do not indicate 
se equivalent H required for calibration of radiation protection 
truments. Rather, they measure basic radiation quantities such 
a in air for photon radiation, and the dose equivalent H is then 
 using appropriate conversion coefficients h:
MR (4.1)
RADIATION MONITORING INSTRUMENTS
where 
NR is the cal
in air) of
MR is the re
quantitie
A referen
radiation qual
zation (ISO)). 
of radiation pr
1-L ionization chamber
FIG. 4.4. Refere
a 137Cs g beam.
109
ibration factor (e.g. in terms of air kerma in air or air kerma rate 
 the reference chamber under reference conditions;
ading of the reference instrument corrected for influence 
s.
ce instrument is calibrated free in air for the range of reference 
ities (defined by the International Organization for Standardi-
The same reference qualities should be used for the calibration 
otection monitoring instruments.
Cs-137 irradiator
nce ionization chamber used for the calibration of area survey meters in 
CHAPTER 4 
110
Typically, calibration of survey meters in terms of the ambient dose 
equivalent H*(10) involves three steps:
● The air kerma in air is measured in a reference field, using a reference 
standard.
● The values of the conversion coefficient:
hH* = [H*
are theo
quality, a
● The surv
point and
the ambi
from the 
4.3.9. Prope
4.3.9.1. Sensit
The sens
Using decade 
higher pressur
ionization cham
Owing to
a few thousan
correction cir
radiation fields
Scintillat
of higher g con
systems are ge
ination monito
be used at high
microseconds o
4.3.9.2. Energ
Survey m
used in situati
survey meters 
range.
(10)/(Kair)air] 
retically available. Using these data for the calibration beam 
 reference instrument reading can be converted to H*(10). 
ey monitor being calibrated is then placed at the calibration 
 its reading M is determined. The calibration factor in terms of 
ent dose equivalent NH* for the survey monitor is determined 
equation NH* = H*(10)/M.
rties of survey meters
ivity
itivity S is defined as the inverse of the calibration coefficient N. 
resistances, larger detector volumes or detector gases under 
es, a wide range of equivalent dose rates can be covered with 
ber based survey meters (e.g. 1 mSv/h–1 Sv/h).
 finite resolving time, GM based systems would saturate beyond 
d counts per second. Low dead time counters or dead time 
cuits enable these detectors to operate at higher intensity 
. 
ion based systems are more sensitive than GM counters because 
version efficiencyand dynode amplification. Scintillation based 
nerally used for surveys at very low radiation levels (e.g. contam-
ring and lost source detection surveys). However, they can also 
er radiation levels, since their resolving time is quite low (a few 
r lower) compared with GM counters.
y dependence
eters are calibrated at one or more beam qualities, but are often 
ons in which the radiation field is complex or unknown. These 
should hence have a low energy dependence over a wide energy 
RADIATION MONITORING INSTRUMENTS
In the past, survey meters were designed to exhibit a flat energy response 
that follows exposure or air kerma in air.
For measuring the equivalent dose:
NH* = [H*(10)/M] = [H*(10)/(Kair)air]/[(Kair)air/M]
a meter’s response with energy should vary as the quantity:
[H*(10)/(
GM counters 
(<80 keV). 
4.3.9.3. Direct
By rotat
response of th
isotropic respo
±60º to ±80º wi
has a much bet
4.3.9.4. Dose 
Survey m
range in use is 
4.3.9.5. Respo
The resp
constant of the
capacitance of
Low dos
values, and so 
to five time co
4.3.9.6. Overlo
Survey m
maximum scal
on saturation. 
111
Kair)air]
exhibit strong energy dependence for low energy photons 
ional dependence
ing the survey monitor about its vertical axis, the directional 
e instrument can be studied. A survey monitor usually exhibits 
nse, as required for measuring ambient dose equivalent, within 
th respect to the reference direction of calibration, and typically 
ter response for higher photon energies (>80 keV). 
equivalent range 
eters may cover a range from nSv/h to Sv/h, but the typical 
mSv/h to mSv/h.
nse time 
onse time of the survey monitor is defined as the RC time 
 measuring circuit, where R is the decade resistor used and C the 
 the circuit.
e equivalent ranges would have high R and hence high RC
the indicator movement would be sluggish. It takes at least three 
nstants for the monitor reading to stabilize.
ad characteristics 
eters must be subjected to dose rates of about ten times the 
e range to ensure that they read full scale rather than near zero 
CHAPTER 4 
112
Some survey meters, especially the older models, may read zero on 
overload (i.e. when the equivalent dose rate exceeds the scale range). Such 
survey meters should not be used for monitoring, since the worker may 
wrongly assume that there is no radiation in an area where the radiation field is 
actually very high.
GM survey meters are not suitable for use in pulsed fields, due to the 
possible overload effect, and ionization chamber based survey meters should 
be used instead
4.3.9.7. Long 
Survey m
with the frequ
typically once 
repair or imme
The long
intervals using
4.3.9.8. Discri
End wind
b from g rays. 
particles to ent
4.3.9.9. Uncer
The stan
calibration, the
measurements
tainties due to 
the variation in
contribute to t
quadrature to
meter measure
The com
k = 3 to corres
uncertainty of
under standard
.
term stability 
eters must be calibrated in a standards dosimetry laboratory 
ency prescribed by the regulatory requirements of the country, 
every three years; they also need calibration immediately after 
diately upon detection of any sudden change in response.
 term stability of survey meters must be checked at regular 
 a long half-life source in a reproducible geometry.
mination between different types of radiation
ow GM counters have a removable buildup cap to discriminate 
For b measurements the end cap must be removed to allow b
er the sensitive volume.
tainties in area survey measurements 
dards laboratory provides, along with the survey monitor 
 uncertainty associated with the calibration factor. Subsequent 
 at the user department provide a type A uncertainty. The uncer-
energy dependence and angular dependence of the detector, and 
 the user field conditions compared with calibration conditions, 
ype B uncertainties. These two types of uncertainty are added in 
 obtain the combined uncertainty associated with the survey 
ments.
bined uncertainty is multiplied by the coverage factor k = 2 or 
pond to the confidence limits of 95% or 99%, respectively. The 
 measurements with area monitors is typically within ±30% 
 laboratory conditions.
RADIATION MONITORING INSTRUMENTS
4.4. INDIVIDUAL MONITORING
Individual monitoring is the measurement of the radiation doses received 
by individuals working with radiation. Individuals who regularly work in 
controlled areas or those who work full time in supervised areas (see Chapter 
16 for the definitions) should wear personal dosimeters to have their doses 
monitored on a regular basis. Individual monitoring is also used to verify the 
effectiveness o
detecting cha
information in
● The mos
thermolu
as radiop
(OSL), a
emulsion
● Self-read
(EPDs) a
dose rate
As expla
monitoring of 
recommended
0.07 mm for w
in these quanti
4.4.1. Film b
A specia
a case or holde
(Fig. 4.5). The 
the type and e
photons of en
necessary for l
Since the
flatten the en
approximate th
113
f radiation control practices in the workplace. It is useful for 
nges in radiation levels in the workplace and to provide 
 the event of accidental exposures. 
t widely used individual monitoring systems are based on 
minescence or film dosimetry, although other techniques, such 
hotoluminescence (RPL) and optically stimulated luminescence 
re in use in some countries. Albedo dosimeters and nuclear track 
s are used for monitoring fast neutron doses.
ing pocket dosimeters and electronic personal dosimeters 
re direct reading dosimeters and show both the instantaneous 
 and the accumulated dose at any point in time.
ined in Section 4.2, the operational quantity for the individual 
external exposure is the personal dose equivalent Hp(d) with the 
 depth d = 10 mm for strongly penetrating radiation and d = 
eakly penetrating radiation. Personal dosimeters are calibrated 
ties. 
adge
l emulsion photographic film in a light-tight wrapper enclosed in 
r with windows, with appropriate filters, is known as a film badge 
badge holder creates a distinctive pattern on the film indicating 
nergy of the radiation received. While one filter is adequate for 
ergy above 100 keV, the use of a multiple filter system is 
ower energy photons.
 film is non-tissue equivalent, a filter system must be used to 
ergy response, especially at lower photon beam qualities, to 
e response of a tissue equivalent material.
CHAPTER 4 
114
● Cumulat
evaluated
filters an
been exp
● Film can
window a
the film b
● Nuclear 
neutrons
material,
create a 
tracks aft
● Films are
and exce
time, lim
condition
Filters
Film
Thermoluminescenc
dosimetry chips
A
C
FIG. 4.5. Person
C) and film badg
ive doses from b, X, g and thermal neutron radiation are 
 by measuring the film optical densities (ODs) under different 
d then comparing the results with calibration films that have 
osed to known doses of well defined radiation of different types.
 also serve as a monitor for thermal neutrons. The cadmium 
bsorbs thermal neutrons and the resulting g radiation blackens 
elow this window as an indication of the neutron dose.
track emulsions are used for monitoring of fast neutrons. The 
 interact with hydrogen nuclei in the emulsion and surrounding 
 producing recoil protons by elastic collisions. These particles 
latent image, which leads to darkening of the film along their 
er processing.
 adversely affected by many external agents, such as heat, liquids 
ssive humidity. The latent image on undeveloped film fades with 
iting possible wearing periods to three months in ideal 
s.
Filterse
E
al dosimeters: examples of thermoluminescence dosimetry badges (A, B, 
es (D, E).
RADIATION MONITORINGINSTRUMENTS
4.4.2. Therm
A thermo
thermolumine
filters. The m
(also referred
Different badg
are in use in di
The dose
evaluated by m
the results with
has been expo
● Badges t
materials
match th
phosphor
Thermolumin
FIG. 4.6. Calibr
137Cs g beam.
115
oluminescence dosimetry badge
luminescence dosimetry badge (see Fig. 4.5) consists of a set of 
scent dosimeter (TLD) chips enclosed in a plastic holder with 
ost frequently used thermoluminescence dosimetry materials 
 to as phosphors) are LiF:Ti,Mg, CaSO4:Dy and CaF2:Mn. 
e designs (thermoluminescence dosimetry materials and filters) 
fferent countries.
s of b, X and g radiation registered by the dosimeter are 
easuring the output under different filters and then comparing 
 calibration curves established for the calibration badge, which 
sed to known doses under well defined conditions.
hat use high atomic number Z thermoluminescence dosimetry 
 are not tissue equivalent and, like film, also require filters to 
eir energy response to that of tissue. Badges using low Z
s do not require such complex filter systems.
Cs-137 irradiator
escence dosimetry badges
ation of personal dosimeters on a PMMA slab phantom using a standard 
CHAPTER 4 
116
● The thermoluminescence signal exhibits fading, but the problem is less 
significant than for films.
● The badges currently used for b monitoring have a relatively high 
threshold for b particles (about 50 keV) because of the thickness of the 
detector and its cover.
● TLDs are convenient for monitoring doses to parts of the body (e.g. eyes, 
arm or wrist, or fingers) using special types of dosimeter, including 
extremity
● Various t
the body
dosimete
sensitivit
4.4.3. Radio
Radioph
state dosimete
dose. The mat
come in the sh
● When sil
luminesc
readout 
registers 
● The RPL
be reanal
lation of 
lifetime d
● Commer
cover the
within 12
● The RPL
environm
monitori
4.4.4. Optica
OSL is 
Optically stimu
oxide (Al2O3:
 dosimeters.
echniques have been used for neutron monitoring, such as using 
 as a moderator to thermalize neutrons (similarly to albedo 
rs) or using LiF enriched with 6Li for enhanced thermal neutron 
y due to the (n, a) reaction of thermal neutrons in 6Li.
photoluminescent glass dosimetry systems 
otoluminescent glass dosimeters are accumulation type solid 
rs that use the phenomenon of RPL to measure the radiation 
erial used is silver activated phosphate glass. The dosimeters 
ape of small glass rods.
ver activated phosphate glass is exposed to radiation, stable 
ence centres are created in silver ions Ag+ and Ag++. The 
technique uses pulsed ultraviolet laser excitation. A PMT 
the orange fluorescence emitted by the glass.
 signal is not erased during the readout, thus the dosimeter can 
ysed several times and the measured data reproduced. Accumu-
the dose is also possible, and may be used for registration of the 
ose.
cially available radiophotoluminescent dosimeters typically 
 dose range of 30 mSv to 10 Sv. They have a flat energy response 
 keV to 8 MeV for Hp(10).
 signal exhibits very low fading and is not sensitive to the 
ental temperature, making it convenient for individual 
ng.
lly stimulated luminescence systems
now commercially available for measuring personal doses. 
lated luminescent dosimeters contain a thin layer of aluminium 
C). During analysis the aluminium oxide is stimulated with 
RADIATION MONITORING INSTRUMENTS
selected frequencies of laser light producing luminescence proportional to the 
radiation exposure.
● Commercially available badges are integrated, self-contained packets 
that come preloaded, incorporating an aluminium oxyde (Al2O3) strip 
sandwiched within a filter pack that is heat sealed. Special filter patterns 
provide qualitative information about conditions during exposure.
● Optically
example,
±10 mSv. 
monitori
a wide do
● The dosim
and may 
4.4.5. Direct
In addit
dosimeters are
● To provid
● For track
● In specia
radiation
Direct re
reading pocket
Self-read
ionization cham
reads zero be
ionization prod
air kerma) is p
light through a
declined in re
problems and 
EPDs ba
with a measure
— Modern E
of Hp(10)
instantan
117
 stimulated luminescent dosimeters are highly sensitive; for 
 the Luxel system can be used down to 10 mSv with a precision of 
This high sensitivity is particularly suitable for individual 
ng in low radiation environments. The dosimeters can be used in 
se range of up to 10 Sv in photon beams from 5 keV to 40 MeV.
eters can be reanalysed several times without losing sensitivity 
be used for up to one year. 
 reading personal monitors
ion to passive dosimetry badges, direct reading personal 
 widely used:
e a direct readout of the dose at any time; 
ing the doses received in day to day activities; 
l operations (e.g. source loading surveys and handling of 
 incidents or emergencies). 
ading personal dosimeters fall into two categories: (1) self-
 dosimeters and (2) electronic personal dosimeters (EPDs).
ing pocket dosimeters resemble a pen and consist of an 
ber that acts as a capacitor. The capacitor is fully charged and 
fore use. On exposure to radiation for a period of time, the 
uced in the chamber discharges the capacitor; the exposure (or 
roportional to the discharge, which can be directly read against 
 built-in eyepiece. However, the use of pocket dosimeters has 
cent years because of their poor useful range, charge leakage 
poor sensitivity compared with EPDs.
sed on miniature GM counters or silicon detectors are available 
ment range of down to 30 keV photon energy.
PDs are calibrated in the personal equivalent dose (i.e. in terms 
 or Hp(0.07) for both photons and b radiation). EPDs provide an 
eous display of accumulated equivalent dose at any time.
CHAPTER 4 
118
— EPDs have automatic ranging facilities and give a visual and an audio 
indication (flashing or a chirping frequency proportional to the dose 
equivalent rate), so that changes in the radiation field can be recognized 
immediately.
— EPDs are very useful in emergency situations for immediate readout of 
the equivalent doses received.
4.4.6. Calibr
Personal
quantities for i
equivalent Hp
penetrating ra
Section 4.2)).
For cali
phantoms that
human body. T
calibration of 
dosimeters: a 
wrist or ankle
standard phan
special water 
practice PMM
Calibrati
● Air kerm
ionizatio
● [Hp(d)/(K
data for t
be conve
● The dosi
point on 
the calib
dosimete
4.4.7. Prope
4.4.7.1. Sensit
Film and
doses as low a
ation of personal dosimeters
 dosimeters should be calibrated in terms of operational 
ndividual monitoring of external exposure (i.e. the personal dose 
(d) with the recommended depth d = 10 mm for strongly 
diation and d = 0.07 mm for weakly penetrating radiation (see 
bration, dosimeters should be irradiated on standardized 
 provide an approximation of the backscatter conditions of the 
hree types of phantom are recommended that cover the needs of 
whole body dosimeters, wrist or ankle dosimeters and finger 
slab phantom to represent a human torso, a pillar phantom for 
 dosimeters and a rod phantom for finger dosimeters. The 
toms are composed of ICRU tissue. The ISO recommends 
phantoms (referred to as ISO slab phantoms), although in 
A phantoms are used with the appropriate corrections.
on of personal dosimeters in terms of Hp(d) involves three steps:
a in air (Kair)air is measured in a reference field, using a reference 
n chamber calibrated by a standards laboratory.
air)air]slab = hkHp values are theoretically available. Using these 
he calibration beam quality, a reference instrument reading can 
rted to [Hp(d)]slab.
meter badge being calibrated is then placed at the calibrationa phantom and its reading M is determined. NHp = Hp(d)/M gives 
ration factor in terms of the personal dose equivalent for the 
r badge. 
rties of personal monitors
ivity
 thermoluminescence dosimetry badges can measure equivalent 
s 0.1 mSv and up to 10 Sv; optically stimulated luminescent and 
RADIATION MONITORING INSTRUMENTS
radiophotoluminescent dosimeters are more sensitive, with a lower detection 
limit of 10–30 mSv. Personal dosimeters are generally linear in the dose range of 
interest in radiation protection.
4.4.7.2. Energy dependence 
Film exhibits a strong energy dependence and film badges are empirically 
designed to red
tissue equivale
CaSO4:Dy sho
reduced by em
Commer
PTW and Tosh
commercially 
Landauer) hav
For direc
±20% over th
compensated d
range from 30 
The ener
the degree of
construction d
4.4.7.3. Uncer
The ICR
uncertainty of
ments of radia
where the ene
not well know
dosimeter will
and still greate
The unce
rates (2 mSv/h
laboratory con
4.4.7.4. Equiv
Personal
can cover both
10 mSv to abou
119
uce their energy response to within ±20%. A LiF TLD is nearly 
nt and exhibits acceptable energy dependence characteristics. 
ws significant energy dependence and its energy response is 
pirical adjustments in the badge design.
cially available radiophotoluminescent dosimeters (e.g. Asahi, 
iba) have a flat energy response from 12 keV to 8 MeV, while 
available optically stimulated luminescent dosimeters (e.g. 
e a flat energy response from 5 keV to 40 MeV. 
t reading pocket dosimeters the energy dependence is within 
e range from 40 keV to 2 MeV. For EPDs containing energy 
etectors the energy dependence is within ±20% over the energy 
keV to 1.3 MeV.
gy response values quoted above can vary in energy range and in 
 flatness, depending on the individual monitor material and 
etails.
tainties in personal monitoring measurements 
P has stated that, in practice, it is usually possible to achieve an 
 about 10% at the 95% confidence level (k = 2) for measure-
tion fields in laboratory conditions. However, in the workplace, 
rgy spectrum and orientation of the radiation field are generally 
n, the uncertainties in a measurement made with an individual 
 be significantly greater, and may be a factor of one for photons 
r for neutrons and electrons.
rtainty in measurements with EPDs is about 10% for low dose 
) and increases to 20% for higher dose rates (<100 mSv/h) in 
ditions.
alent dose range 
 monitors must have as wide a dose range as possible so that they 
 radiation protection and accidental situations (typically from 
t 10 Sv). The dose range normally covered by film and TLDs is 
CHAPTER 4 
120
from about 100 mSv to 10 Sv and that by optically stimulated luminescent and 
radiophotoluminescent dosimeters is 10 mSv to 10 Sv.
Self-reading pocket dosimeters can measure down to about 50 mSv; the 
upper dose limit of the available pocket dosimeters is around 200 mSv. EPDs 
measure in the range from 0.1 mSv to 10 Sv. 
4.4.7.5. Directional dependence 
Accordin
(i.e. its angula
directional do
directional de
derived.
4.4.7.6. Discri
Film dos
particles and th
radiophotolum
rays and g and
ATTIX, F.H., In
New York (1986
CLARK, M.J., 
Guidance on the
FOOD AND A
INTERNATION
ORGANISATIO
HEALTH ORG
Basic Safety Sta
Radiation Sourc
INTERNATION
Protection Moni
g to the ICRU, an individual dosimeter must be iso-directional, 
r response relative to normal incidence must vary as the ICRU 
se equivalent quantity H¢(10, W)) (see Section 4.2). The 
pendence must be evaluated and the appropriate corrections 
mination between different types of radiation 
imeters can identify and estimate doses of X rays, g rays, b
ermal neutrons. TLDs and optically stimulated luminescent and 
inescent dosimeters generally identify and estimate doses of X 
 b radiation.
BIBLIOGRAPHY
troduction to Radiological Physics and Radiation Dosimetry, Wiley, 
).
et al., Dose quantities for protection against external radiations: 
 1990 recommendations of ICRP, Doc. NRPB 4 3 (1993).
GRICULTURE ORGANIZATION OF THE UNITED NATIONS, 
AL ATOMIC ENERGY AGENCY, INTERNATIONAL LABOUR 
N, OECD NUCLEAR ENERGY AGENCY, PAN AMERICAN 
ANIZATION, WORLD HEALTH ORGANIZATION, International 
ndards for Protection against Ionizing Radiation and for the Safety of 
es, Safety Series No. 115, IAEA, Vienna (1996).
AL ATOMIC ENERGY AGENCY, Calibration of Radiation 
toring Instruments, Safety Reports Series No. 16, IAEA, Vienna (2000).
RADIATION MONITORING INSTRUMENTS
INTERNATIONAL COMMISSION ON RADIATION UNITS AND 
MEASUREMENTS, Determination of Dose Equivalents Resulting from External 
Radiation Sources, Rep. 43, ICRU, Bethesda, MD (1988).
— Measurement of Dose Equivalents from External Photon and Electron Radiations, 
Rep. 47, ICRU, Bethesda, MD (1992).
— Quantities and Units in Radiation Protection Dosimetry, Rep. 51, ICRU, Bethesda, 
MD (1993).
INTERNATION
Conversion Coe
Publication 74, P
INTERNATION
Reference Rad
Determining the
Series of Filtered
of Filtered X-rad
— Reference Be
Determining the
Geneva (1984).
— Dosimetry of
Protection Leve
9 MeV, ISO/DP
— Dosimetry of
Energy Range fr
KNOLL, G.F., R
NATIONAL RA
Recommended 
Implementation
121
AL COMMISSION ON RADIOLOGICAL PROTECTION, 
fficients for Use in Radiological Protection Against External Radiation, 
ergamon Press, Oxford and New York (1997).
AL ORGANIZATION FOR STANDARDIZATION, X and Gamma 
iations for Calibrating Dosemeters and Dose Ratemeters and for 
ir Response as a Function of Energy, ISO 4037. See also High Rate 
 X-radiations, ISO 4037-1979/Addendum 1(1983); and Low Rate Series 
iations, ISO 4037-1979/Amendment 1-1983 (E), ISO, Geneva (1979).
ta Radiations for Calibrating Dosimeters and Dose Rate Meters and for 
ir Response as a Function of Beta Radiation Energy, ISO 6980, ISO, 
 the Reference Radiation Fields Used for Determining the Response of 
l Dosimeters and Dose-rate Meters at Photon Energies Between 4 and 
 9991, ISO, Geneva (1988).
 X and Gamma Reference Radiations for Radiation Protection over the 
om 9 keV to 1.3 MeV, ISO/DIS 8963, ISO, Geneva (1988).
adiation Detection and Measurement, Wiley, New York (1979).
DIOLOGICAL PROTECTION BOARD, New Radiation Quantities 
by ICRU for Practical Use in Radiation Protection: Their 
 in the United Kingdom, NRPB, Didcot, UK (1986).
BLANK
Chapter 5
TREATMENT MACHINES FOR EXTERNAL BEAM 
RADIOTHERAPY
E.B. PODGORSAK
Departm
McGill U
Montrea
5.1. INTROD
Since the
Roentgen in 1
towards ever h
more recently
delivery. Durin
was relatively 
and betatrons.
The inven
early 1950s p
energies and 
number of yea
eclipsed coba
generations an
radiotherapy. W
versatility for 
either electron
In additi
with other typ
particles, such
produced by s
however, mos
teletherapy co
123
ent of Medical Physics,
niversity Health Centre,
l, Quebec, Canada
UCTION
 inception of radiotherapy soon after the discovery of X rays by 
895, the technology of X ray production has first been aimed 
igher photon and electron beam energies and intensities, and 
 towards computerization and intensity modulated beam 
g the first 50 years of radiotherapy the technological progress 
slow and mainly based on X ray tubes, van de Graaff generators 
 
tion of the 60Co teletherapy unit by H.E. Johns in Canada in the 
rovided a tremendous boost in the quest for higher photon 
placed the cobalt unit at the forefront of radiotherapy for a 
rs. The concurrently developed medical linacs, however, soon 
lt units, moved through five increasingly sophisticated 
d became the most widely used radiation source in modern 
ith its compact and efficient design, the linac offers excellent 
use in radiotherapy throughisocentric mounting and provides 
 or megavoltage X ray therapy with a wide range of energies. 
on to linacs, electron and X ray radiotherapy is also carried out 
es of accelerator, such as betatrons and microtrons. More exotic 
 as protons, neutrons, heavy ions and negative p mesons, all 
pecial accelerators, are also sometimes used for radiotherapy; 
t contemporary radiotherapy is carried out with linacs or 
balt units.
CHAPTER 5
124
5.2. X RAY BEAMS AND X RAY UNITS
Clinical X ray beams typically range in energy between 10 kVp and 
50 MV and are produced when electrons with kinetic energies between 10 keV 
and 50 MeV are decelerated in special metallic targets.
Most of the electron’s kinetic energy is transformed in the target into 
heat, and a small fraction of the energy is emitted in the form of X ray photons, 
which are divid
rays.
5.2.1. Chara
Characte
incident electr
loss).
In a give
orbital electro
from a highe
difference betw
form of a cha
orbital electron
● The fluor
photons e
for low Z
for K she
istic X ra
● The pho
energies 
transition
5.2.2. Brems
Bremsstr
incident electr
interaction bet
is decelerated 
photons (radia
ed into two groups: characteristic X rays and bremsstrahlung X 
cteristic X rays 
ristic X rays result from Coulomb interactions between the 
ons and atomic orbital electrons of the target material (collision 
n Coulomb interaction between the incident electron and an 
n, the orbital electron is ejected from its shell and an electron 
r level shell fills the resulting orbital vacancy. The energy 
een the two shells may either be emitted from the atom in the 
racteristic photon (characteristic X ray) or transferred to an 
 that is ejected from the atom as an Auger electron.
escent yield w gives the number of fluorescent (characteristic) 
mitted per vacancy in a shell (0 _< w _< 1) and ranges from zero 
 atoms through 0.5 for copper (Z = 29) to 0.96 for high Z atoms 
ll vacancies, which are the most prominent sources of character-
ys.
tons emitted through electronic shell transitions have discrete 
that are characteristic of the particular target atom in which the 
s have occurred; hence the term characteristic radiation.
strahlung (continuous) X rays 
ahlung X rays result from Coulomb interactions between the 
on and the nuclei of the target material. During the Coulomb 
ween the incident electron and the nucleus, the incident electron 
and loses part of its kinetic energy in the form of bremsstrahlung 
tive loss).
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● Photons with energies ranging from zero to the kinetic energy of the 
incident electron may be produced, resulting in a continuous brems-
strahlung spectrum;
● The bremsstrahlung spectrum produced in a given X ray target depends 
on the kinetic energy of the incident electron as well as on the thickness 
and atomic number Z of the target.
5.2.3. X ray 
Accordin
target material
A thin ta
a thick target i
is proportional
The intensity v
to the kinetic 
above EK.
A thick 
superimposed 
expressed as:
I(hn) = C
where
C is a propo
hn is the pho
X rays a
radiation onco
electrons with
superficial X r
500 keV are 
energies above
Superfici
(machines), w
linacs and som
Typical t
100 keV electr
Fig. 5.1.
125
targets 
g to the range R of electrons of a given kinetic energy EK in the 
, targets are divided into two main groups: thin and thick.
rget has a thickness much smaller than R, while the thickness of 
s of the order of R. For thin target radiation, the energy radiated 
 to the product EKZ, where Z is the atomic number of the target. 
ersus photon energy (photon spectrum) is constant from zero 
energy EK of the incident electron, and zero for all energies 
target may be considered as consisting of a large number of 
thin targets. The intensity I(hn) of a thick target spectrum is 
Z(EK – hn) (5.1)
rtionality constant;
ton energy.
re used in diagnostic radiology for diagnosis of disease and in 
logy (radiotherapy) for treatment of disease. X rays produced by 
 kinetic energies between 10 keV and 100 keV are called 
ays, those with electron kinetic energies between 100 keV and 
called orthovoltage X rays, while those with electron kinetic 
 1 MeV are called megavoltage X rays.
al and orthovoltage X rays are produced with X ray tubes 
hile megavoltage X rays are most commonly produced with 
etimes with betatrons and microtrons.
hin and thick target bremsstrahlung spectra originating from 
ons striking a thin and thick target, respectively, are shown in 
CHAPTER 5
126
5.2.4. Clinical X ray beams
A typical spectrum of a clinical X ray beam consists of line spectra that 
are characteristic of the target material and that are superimposed on to the 
continuous bremsstrahlung spectrum. The bremsstrahlung spectrum originates 
in the X ray target, while the characteristic line spectra originate in the target 
and in any attenuators placed into the beam.
● The rela
bremsstr
electron 
example,
contain 
photons, 
photons 
FIG. 5.1. Typica
ray tube in whi
producing a con
electrons striking
the X ray tube) f
spectrum of curv
are filtered out);
and additional fi
tive proportion of the number of characteristic photons to 
ahlung photons in an X ray beam spectrum varies with the 
beam kinetic energy and atomic number of the target. For 
 X ray beams produced in a tungsten target by 100 keV electrons 
about 20% characteristic photons and 80% bremsstrahlung 
while in the megavoltage range the contribution of characteristic 
to the total spectrum is negligible.
l thin target (curve 1) and thick target (curves 2, 3 and 4) spectra for an X 
ch 100 keV electrons strike the target. Curve (1) is for a thin target 
stant intensity for photon energies from zero to the kinetic energy of 
 the target (100 keV). Curve (2) represents an unfiltered spectrum (inside 
or a thick target and a superposition of numerous thin target spectra; the 
e (3) is for a beam filtered by an X ray tube window (low energy photons 
 the spectrum of curve (4) is for a beam filtered by the X ray tube window 
ltration.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● In the diagnostic energy range (10–150 kV) most photons are produced at 
90º from the direction of electron acceleration, while in the megavoltage 
energy range (1–50 MV) most photons are produced in the direction of 
electron acceleration (forward direction: 0º).
5.2.5. X ray beam quality specifiers 
Various p
nominal accel
equivalent me
and 9.8.2 for d
● A compl
the most 
● The HVL
in alumin
not prac
range the
energy.
● The effec
energy o
does the 
● The NAP
The NAP
phantom
source to
● Recent d
or perce
phantom
quality in
5.2.6. X ray 
Superfici
with X ray m
machine are: a
cooling system
diagram of a ty
● The elec
tube) ori
127
arameters, such as photon spectrum, half-value layer (HVL), 
erating potential (NAP) and beam penetration into tissue 
dia, are used as X ray beam quality indices (see Sections 9.8.1 
etails):
ete X ray spectrum is very difficult to measure; however, it gives 
rigorous description of beam quality.
 is practical for beam quality description in the superficial (HVL 
ium) and orthovoltage (HVL in copper) X ray energy range, but 
tical in the megavoltage energy range because in this energy 
 attenuation coefficient is only a slowly varying function of beam 
tive energy of a heterogeneous X ray beam is defined as that 
f a monoenergetic photon beam that yields the same HVL as 
heterogeneous beam.
 is sometimes used for describing the megavoltage beam quality. 
 is determined by measuring the ionization ratio in a water 
 at depths of 10 and 20 cm for a 10 × 10 cm2 field at the nominal 
 axis distance (SAD) of 100 cm.
osimetryprotocols recommend the use of tissue–phantom ratios 
ntage depth doses (PDDs) at a depth of 10 cm in a water 
 as an indicator of megavoltage beam effective energy (beam 
dex).
machines for radiotherapy
al and orthovoltage X rays used in radiotherapy are produced 
achines. The main components of a radiotherapeutic X ray 
n X ray tube; a ceiling or floor mount for the X ray tube; a target 
; a control console; and an X ray power generator. A schematic 
pical therapy X ray tube is shown in Fig. 5.2.
trons producing the X ray beams in the X ray tube (Coolidge 
ginate in the heated filament (cathode) and are accelerated in a 
CHAPTER 5
128
vacuum towards the target (anode) by an essentially constant potential 
electrostatic field supplied by the X ray generator. 
● The efficiency for X ray production in the superficial and orthovoltage 
energy range is of the order of 1% or less. Most of the electron kinetic 
energy deposited in the X ray target (~99%) is transformed into heat and 
must be dissipated through an efficient target cooling system.
● To maximize the X ray yield in the superficial and orthovoltage energy 
range the
melting p
● With X 
treatmen
6.16), wh
compone
● The X r
electrons
(thermio
current i
voltage i
voltages 
anode.
FIG. 5.2. Typica
with permission)
 target material should have a high atomic number Z and a high 
oint.
ray tubes, the patient dose is delivered using a timer and the 
t time must incorporate the shutter correction time (see Section 
ich accounts for the time required for the power supply 
nts to attain the steady state operating conditions.
ay tube current is controlled by a hot filament emission of 
, which, in turn, is controlled by the filament temperature 
nic emission). For a given filament temperature the X ray tube 
ncreases with the tube (anode) voltage, first rising linearly with 
n the space charge limited region and saturating at higher 
when all electrons emitted from the cathode are pulled to the 
l therapy X ray tube (reprinted from Johns, H.E., and Cunningham, J.R., 
.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● Research is currently being carried out on cold field emission cathodes 
produced with carbon nanotubes (CNTs). The CNT based cold cathode X 
ray technology may lead to more durable as well as miniature and 
portable X ray sources for industrial and medical applications.
5.3. GAMMA RAY BEAMS AND GAMMA RAY UNITS
5.3.1. Basic 
For use in
designed and 
radioactive ma
● The pare
daughter
(g decay
● The imp
therapy a
— High 
— High 
— Relat
— Large
● The spec
inversely
where
NA is Av
A is the
● The air k
a
m
= =A
( )�Kair air
129
properties of gamma rays
 external beam radiotherapy, g rays are obtained from specially 
built sources that contain a suitable, artificially produced 
terial. 
nt source material undergoes a b decay, resulting in excited 
 nuclei that attain ground state through emission of g rays 
).
ortant characteristics of radioisotopes in external beam radio-
re: 
g ray energy; 
specific activity; 
ively long half-life; 
 specific air kerma rate constant GAKR.
ific activity a (activity A per mass m of radioactive nuclide) is 
 proportional to the half-life t1/2:
(5.2)
ogadro’s number (6.022 × 1023 atoms/g-atom);
 atomic mass number.
erma rate in air is given by the following relation:
(5.3)
N
t A
A ln
/
2
1 2
( )�Kair air
d
AKR= AG 2
CHAPTER 5
130
where 
A is the source activity;
d is the distance between the point of interest and the point source.
● The basic physical properties of the two g emitters (60Co and 137Cs) 
currently used for external beam teletherapy and a potential source for 
telethera
topes, 60C
approach
emitted p
5.3.2. Teleth
Treatmen
radiotherapy a
isocentrically, 
Modern teleth
The main
a source housin
a gantry and s
stand-alone ma
5.3.3. Teleth
The mo
contained insid
double welded
● To facilit
another 
source ca
● The typic
and 2 cm
source d
expensiv
comprom
● Typical so
and prov
the order
py units (152Eu) are listed in Table 5.1. Of the three radioiso-
o is the most widely used, since it offers the most practical 
 to external beam radiotherapy, considering the energy of 
hotons, half-life, specific activity and means of production.
erapy machines
t machines incorporating g ray sources for use in external beam 
re called teletherapy machines. They are most often mounted 
allowing the beam to rotate about the patient at a fixed SAD. 
erapy machines have SADs of 80 or 100 cm.
 components of a teletherapy machine are: a radioactive source; 
g, including beam collimator and source movement mechanism; 
tand in isocentric machines or a housing support assembly in 
chines; a patient support assembly; and a machine console.
erapy sources 
st widely used teletherapy source uses 60Co radionuclides 
e a cylindrical stainless steel capsule and sealed by welding. A 
 seal is used to prevent any leakage of the radioactive material. 
ate interchange of sources from one teletherapy machine to 
and from one isotope production facility to another, standard 
psules have been developed.
al diameter of the cylindrical teletherapy source is between 1 
; the height of the cylinder is about 2.5 cm. The smaller the 
iameter, the smaller is its physical penumbra and the more 
e is the source. Often a diameter of 1.5 cm is chosen as a 
ise between the cost and penumbra. 
urce activities are of the order of 5000–10 000 Ci (185–370 TBq) 
ide a typical dose rate at 80 cm from the teletherapy source of 
 of 100–200 cGy/min. Often the output of a teletherapy machine 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
is stated 
source st
● Telethera
are insta
source us
● The 60Co
5.26 year
maximum
and 1.33
electrons
they pro
strahlung
5.3.4. Teleth
The hou
consists of a st
bringing the so
ray beam.
TABLE 5.1. PHYSICAL PROPERTIES OF RADIONUCLIDES USED IN 
EXTERNAL BEAM RADIOTHERAPY
Co-60 Cs-137 Eu-152
Half-life (a) 5.3 30 13.4
Specific activity (Ci/g) 1100a (~250b) 80 180a (~150b)
Photon energy (
Specific g rate c
 G [Rm2/(Ci·h)
Specific air kerm
 GAKR [mGy·m
2
HVL (cm Pb)
Means of produ
a Theoretical s
b The practical
the source is 
radioactive is
131
in Rmm (roentgens per minute at 1 m) as a rough guide for the 
rength.
py sources are usually replaced within one half-life after they 
lled; however, financial considerations often result in longer 
age.
 radionuclides in a teletherapy source decay with a half-life of 
s into 60Ni with the emission of electrons (b particles) with a 
 energy of 320 keV and two g rays with energies of 1.17 MeV 
 MeV. The emitted g rays constitute the therapy beam; the 
 are absorbed in the cobalt source or the source capsule, where 
duce relatively low energy and essentially negligible brems-
 X rays and characteristic X rays.
erapy source housing 
sing for the teletherapy source is called the source head, and 
eel shell with lead for shielding purposes and a mechanism for 
urce in front of the collimator opening to produce the clinical g
MeV) 1.17 and 1.33 0.662 0.6–1.4
onstant 
]
1.31 0.33 1.06
a rate constant 
/(GBq·h)]
309 78 250
1.1 0.5 1.1
ction 59Co + n 
in reactor
Fission 
by-product
151Eu + n 
in reactor
pecific activity: a = (NA ln 2)/(t1/2A).
 specific activity is smaller than the theoretical specific activity because 
not carrier free (i.e. the source contains stable isotopes in addition to 
otopes (e.g. 59Co mixed with 60Co)).
CHAPTER 5
132
● Currently two methods are in use for moving the teletherapy source from 
the beam off into the beam on position and back: (i) a source on a sliding 
drawer and (ii) a source on a rotatingcylinder. Both methods incorporate 
a safety feature in which the beam is terminated automatically in the 
event of a power failure or emergency.
● When the source is in the beam off position, a light source appears in the 
beam on position above the collimator opening, allowing an optical 
visualizat
and any s
● Some rad
beam of
1 mR/h (
require t
than 2 m
5.3.5. Dose 
The pres
timers: prima
treatment time
primary timer’
The set 
accounts for th
the beam on p
end of irradiat
5.3.6. Collim
Collimat
radiation field
source. The ge
may be minim
trimmers as cl
discussion of th
5.4. PARTIC
Numerou
nuclear and hi
ion of the radiation field, as defined by the machine collimators 
pecial shielding blocks.
iation will escape from the unit even when the source is in the 
f position. The head leakage typically amounts to less than 
0.01 mSv/h) at 1 m from the source. International regulations 
hat the average leakage of a teletherapy machine head be less 
R/h (0.02 mSv/h) at 1 m from the source.
delivery with teletherapy machines
cribed target dose is delivered with the help of two treatment 
ry and secondary. The primary timer actually controls the 
, the secondary timer serves as a backup timer in case of the 
s failure.
treatment time must incorporate the shutter error, which 
e travel time of the source from the beam off position towards 
osition at the start of irradiation and for the reverse travel at the 
ion.
ator and penumbra 
ors of teletherapy machines provide square and rectangular 
s typically ranging from 5 × 5 to 35 × 35 cm2 at 80 cm from the 
ometric penumbra, which results from a finite source diameter, 
ized by using small diameter sources and by using penumbra 
ose as possible to the patient’s skin (see Section 6.9 for further 
e penumbra).
LE ACCELERATORS 
s types of accelerator have been built for basic research in 
gh energy physics, and most of them have been modified for at 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
least some limited use in radiotherapy. Irrespective of the accelerator type, two 
basic conditions must be met for particle acceleration: 
● The particle to be accelerated must be charged; 
● An electric field must be provided in the direction of particle acceler-
ation.
The vario
erating electric
As far as the a
of accelerator:
— In electro
electrosta
whose va
Since the
particle c
arrival a
sponding
energy t
discharge
the accel
value (ty
— The elec
conserva
some clo
differs fro
times ov
limited to
final kine
particle t
of times, 
of the pa
Example
and orthovolta
of a cyclic acce
cyclotrons. 
133
us types of accelerator differ in the way they produce the accel-
 field and in how the field acts on the particles to be accelerated. 
ccelerating electric field is concerned there are two main classes 
 electrostatic and cyclic. 
static accelerators the particles are accelerated by applying an 
tic electric field through a voltage difference, constant in time, 
lue fixes the value of the final kinetic energy of the particle. 
 electrostatic fields are conservative, the kinetic energy that the 
an gain depends only on the point of departure and point of 
nd hence cannot be larger than the potential energy corre-
 to the maximum voltage drop existing in the machine. The 
hat an electrostatic accelerator can reach is limited by the 
s that occur between the high voltage terminal and the walls of 
erator chamber when the voltage drop exceeds a certain critical 
pically 1 MV).
tric fields used in cyclic accelerators are variable and non-
tive, associated with a variable magnetic field and resulting in 
se paths along which the kinetic energy gained by the particle 
m zero. If the particle is made to follow such a closed path many 
er, one obtains a process of gradual acceleration that is not 
 the maximum voltage drop existing in the accelerator. Thus the 
tic energy of the particle is obtained by submitting the charged 
o the same, relatively small, potential difference a large number 
each cycle adding a small amount of energy to the kinetic energy 
rticle.
s of electrostatic accelerators used in medicine are superficial 
ge X ray tubes and neutron generators. The best known example 
lerator is the linac; other examples are microtrons, betatrons and 
CHAPTER 5
134
5.4.1. Betatron
The betatron was developed in 1940 by D.W. Kerst as a cyclic electron 
accelerator for basic physics research; however, its potential for use in radio-
therapy was realized soon after. 
● The machine consists of a magnet fed by an alternating current of 
frequenc
a toroida
between 
Fig. 5.3(a
● Conceptu
former: t
and the 
vacuum c
● The elec
doughnu
kept in a
● In the 19
therapy. 
because 
such as: 
1 Gy/min
compact 
5.4.2. Cyclo
The cyclo
of ions to a ki
was used for 
medical uses in
in the product
introduction o
(CT) machine
increased the i
glucose labelle
● In a cyc
guided in
dees bec
y between 50 and 200 Hz. The electrons are made to circulate in 
l (doughnut shaped) vacuum chamber that is placed into the gap 
two magnet poles. A schematic diagram of a betatron is given in 
).
ally, the betatron may be considered an analogue of a trans-
he primary current is the alternating current exciting the magnet 
secondary current is the electron current circulating in the 
hamber (doughnut). 
trons are accelerated by the electric field induced in the 
t shape by the changing magnetic flux in the magnet; they are 
 circular orbit by the magnetic field present.
50s betatrons played an important role in megavoltage radio-
However, the development of linacs pushed them into oblivion 
of the numerous advantages offered by linacs over betatrons, 
much higher beam output (up to 10 Gy/min for linacs versus 
 for betatrons); larger field size; full isocentric mounting; more 
design; and quieter operation.
tron
tron was developed in 1930 by E.O. Lawrence for acceleration 
netic energy of a few megaelectronvolts. Initially, the cyclotron 
basic nuclear physics research, but later on found important 
 the production of radioisotopes for nuclear medicine as well as 
ion of proton and neutron beams for radiotherapy. The recent 
f positron emission tomography (PET)/computed tomography 
s for use in radiotherapy (see Section 15.10) has dramatically 
mportance of cyclotrons in medicine. PET/CT machines rely on 
d with positron emitting 18F produced by proton cyclotrons.
lotron the particles are accelerated along a spiral trajectory 
side two evacuated half-cylindrical electrodes (referred to as 
ause of their D shaped form) by a uniform magnetic field (1 T) 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
that is produced between the pole pieces of a large magnet. Figure 5.3(b) 
is a diagram of a cyclotron.
● A radiofrequency (RF) voltage with a constant frequency between 10 and 
30 MHz is applied between the two electrodes and the charged particle is 
accelerated while crossing the gap between the two electrodes. 
● Inside the electrodes there is no electric field and the particle drifts under 
the influence of the magnetic field in a semicircular orbit with a constant 
speed un
has rever
gap, gain
a semicir
orbit and
crossings
5.4.3. Micro
The micr
linac with a 
FIG. 5
135
til it crosses the gap again. If, in the meantime, the electric field 
sed its direction, the particle will again be accelerated across the 
 a small amount of energy and drift in the other electrode along 
cle of a larger radius than the former one, resulting in a spiral 
 a gradual increase in kinetic energy after a large number of gap 
.
tron
otron is an electron accelerator that combines the features of a 
cyclotron. The concept of the microtron was developed by 
.3. Two cyclic accelerators: (a)a betatron and (b) a cyclotron.
CHAPTER 5
136
V.I. Veksler in 1944, and the machine is used in modern radiotherapy, albeit to 
a much smaller extent than linacs.
Two types of microtron have been developed: circular and racetrack.
● In the circular microtron the electron gains energy from a microwave 
resonant cavity and describes circular orbits of increasing radius in a 
uniform magnetic field. To keep the particle in phase with the microwave 
power, th
such a w
an energ
magnetic
● In the ra
pieces th
efficient 
use of m
The elect
5.5. LINACS
Medical 
energies from 
frequency rang
majority runni
In a linac
special evacua
linear path thr
hence linacs a
cyclic machine
betatrons).
The high
ating waveguid
retarding pote
klystrons.
Various t
only in the low
rays and elect
energy linac w
electron energ
e cavity voltage, frequency and magnetic field are adjusted in 
ay that after each passage through the cavity the electrons gain 
y increment, resulting in an increase in the transit time in the 
 field equal to an integral number of microwave cycles.
cetrack microtron the magnet is split into two D shaped pole 
at are separated to provide greater flexibility in achieving 
electron injection and higher energy gain per orbit through the 
ulticavity accelerating structures similar to those used in linacs. 
ron orbits consist of two semicircular and two straight sections.
linacs are cyclic accelerators that accelerate electrons to kinetic 
4 to 25 MeV using non-conservative microwave RF fields in the 
e from 103 MHz (L band) to 104 MHz (X band), with the vast 
ng at 2856 MHz (S band). 
 the electrons are accelerated following straight trajectories in 
ted structures called accelerating waveguides. Electrons follow a 
ough the same, relatively low, potential difference several times; 
lso fall into the class of cyclic accelerators, just like the other 
s that provide curved paths for the accelerated particles (e.g. 
 power RF fields used for electron acceleration in the acceler-
es are produced through the process of decelerating electrons in 
ntials in special evacuated devices called magnetrons and 
ypes of linac are available for clinical use. Some provide X rays 
 megavoltage range (4 or 6 MV), while others provide both X 
rons at various megavoltage energies. A typical modern high 
ill provide two photon energies (6 and 18 MV) and several 
ies (e.g. 6, 9, 12, 16 and 22 MeV).
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
5.5.1. Linac generations
During the past 40 years medical linacs have gone through five distinct 
generations, making the contemporary machines extremely sophisticated in 
comparison with the machines of the 1960s. The five generations introduced 
the following new features:
● Low ene
filter; ex
chamber
● Medium 
target an
chamber
● High ene
multiple 
foils or s
independ
● High en
dynamic 
collimato
● High ene
with ML
modulate
5.5.2. Safety
The comp
from the poin
technical Com
nearly as possi
subjects; electr
on the safety o
“The use
patients t
patient, o
and mech
the vicini
if there ar
137
rgy photons (4–8 MV): straight-through beam; fixed flattening 
ternal wedges; symmetric jaws; single transmission ionization 
; isocentric mounting.
energy photons (10–15 MV) and electrons: bent beam; movable 
d flattening filter; scattering foils; dual transmission ionization 
; electron cones.
rgy photons (18–25 MV) and electrons: dual photon energy and 
electron energies; achromatic bending magnet; dual scattering 
canned electron pencil beam; motorized wedge; asymmetric or 
ent collimator jaws.
ergy photons and electrons: computer controlled operation; 
wedge; electronic portal imaging device (EPID); multileaf 
r (MLC).
rgy photons and electrons: photon beam intensity modulation 
C; full dynamic conformal dose delivery with intensity 
d beams produced with an MLC.
 of linac installations
lexity of modern linacs raises concerns as to safety of operation 
t of view of patients and operators. The International Electro-
mission (IEC) publishes international standards that express, as 
ble, an international consensus of opinion on relevant technical 
on linacs are addressed in detail by the IEC. The IEC statement 
f linacs (IEC 60601-2-1, p. 13) is as follows: 
 of electron accelerators for radiotherapy purposes may expose 
o danger if the equipment fails to deliver the required dose to the 
r if the equipment design does not satisfy standards of electrical 
anical safety. The equipment may also cause danger to persons in 
ty if the equipment fails to contain the radiation adequately and/or 
e inadequacies in the design of the treatment room.” 
CHAPTER 5
138
The IEC document addresses three categories of safety issues — 
electrical, mechanical and radiation — and establishes specific requirements 
mainly for the manufacturers of linacs in the design and construction of linacs 
for use in radiotherapy. It also covers some radiation safety aspects of linac 
installation in customer’s treatment rooms.
5.5.3. Components of modern linacs
Linacs ar
distributed ove
● Gantry;
● Gantry st
● Modulato
● Patient su
● Control c
A schem
Fig. 5.4. Also s
linac compone
linac’s compo
commercial m
energy as well 
— The leng
kinetic en
— The mai
usually g
(i) Inje
(ii) RF 
(iii) Acc
(iv) Aux
(v) Bea
(vi) Bea
5.5.4. Config
At mega
in the X ray ta
produced in th
e usually mounted isocentrically and the operational systems are 
r five major and distinct sections of the machine, the:
and or support; 
r cabinet; 
pport assembly (i.e. treatment table); 
onsole.
atic diagram of a typical modern S band medical linac is shown in 
hown are the connections and relationships among the various 
nts listed above. The diagram provides a general layout of a 
nents; however, there are significant variations from one 
achine to another, depending on the final electron beam kinetic 
as on the particular design used by the manufacturer.
th of the accelerating waveguide depends on the final electron 
ergy, and ranges from ~30 cm at 4 MeV to ~150 cm at 25 MeV.
n beam forming components of a modern medical linac are 
rouped into six classes: 
ction system; 
power generation system; 
elerating waveguide; 
iliary system; 
m transport system; 
m collimation and beam monitoring system.
uration of modern linacs
voltage electron energies the bremsstrahlung photons produced 
rget are mainly forward peaked and the clinical photon beam is 
e direction of the electron beam striking the target.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● In the simplest and most practical configuration, the electron gun and the 
X ray target form part of the accelerating waveguide and are aligned 
directly with the linac isocentre, obviating the need for a beam transport 
system. A straight-through photon beam is produced and the RF power 
source is mounted in the gantry. 
● The simplest linacs are isocentrically mounted 4 or 6 MV machines, with 
the electron gun and target permanently built into the accelerating 
waveguid
therapy o
● Accelera
MeV) ele
thus are l
or in the 
the elect
The RF p
the gantr
linacs are
139
e, thereby requiring no beam transport nor offering an electron 
ption.
ting waveguides for intermediate (8–15 MeV) and high (15–30 
ctron energies are too long for direct isocentric mounting and 
ocated either in the gantry, parallel to the gantry axis of rotation, 
gantry stand. A beam transport system is then used to transport 
ron beam from the accelerating waveguide to the X ray target. 
ower source in the two configurations is commonly mounted in 
y stand. Various design configurations for modern isocentric 
 shown in Fig. 5.5. 
FIG. 5.4. Medical linac.
CHAPTER 5
140
5.5.5.Injection system 
The injection system is the source of electrons; it is essentially a simple 
electrostatic accelerator called an electron gun.
● Two types of electron gun are in use as sources of electrons in medical 
linacs: 
— Diod
— Triod
● Both ele
perforate
incorpora
e type; 
e type. 
ctron gun types contain a heated filament cathode and a 
d grounded anode; in addition, the triode electron gun also 
tes a grid.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● Electrons are thermionically emitted from the heated cathode, focused 
into a pencil beam by a curved focusing electrode and accelerated 
towards the perforated anode through which they drift to enter the accel-
erating waveguide.
● The electrostatic fields used to accelerate the electrons in the diode gun 
are supplied directly from the pulsed modulator in the form of a negative 
pulse delivered to the cathode of the gun.
● In a triod
(typically
negative 
The inje
controlle
synchron
removab
FIG. 5.5. Design
design; the elec
waveguide; the m
generator is mou
to the isocentre a
system; the RF p
megavoltage X r
generator are lo
through a beam 
electrons.
141
e gun, however, the cathode is held at a static negative potential 
 –20 kV). The grid of the triode gun is normally held sufficiently 
with respect to the cathode to cut off the current to the anode. 
ction of electrons into the accelerating waveguide is then 
d by voltage pulses, which are applied to the grid and must be 
ized with the pulses applied to the microwave generator. A 
le triode gun of a high energy linac is shown in Fig. 5.6(a). 
 configurations for isocentric medical linacs. (a) Straight-through beam 
tron gun and target are permanently embedded into the accelerating 
achine produces only X rays with energies of 4–6 MV; the RF power 
nted in the gantry. (b) The accelerating waveguide is in the gantry parallel 
xis; electrons are brought to the movable target through a beam transport 
ower generator is located in the gantry stand; the machine can produce 
ays as well as electrons. (c) The accelerating waveguide and RF power 
cated in the gantry stand; electrons are brought to the movable target 
transport system; the machine can produce megavoltage X rays as well as 
CHAPTER 5
142
(a)
(b)
FIG. 5.6. Remo
high energy lina
modes. The targ
the pencil electro
electron beam p
vable electron triode gun (a) and removable X ray target (b) for a typical 
c (Varian Clinac-18), allowing two photon modes and several electron 
et is water cooled and mounted with bellows to allow for movement into 
n beam for X ray production and movement out of the pencil beam for 
roduction.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
5.5.6. Radiofrequency power generation system
The microwave radiation used in the accelerating waveguide to accelerate 
electrons to the desired kinetic energy is produced by the RF power generation 
system, which consists of two major components:
● An RF power source;
● A pulsed
The RF 
devices that u
production of 
electrons from
in a pulsed ele
different.
— The high
pulses re
injection
circuitry 
which, de
the treat
room or 
— A magne
ation, wh
power RF
5.5.7. Accel
Waveguid
or circular cro
waveguide are
ating waveguid
from the powe
accelerated.
● The elect
an energ
accelerat
● The sim
cylindrica
143
 modulator.
power source is either a magnetron or a klystron. Both are 
se electron acceleration and deceleration in a vacuum for the 
high power RF fields. Both types use a thermionic emission of 
 a heated cathode and accelerate the electrons towards an anode 
ctrostatic field; however, their design principles are completely 
 voltage (~100 kV), high current (~100 A), short duration (~1 s) 
quired by the RF power source (magnetron or klystron) and the 
 system (electron gun) are produced by a pulsed modulator. The 
of the pulsed modulator is housed in the modulator cabinet, 
pending on the particular linac installation design, is located in 
ment room, in a special mechanical room next to the treatment 
in the linac control room.
tron is a source of high power RF required for electron acceler-
ile a klystron is an RF power amplifier that amplifies the low 
 generated by an RF oscillator commonly called the RF driver.
erating waveguide
es are evacuated or gas filled metallic structures of rectangular 
ss-section used in the transmission of microwaves. Two types of 
 used in linacs: RF power transmission waveguides and acceler-
es. The power transmission waveguides transmit the RF power 
r source to the accelerating waveguide in which the electrons are 
rons are accelerated in the accelerating waveguide by means of 
y transfer from the high power RF fields, which are set up in the 
ing waveguide and are produced by the RF power generators.
plest kind of accelerating waveguide is obtained from a 
l uniform waveguide by adding a series of discs (irises) with 
CHAPTER 5
144
circular holes at the centre, placed at equal distances along the tube. 
These discs divide the waveguide into a series of cylindrical cavities that 
form the basic structure of the accelerating waveguide in a linac.
The accelerating waveguide is evacuated to allow free propagation of 
electrons. The cavities of the accelerating waveguide serve two purposes:
— To couple
— To provid
Two typ
acceleration of
(i) Travellin
(ii) Standing
In the tr
waveguide on 
waveguide, wh
waveguide to b
of the accelera
at any given m
field in the dire
In the sta
terminated wit
a buildup of sta
every second c
for the electro
can be moved 
the acceleratin
accelerating w
5.5.8. Micro
The micr
accelerating w
are either eva
(Freon or sulp
An impo
mission circuit
 and distribute microwave power between adjacent cavities;
e a suitable electric field pattern for the acceleration of electrons.
es of accelerating waveguide have been developed for the 
 electrons: 
g wave structure;
 wave structure.
avelling wave structure the microwaves enter the accelerating 
the gun side and propagate towards the high energy end of the 
ere they either are absorbed without any reflection or exit the 
e absorbed in a resistive load or to be fed back to the input end 
ting waveguide. In this configuration only one in four cavities is 
oment suitable for electron acceleration, providing an electric 
ction of propagation.
nding wave structure each end of the accelerating waveguide is 
h a conducting disc to reflect the microwave power, resulting in 
nding waves in the waveguide. In this configuration, at all times, 
avity carries no electric field and thus produces no energy gain 
ns. These cavities therefore serve only as coupling cavities and 
out to the side of the waveguide structure, effectively shortening 
g waveguide by 50%. A cut-away view of a 6 MV standing wave 
aveguide is shown in Fig. 5.7.
wave power transmission
owave power produced by the RF generator is carried to the 
aveguide through rectangular uniform S band waveguides that 
cuated or, more commonly, pressurized with a dielectric gas 
hur hexafluoride, SF6) to twice the atmospheric pressure.
rtant component that must be inserted into the RF power trans-
 between the RF generator and the accelerating waveguide is a 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
circulator (som
from the RF 
reflected radia
source from th
5.5.9. Auxili
The linac
involved with e
linac viable for
The linac
● A vacuum
the accel
● A water 
circulato
● An optio
and othe
● Shielding
FIG. 5.7. Cutaw
cavities are clear
cavities are off-s
nently embedded
145
etimes referred to as an isolator), which transmits the RF power 
generator to the accelerating waveguide but is impervious to 
tion moving in the opposite direction, therebyprotecting the RF 
e reflected power.
ary system
 auxiliary system consists of several services that are not directly 
lectron acceleration, yet make the acceleration possible and the 
 clinical operation.
 auxiliary system comprises four systems:
 pumping system producing a vacuum pressure of ~10–6 torr in 
erating guide and the RF generator;
cooling system used for cooling the accelerating guide, target, 
r and RF generator;
nal air pressure system for pneumatic movement of the target 
r beam shaping components;
 against leakage radiation.
ay view of a standing wave accelerating waveguide for a 6 MV linac. The 
ly visible: the accelerating cavities are on the central axis; the coupling 
ide. The electron gun is on the left, the target on the right, both perma-
.
CHAPTER 5
146
5.5.10. Electron beam transport
In low energy linacs the target is embedded in the accelerating waveguide 
and no beam transport between the accelerating waveguide and target is 
required.
Bending magnets are used in linacs operating at energies above 6 MeV, 
where the accelerating waveguides are too long for straight-through mounting. 
The accelerati
axis and the ele
able to exit thr
have been dev
● 90º bend
● 270º bend
● 112.5º (sl
In mediu
beam transpor
accelerating w
electron beam
bending magne
and focusing o
beam transpor
5.5.11. Linac 
The lina
production, sh
electron beam
Electron
ating waveguid
a pencil beam
head, where th
● The impo
generatio
—Severa
—Flatten
filters)
—Primar
—Dual tr
ng waveguide is usually mounted parallel to the gantry rotation 
ctron beam must be bent to make it strike the X ray target or be 
ough the beam exit window. Three systems for electron bending 
eloped:
ing;
ing (achromatic);
alom) bending.
m (10 MV) and high energy (above 15 MV) linacs an electron 
t system is used for transporting the electron beam from the 
aveguide to the X ray target or to the linac exit window for 
 therapy. The system consists of evacuated drift tubes and 
ts. In addition, steering coils and focusing coils, used for steering 
f the accelerated electron beam, also form components of the 
t system.
treatment head
c head contains several components that influence the 
aping, localizing and monitoring of the clinical photon and 
s.
s originating in the electron gun are accelerated in the acceler-
e to the desired kinetic energy and then brought, in the form of 
, through the beam transport system into the linac treatment 
e clinical photon and electron beams are produced.
rtant components found in a typical head of a fourth or fifth 
n linac include: 
l retractable X ray targets;
ing filters and electron scattering foils (also called scattering 
;
y and adjustable secondary collimators;
ansmission ionization chambers;
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
—A field defining light and a range finder;
—Optional retractable wedges;
—Optional MLC. 
● Clinical photon beams are produced with a target–flattening filter combi-
nation.
● Clinical electron beams are produced by retracting the target and 
flattening filter from the electron pencil beam and:
—Either
—Deflec
size req
Special c
● Each clin
nation. T
beams) a
mechanic
● The prim
further tr
two uppe
and squa
isocentre
ray beam
open bea
● Dual tra
photon a
transvers
● The field
methods 
reference
radiation
used to p
centimet
distance 
5.5.12. Produ
Clinical p
X ray target an
target is shown
At electr
optimal targets
15 MeV (phot
147
 scattering the pencil beam with a single or dual scattering foil; or
ting and scanning the pencil beam magnetically to cover the field 
uired for electron treatment.
ones (applicators) are used to collimate the electron beams.
ical photon beam has its own target–flattening filter combi-
he flattening filters and scattering foils (if used for electron 
re mounted on a rotating carousel or sliding drawer for ease of 
al positioning into the beam, as required.
ary collimator defines a maximum circular field, which is then 
uncated with an adjustable rectangular collimator consisting of 
r and two lower independent jaws and producing rectangular 
re fields with a maximum dimension of 40 × 40 cm2 at the linac 
. The IEC recommends that the transmission of the primary X 
 through the rectangular collimator should not exceed 2% of the 
m value.
nsmission ionization chambers are used for monitoring the 
nd electron radiation beam output as well as the radial and 
e beam flatness (see Section 5.5.14).
 defining light and the range finder provide convenient visual 
for correctly positioning the patient for treatment using 
 marks. The field light illuminates an area that coincides with the 
 treatment field on the patient’s skin, while the range finder is 
lace the patient at the correct treatment distance by projecting a 
re scale whose image on the patient’s skin indicates the vertical 
from the linac isocentre.
ction of clinical photon beams in a linac
hoton beams emanating from a medical linac are produced in an 
d flattened with a flattening filter. A high energy linac movable 
 in Fig. 5.6(b).
on energies below 15 MeV (photon beam energies 15 MV) 
 have a high atomic number Z, while at electron energies above 
on beam energies above 15 MV) the optimal targets have a low 
CHAPTER 5
148
atomic number Z. Optimal flattening filters have a low Z irrespective of beam 
energy.
5.5.13. Beam collimation
In a typical modern medical linac, the photon beam collimation is 
achieved with two or three collimator devices:
● A primar
● Secondar
● An MLC
In additi
beams also rel
— The prim
is a conic
sides of t
end of th
thickness
average p
(three te
the maxim
— The seco
forming t
can prov
of the ord
— Modern 
provide 
blocked 
coinciden
— MLCs ar
In princi
reliable M
— The num
models w
requiring
circuits a
— MLCs ar
conforma
continuo
y collimator;
y movable beam defining collimators;
 (optional).
on to the primary and secondary collimators, clinical electron 
y on electron beam applicators (cones) for beam collimation.
ary collimator defines the largest available circular field size and 
al opening machined into a tungsten shielding block, with the 
he conical opening projecting on to edges of the target on one 
e block and on to the flattening filter on the other end. The 
 of the shielding block is usually designed to attenuate the 
rimary X ray beam intensity to less than 0.1% of the initial value 
nth-value layers (TVLs)). According to IEC recommendations, 
um leakage should not exceed 0.2% of the open beam value.
ndary beam defining collimators consist of four blocks, two 
he upper and two forming the lower jaws of the collimator. They 
ide rectangular or square fields at the linac isocentre, with sides 
er of few millimetres up to 40 cm.
linacs incorporate independent (asymmetric) jaws that can 
asymmetric fields, most commonly one half or three quarter 
fields in which one or two beam edges, respectively, are 
t with the beam central axis.
e a relatively recent addition to linac dose delivery technology. 
ple, the idea behind an MLC is simple; however, building a 
LC system presents a substantial technological challenge.
ber of leaves in commercial MLCs is steadily increasing, and 
ith 120 leaves (60 pairs) covering fields up to 40 × 40 cm2 and 
 120 individually computer controlled motors and control 
re currently available.
e becoming invaluable in supplying intensity modulated fields in 
l radiotherapy, either in the step and shoot mode or in a 
us dynamic mode.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
— Miniature versions of MLCs (micro MLCs) projecting 1.5–6 mm leaf 
widths and up to 10 × 10 cm2 fields at the linac isocentre are currently 
commercially available.They may be used in radiosurgery as well as for 
head and neck treatments.
5.5.14. Production of clinical electron beams in a linac
The majo
dual photon 
electron beam
● To activa
filter of t
● The elect
three ord
clinical p
● The elec
through 
atomic n
strahlung
● Two tech
electron 
—Pencil 
the rel
achiev
the pen
—Pencil 
albeit 
beams.
contro
planes,
field. 
5.5.15. Dose 
IEC 606
installed in cl
radiation dete
and monitorin
149
rity of higher energy linacs, in addition to providing single or 
energies, also provide electron beams with several nominal 
 energies in the range from 6 to 30 MeV.
te an electron beam mode, both the target and the flattening 
he X ray beam mode are removed from the electron beam.
ron beam currents producing clinical electron beams are two to 
ers of magnitude lower than the electron currents producing the 
hoton beams in the linac X ray target.
tron pencil beam exits the evacuated beam transport system 
a thin window usually made of beryllium, which, with its low 
umber Z, minimizes the pencil beam scattering and brems-
 production.
niques are available for producing clinical electron beams from 
pencil beams: 
beam scattering. The scattering of the electron pencil beam over 
atively large area used in radiotherapy (up to 25 × 25 cm2) is 
ed by placing thin foils of high Z material (copper or lead) into 
cil beam at the level of the flattening filter in the X ray mode.
beam scanning. Electron pencil beam scanning is an alternative, 
infrequently used, technique for producing clinical electron 
 The technique is usually implemented with two computer 
lled magnets, which deflect the pencil beam in two orthogonal 
 thereby scanning the pencil beam across the clinical treatment 
monitoring system
01-2-1 specifies in detail the standards for radiation monitors 
inical electron linacs. It deals with standards for the type of 
ctors, display of monitor units (MUs), termination of radiation 
g of beam flatness and dose rate.
CHAPTER 5
150
● Most common dose monitors in linacs are transmission ionization 
chambers permanently imbedded in the linac clinical photon and electron 
beams to monitor the beam output continuously during patient 
treatment. 
● Most linacs use sealed ionization chambers to make their response 
independent of ambient temperature and pressure.
● The customary position of the dose monitor chambers is between the 
flattening
collimato
● For patie
separatel
biasing p
chamber
terminate
per cent 
● In the ev
ionizatio
minimal 
● The mai
follows: 
—Chamb
radiati
—Chamb
pressur
conditi
—Chamb
● The prim
of the cha
correspo
of dose 
10 × 10 c
● Once the
ionizatio
delivery 
necessary
not possi
● In additio
system a
energy, f
paramete
primary a
 filter or scattering foil and the photon beam secondary 
r.
nt safety, the linac dosimetry system usually consists of two 
y sealed ionization chambers with completely independent 
ower supplies and readout electrometers. If the primary 
 fails during patient treatment, the secondary chamber will 
 the irradiation, usually after an additional dose of only a few 
above the prescribed dose has been delivered. 
ent of a simultaneous failure of both the primary and secondary 
n chambers, the linac timer will shut the machine down with a 
overdose to the patient.
n requirements for the ionization chamber monitors are as 
ers must have a minimal effect on clinical photon and electron 
on beams; 
er response should be independent of ambient temperature and 
e (most linacs use sealed ionization chambers to satisfy this 
on); 
ers should be operated under saturation conditions.
ary ionization chamber measures MUs. Typically, the sensitivity 
mber electrometer circuitry is adjusted in such a way that 1 MU 
nds to a dose of 1 cGy delivered in a water phantom at the depth 
maximum on the central beam axis when irradiated with a 
m2 field at a source to surface distance (SSD) of 100 cm.
 operator preset number of MUs has been reached, the primary 
n chamber circuitry shuts the linac down and terminates the dose 
to the patient. Before a new irradiation can be initiated, it is 
 to reset the MU displays to zero. Furthermore, irradiation is 
ble until a new selection of MUs has been made.
n to monitoring the primary dose in MUs, the dose monitoring 
lso monitors other operating parameters such as the beam 
latness and symmetry. Measurement of all these additional 
rs requires that the ionization chamber electrodes of the 
nd secondary chambers be divided into several sectors, with the 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
resulting signals used in automatic feedback circuits to steer the electron 
beam through the accelerating waveguide, beam transport system and on 
to the target or scattering foil, thereby ensuring beam flatness and 
symmetry. The particular design of the ionization chamber electrodes and 
sectors varies from one manufacturer to another.
● Linacs must be equipped with a monitoring system that continuously 
displays the machine isocentre dose rate and terminates the beam when 
the meas
technical
● When th
more tha
irradiatio
and beam
console.
● Similarly
therapy, 
until stat
selected a
5.6. RADIOT
HEAVY
External
produce either
world, externa
such as:
● Neutrons
● Protons p
● Heavy io
cyclotron
These pa
and electron m
— Consider
Section 1
— Improved
(see Sect
151
ured dose rate exceeds twice the maximum specified by the 
 machine description.
e linac is capable of producing more than one beam energy or 
n one beam mode (X rays or electrons), after termination of 
n further irradiation is prevented until the selection of energy 
 mode has been made afresh and entered into the control 
, for linacs capable of stationary as well as moving beam radio-
after termination of irradiation further irradiation is prevented 
ionary radiotherapy or moving beam radiotherapy has been 
fresh and entered into the control console.
HERAPY WITH PROTONS, NEUTRONS AND 
 IONS
 beam radiotherapy is carried out mainly with machines that 
 X rays or electrons. In a few specialized centres around the 
l beam radiotherapy is also carried out with heavier particles, 
 produced by neutron generators and cyclotrons;
roduced by cyclotrons and synchrotrons; 
ns (helium, carbon, nitrogen, argon, neon) produced by synchro-
s and synchrotrons.
rticles offer some distinct advantages over the standard X ray 
odalities, such as:
ably lower oxygen enhancement ratio (OER) for neutrons (see 
4.10);
 dose–volume histograms (DVHs) for protons and heavy ions 
ion 7.6).
CHAPTER 5
152
However, equipment for production of protons, neutrons and heavy ions 
is considerably more expensive than standard radiotherapy equipment, both in 
capital costs and in maintenance and servicing costs, thus precluding a 
widespread use in standard radiotherapy departments. The decreasing costs of 
proton cyclotrons are likely to result in a wider use of proton beam therapy in 
the future.
5.7. SHIELD
External
equipment tha
● X ray ma
● Telethera
● Linacs.
All radi
treatment room
adjacent to the
with structura
regulations tha
from the radia
radiotherapy m
required thick
information to
architectural d
Superfici
with ordinary 
electric effect 
making the use
Megavol
because of th
commonly shi
costs. The Com
shielding mate
materials may 
to the density 
(5 g/cm3) will 
approximately
cost by a facto
ING CONSIDERATIONS
 beam radiotherapy is carried out mainly with three types of 
t produces either X rays or electrons:
chines (superficial and orthovoltage);
py (60Co) machines; 
otherapy equipment must be housed in specially shielded 
s in order to protect personnel and the general public in areastreatment rooms. The treatment rooms must comply not only 
l building codes but also with national and international 
t deal with shielding requirements to render an installation safe 
tion protection point of view. During the planning stage for a 
achine installation, a qualified medical physicist determines the 
ness of primary and secondary barriers and provides the 
 the architect and structural engineer for incorporation into the 
rawing for the treatment room. 
al and orthovoltage X ray therapy rooms are shielded either 
concrete (2.35 g/cm3) or lead. In this energy range the photo-
is the predominant mode of photon interaction with matter, 
 of lead very efficient for shielding purposes.
tage treatment rooms (often referred to as bunkers or vaults 
e large barrier thickness required for shielding) are most 
elded with ordinary concrete so as to minimize construction 
pton effect is the predominant mode of photon interaction with 
rial in this energy range. To conserve space, other higher density 
be used, with the required wall thickness inversely proportional 
of the shielding material. Thus the use of high density concrete 
cut the required thickness of an ordinary concrete barrier by 
 one half; however, it will also increase the construction material 
r of 30. 
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
Shielding issues related to linac bunkers are discussed in more detail in 
Section 16.17. 
5.8. COBALT-60 TELETHERAPY UNITS VERSUS LINACS
After the inception of radiotherapy soon after the discovery of X rays by 
Roentgen in 1
towards ever h
computerizatio
50 years of rad
based on X ray
The first
teletherapy ma
teletherapy pr
energies and p
of years, main
terized by feat
The impo
as follows:
● Relativel
● Relativel
● Relativel
● Relativel
Figure 5.
issued by Can
the 60Co machi
Linacs w
at Stanford Un
tions Research
for research 
technology de
frequency. 
The pote
1950s, and the 
Hospital in Lo
and became th
with several t
153
895, the technology of radiation production was first aimed 
igher photon energies and intensities and more recently towards 
n and intensity modulated beam delivery. During the first 
iotherapy, technological progress was relatively slow and mainly 
 tubes, van de Graaff generators and betatrons.
 truly practical megavoltage therapy machine was the 60Co 
chine developed in Canada in the 1950s. The invention of 60Co 
ovided a tremendous boost in the quest for higher photon 
laced the 60Co unit in the forefront of radiotherapy for a number 
ly because it incorporated a radioactive source that is charac-
ures extremely useful for radiotherapy.
rtant features of 60Co teletherapy machines can be summarized 
y high energy g ray emission;
y long half-life;
y high specific activity;
y simple means of production.
8(a) shows a 60Co teletherapy machine; Fig. 5.8(b) shows a stamp 
ada Post commemorating Canada’s role in the development of 
ne.
ere developed concurrently by two groups: W.W. Hansen’s group 
iversity in the USA and D.D. Fry’s group at the Telecommunica-
 Establishment in the UK. Both groups were interested in linacs 
purposes and profited heavily from the microwave radar 
veloped during World War II, using 3000 MHz as the design 
ntial for the use of linacs in radiotherapy became apparent in the 
first clinical linac was installed in the 1950s at the Hammersmith 
ndon. During subsequent years, the linac eclipsed the cobalt unit 
e most widely used radiation source in modern radiotherapy, 
housand units in clinical practice around the world today. In 
CHAPTER 5
154
contrast to a 6
MeV, a linac c
wide range of e
In compa
design:
(a)
FIG. 5.8. Cobal
beam therapy sy
Canada (publish
cobalt unit depi
H.E. Johns, who
reproduced with
0Co unit, which provides essentially only one g energy of 1.25 
an provide either megavoltage electron or X ray therapy with a 
nergies. Figure 5.9 shows a modern dual energy linac.
rison with 60Co machines, linacs have become very complex in 
(b)
t-60 teletherapy machine. (a) Theratron Equinox, a megavoltage external 
stem using cobalt technology, manufactured by MDS Nordion, Ottawa, 
ed with permission from MDS Nordion). (b) Schematic diagram of a 
cted on a postage stamp issued by Canada Post in 1988 in honour of 
 invented the 60Co unit in the 1950s (© Canada Post Corporation, 1988; 
 permission).
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
(b)
(a)
FIG. 5.9. Mode
patient support 
portal imager is 
155
rn dual photon energy linac manufactured by Varian; the gantry and the 
assembly are clearly shown. (a) The portal imager is retracted; (b) the 
activated. (Photographs courtesy of Varian Oncology Systems.)
CHAPTER 5
156
— In part because of the multimodality capabilities that have evolved and 
are available on most modern machines;
— In part because of an increased use of computer logic and microproc-
essors in the control systems of these machines;
— In part because of added features, such as high dose rate modes, multileaf 
collimation, electron arc therapy and the dynamic treatment option, 
which is characterized by a controlled motion on the collimators 
(dynamic
turned on
Despite 
60Co machines
armamentariu
and maintena
developing wo
simplicity of d
in cancer thera
Many m
dynamic opera
lower cost, a si
manufacturers
developments 
even in areas 
machines than
5.9. SIMULA
Simulato
used in radioth
process that ar
important, as 
planning and s
volume that is
position relativ
methods. Thes
imaging to the
in conjunction
simulators and
X ray tube and
The majo
 wedge), MLC leaves (IMRT), gantry or table while the beam is 
. 
the clear technological and practical advantages of linacs over 
, the latter still occupy an important place in the radiotherapy 
m, mainly because of the considerably lower capital, installation 
nce costs of 60Co machines compared with linacs. In the 
rld, 60Co machines, because of their relatively lower costs, 
esign and ease of operation, are likely to play an important role 
py for the foreseeable future.
odern features of linacs, such as MLCs, dynamic wedges and 
tion, could be installed on modern 60Co machines to allow, at a 
milar sophistication in treatment as linacs. It is unfortunate that 
 of 60Co units are very slow in reacting to new technological 
in radiotherapy, conceding pre-eminence to linac manufacturers 
where it would be much easier and more practical to run 60Co 
 linacs. 
TORS AND COMPUTED TOMOGRAPHY SIMULATORS
rs and CT simulators are important components of equipment 
erapy. They cover several crucial steps in the radiotherapeutic 
e not related to the actual dose delivery but are nonetheless very 
they deal with the determination of target location, treatment 
patial accuracy in dose delivery. The determination of the target 
 related to the extent of the disease (see Section 7.2) and its 
e to adjacent critical normal tissues can be achieved with various 
e range from a simple clinical examination through planar X ray 
 use of complex modern imaging equipment such as CT scanners 
 with magnetic resonance (MR) and PET scanners. Both 
 CT simulators incorporate three major systems: the mechanical, 
 imaging equipment.
r steps in the target localization and field design are:
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
● Acquisition of the patient data set;
● Localization of target and adjacent structures;
● Definition and marking of the patient coordinate system;
● Design of treatment fields;
● Transfer of data to the treatment planning system (TPS);
● Production of an image for treatment verification.
The six s
or with a CT 
elegant, reliab
providing relia
mation.
5.9.1. Radio
A radioth
a rotating ga
megavoltage th
or isocentric lin
megavoltagem
treatment it p
either in the r
the fluoroscop
intensifier).
A mode
geometric field
60Co machines
100 cm.
In megav
(upper and low
are defined wi
of healthy tissu
A moder
● Tumour a
● Treatmen
● Treatmen
● Monitori
157
teps above can be achieved either with a conventional simulator 
simulator; however, the CT simulator provides for the more 
le and practical means to achieve the six steps, in addition to 
ble external and internal contours and electron density infor-
therapy simulator
erapy simulator consists of a diagnostic X ray tube mounted on 
ntry, simulating geometries identical to those found on 
erapy machines that are either isocentric teletherapy 60Co units 
acs. Thus the simulator enjoys the same degrees of freedom as a 
achine, but rather than providing a megavoltage beam for 
rovides a diagnostic quality X ray beam suitable for imaging, 
adiographic mode (image recorded on radiographic film) or in 
ic mode (image recorded on a TV monitor using an image 
rn simulator should mimic all the mechanical features and 
 arrangements of various megavoltage machines, ranging from 
 with an SAD of 80 cm to high energy linacs with an SAD of 
oltage machines, radiation fields are defined with collimators 
er jaws), while in simulators the rectangular and square fields 
th delineator wires to enable visualization of the target as well as 
es adjacent to the target.
n simulator covers the following processes:
nd adjacent normal tissue localization;
t simulation;
t plan verification;
ng of treatment.
CHAPTER 5
158
5.9.2. Computed tomography simulator
CT simulators are CT scanners equipped with special features that make 
them useful for certain stages in the radiotherapeutic process. The special 
features typically are:
● A flat table top surface to provide a patient position during simulation 
that will 
machine.
● A laser 
isocentre
of the pa
mounted
sagittal la
● A virtual
define an
using dig
A CT sim
by carrying ou
— Physical 
zation ste
— Virtual si
steps liste
In CT sim
carried out us
DRRs. A lase
software packa
Transfer of all 
The plan
the treatment 
structures. CT,
definition but 
A DRR 
also Section 7
simulation sof
computed radi
senting the ac
accounts for th
be identical to the position during treatment on a megavoltage 
marking system to transfer the coordinates of the tumour 
, derived from the contouring of the CT data set, to the surface 
tient. Two types of laser marking systems are used: a gantry 
 laser and a system consisting of a wall mounted moveable 
ser and two stationary lateral lasers.
 simulator consisting of software packages that allow the user to 
d calculate a treatment isocentre and then simulate a treatment 
itally reconstructed radiographs (DRRs).
ulator essentially obviates the need for conventional simulation 
t two distinct functions:
simulation, which covers the first three of the six target locali-
ps listed above;
mulation, which covers the last three of the six target localization 
d above.
ulation the patient data set is collected and target localization is 
ing CT images with fluoroscopy and radiography replaced by 
r alignment system is used for marking and a virtual simulator 
ge is used for field design and production of verification images. 
necessary information to the TPS is achieved electronically.
ar simulation X ray film provides a beam’s eye view (BEV) of 
portal but does not provide 3-D information about anatomical 
 on the other hand, provides anatomical information and target 
does not allow a direct correlation with the treatment portals.
is the digital equivalent of a planar simulation X ray film (see 
.4.8). It is reconstructed from a CT data set using virtual 
tware available on a CT simulator or a TPS and represents a 
ograph of a virtual patient generated from a CT data set repre-
tual patient. Just like a conventional radiograph, the DRR 
e divergence of the beam.
TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY
The basic approach to producing a DRR involves several steps: choice of 
virtual source position; definition of image plane; ray tracing from virtual 
source to image plane; determination of the CT value for each volume element 
traversed by the ray line to generate an effective transmission value at each 
pixel on the image plane; summation of CT values along the ray line (line 
integration); and grey scale mapping.
An extension of the DRR approach is the digitally composited 
radiograph (D
landmarks an
weighting rang
enhanced or su
5.10. TRAINI
The incr
equipment be 
minimize the p
the lessons lea
the American
addressed med
Of vital i
radiotherapy e
(a) Preparat
(b) Design o
(c) Acceptan
(d) Commiss
(e) A quality
Items (a)
addressed in C
159
CR), which provides an enhanced visualization of bony 
d soft tissue structures. This is achieved by differentially 
es of CT numbers that correspond to different tissues to be 
ppressed in the resulting DCR images.
NG REQUIREMENTS
eased complexity of radiotherapy equipment demands that 
used only by highly trained and competent staff, in order to 
otential for accidents. A recent report by the IAEA summarized 
rned from accidental exposures in radiotherapy, and a report by 
 Association of Physicists in Medicine (AAPM) specifically 
ical accelerator safety considerations.
mportance in the purchase, installation and clinical operation of 
quipment are the following:
ion of an equipment specification document;
f the treatment room and radiation safety;
ce testing of equipment;
ioning of equipment;
 assurance programme.
, (c) and (d) are addressed in detail in Chapter 10, item (e) is 
hapter 12 and item (b) is addressed in Chapter 16. 
CHAPTER 5
160
BIBLIOGRAPHY
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COIA, L., SHU
Advanced Medi
GREENE, D., W
of Physics Publis
INTERNATION
Accidental Exp
(2000).
INTERNATION
Equipment: Par
Range 1 MeV to
JOHNS, H.E., C
IL (1984).
KARZMARK, 
McGraw-Hill, N
KHAN, F., The
Baltimore, MD 
PODGORSAK
Modern Techno
Radiation Onco
(1999) 349–435.
LTHEISS, T.E., HANKS, G.E., A Practical Guide to CT Simulation, 
cal Publishing, Madison, WI (1995).
ILLIAMS, P.C., Linear Accelerators for Radiation Therapy, Institute 
hing, Bristol (1997).
AL ATOMIC ENERGY AGENCY, Lessons Learned from 
osures in Radiotherapy, Safety Reports Series No. 17, IAEA, Vienna 
AL ELECTROTECHNICAL COMMISSION, Medical Electrical 
ticular Requirements for the Safety of Electron Accelerators in the 
 50 MeV, Rep. 60601-2-1, IEC, Geneva (1998).
UNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, 
C.J., NUNAN, C.S., TANABE, E., Medical Electron Accelerators, 
ew York (1993).
 Physics of Radiation Therapy, Lippincott, Williams and Wilkins, 
(2003).
, E.B., METCALFE, P., VAN DYK, J., “Medical accelerators”, The 
logy in Radiation Oncology: A Compendium for Medical Physicists and 
logists (VAN DYK, J., Ed.), Medical Physics Publishing, Madison, WI 
Chapter 6
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
E.B. PODGORSAK
Department of Medical Physics,
McGill U
Montrea
6.1. INTROD
Radiothe
radiotherapy a
source is at a c
is irradiated w
13) radiation s
or interstitial b
radiotherapy).
beams, some w
particles such a
This cha
external beam
into various c
energy. There 
radioactive nu
energetic elect
and characteri
ficial or orthov
6.2. QUANT
Radiatio
describes the p
of photons con
energy the pho
biological mate
161
niversity Health Centre,
l, Quebec, Canada
UCTION
rapy procedures fall into two main categories: external beam 
nd brachytherapy. In external beam radiotherapythe radiation 
ertain distance from the patient and the target within the patient 
ith an external radiation beam. In brachytherapy (see Chapter 
ources are placed directly into the target volume (intracavitary 
rachytherapy) or on to a target (surface mould or intraoperative 
 Most external beam radiotherapy is carried out with photon 
ith electron beams and a very small fraction with more exotic 
s protons, heavier ions or neutrons.
pter deals with external photon beam radiotherapy. Photon 
s are all characterized by the same physical parameters, but fall 
ategories depending on their origin, means of production and 
are two origins of photon beams: g rays, which originate from 
clei, and X rays, which originate in a target bombarded with 
rons. The X rays from a target consist of bremsstrahlung photons 
stic photons. X rays are produced either in an X ray tube (super-
oltage X rays) or in a linac (megavoltage X rays).
ITIES USED IN DESCRIBING A PHOTON BEAM
n dosimetry deals with two distinctly different entities: one 
hoton radiation beam itself in terms of the number and energies 
stituting the photon beam and the other describes the amount of 
ton beam may deposit in a given medium such as air, water or 
rial.
CHAPTER 6
162
6.2.1. Photon fluence and photon fluence rate 
The photon fluence f is defined as the quotient dN by dA, where dN is the 
number of photons that enter an imaginary sphere of cross-sectional area dA:
(6.1)
The unit of ph
The photon flu
The unit of ph
6.2.2. Energ
The ener
defined as the 
The unit of ene
For a mo
energy hn, and
Y = fhn
The energy flu
The unit of ene
f �
d
d
N
A
j
f= d
dt
�
d
d
=
E
A
Y = d
d
y
t
oton fluence f is cm–2.
ence rate is defined as the photon fluence per unit time:
(6.2)
oton fluence rate is cm–2·s–1.
y fluence and energy fluence rate
gy fluence Y describes the energy flow in a photon beam and is 
amount of energy dE crossing a unit area dA:
(6.3)
rgy fluence Y is MeV/cm2.
noenergetic beam, dE is the number of photons dN times their 
 the energy fluence Y in terms of photon fluence f is:
(6.4)
ence rate Y is defined as the energy fluence per unit time:
(6.5)
rgy fluence rate is MeV·cm–2·s–1.
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
6.2.3. Air kerma in air
For a monoenergetic photon beam in air the air kerma in air (Kair)air at a 
given point away from the source is proportional to the energy fluence Y or 
photon fluence f as follows:
where (mtr/r)air
hn.
Kerma K
radiative kerm
K = Kcol +
For mono
to Y and f thro
where (mab/r)a
energy hn. Of
denoted as men
The mass
coefficient (mab
where is the
charged partic
deposited in t
energies below
( )Kair air
K col =y
m
r
mab =
g
163
(6.6)
 is the mass–energy transfer coefficient for air at photon energy 
 consists of two components: the collision kerma Kcol and the 
a Krad:
 Krad (6.7)
energetic photons in air the collision kerma Kcol is proportional 
ugh the following relationship:
(6.8)
ir is the mass–energy absorption coefficient for air at photon 
ten in the literature the energy absorption coefficient mab is 
. 
–energy transfer coefficient (mtr/r) and mass–energy absorption 
/r) are related through the following relationship:
(6.9)
 radiative fraction (i.e. the fraction of the energy of secondary 
les (electrons) that is lost to bremsstrahlung rather than being 
he medium). For low atomic number Z materials and photon 
 1 MeV, the radiative fraction , (µtr/r) ª (µab/r) and K ª K
col.
htr
air
tr
air
 = ÊËÁ ˆ˜¯ = ÊËÁ ˆ˜¯y mr f n mr
hab
air
ab
air
 
ÊËÁ ˆ˜¯ = ÊËÁ ˆ˜¯mr nf mr
r
tr -( )1 g
g ª 0
CHAPTER 6
164
6.2.4. Exposure in air
The collision air kerma in air is related to exposure in air X
through the following relationship:
(6.10)
where (Wair/e),
produce an ion
The spec
2.58 × 10–4 C/k
with the expos
6.2.5. Dose 
The conc
free space’, w
output of a rad
tions involving
‘dose to small 
measurement o
orthovoltage a
therapy.
The step
air’ D′med at po
ionization cham
where MP is th
corrected for 
recombination
( )Kair
col
air
( ) / )K X W eair
col
air air(=
( )Kair
col
air
MP Æ( )1
 as discussed in Section 9.1.3, is the average energy required to 
 pair in dry air (33.97 eV/ion pair). 
ial unit of exposure is the roentgen (R), while the SI unit is 
g with 1 R = 2.58 × 10–4 C/kg. Thus:
(6.11)
ure X given in roentgens.
to small mass of medium in air
ept ‘dose to small mass of medium in air’, also known as ‘dose in 
as introduced by Johns and Cunningham to characterize the 
iation unit and to gain a reference dose for dosimetric calcula-
 tissue–air ratios (TARs) and peak scatter factors (PSFs). The 
mass of medium in air’ is designated as D′med and is based on a 
f the air kerma in air. The concept has gained widespread use in 
nd 60Co therapy, but is of limited use in megavoltage linac beam 
s involved in determining the ‘dose to small mass of medium in 
int P in a radiation beam from a signal MP measured with an 
ber centred at point P in air are:
(6.12)
e signal measured with an ionization chamber at point P and 
influence quantities such as air temperature, air pressure and 
 loss (see Section 9.3). The ionization chamber should have an 
. . .X
air
C
kg R
 
J
C
cGy
R
= ¥ÊËÁ ˆ˜¯ = ÊËÁ ˆ-2 58 10 33 97 0 8764 ¯˜¯ X 
X K K KmP air air air med air ( ( Æ Æ Æ Æ( ) ( ) ( ) (( ) ) )2 3 4 5D )) med¢D
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
appropriate buildup cap and an exposure calibration coefficient in air NX or an 
air kerma in air calibration coefficient NK.
● Step 1: Determine XP , the exposure at point P, through:
XP = MP NX (6.13)
● Step 2: D
Alternati
chamber
(Kair)air =
● Step 3: D
other ma
where 
absorptio
● Step 4: D
around P
particle e
(Kmed)air 
where k(
attenuati
(µab/r)med
the dens
( )Kair air
( )K mD air
(
k r( )med ª
165
etermine (Kair)air, the air kerma in air at point P, through:
(6.14)
vely, (Kair)air may be determined from MP directly, if NK for the 
 is known, as follows:
 MPNK (6.15)
etermine collision kerma to Dm, an infinitesimal mass of any 
terial (e.g. water), in air from:
(6.16)
 is the ratio of spectrum averaged mass–energy 
n coefficients for Dm and air.
etermine collision kerma to a spherical mass of medium centred 
 and having a radius rmed just large enough to provide charged 
quilibrium (CPE) at point P:
= (K
Dm)air(rmed) (6.17)
rmed) is a correction factor accounting for the photon beam 
on in the spherical mass of medium and approximated as:
(6.18)
 in Eq. (6.18) is the mass–energy absorption coefficient and r is 
ity of the medium. For water, which is usually chosen as the 
X P0.876
cGy
R
=
( )K
mD
air air
ab
air
 = ÊËÁ ˆ˜¯mr
/ )m rab air
Dm
e
rab
med
med-ÊËÁ ˆ˜¯mr r
CHAPTER 6
166
medium, k(rmed) ª 0.985 for 
60Co photons and approximately 1 for lower 
photon energies.
● Step 5: ‘Dose to small mass of medium in free space’ D′med is obtained 
from the following relationship:
(6.19)
where b 
60Co, 137C
equal to 
The prod
is usually
the ‘dose
written a
D′med = fm
6.3. PHOTON
Photon s
monoenergetic
sources used 
isotope source
● An isotro
direction
depends 
● A plot of
referred 
and a he
respectiv
number o
¢ = = ÊÁ ˆ˜D K X k rmed med air ab med P med( . cGyb b m) ( )0 876
0 876. 
cG
R
is a proportionality constant equal to 1.003, 1.001 and 1.0 for 
s and X rays below 350 kVp, respectively. Often b is assumed 
1, even for 60Co g rays.
uct:
 referred to as the roentgen to cGy conversion factor fmed, and 
 to small mass of medium in air’,assuming that b ª 1, can then be 
s:
ed Xk(rmed) (6.20)
 BEAM SOURCES
ources are either isotropic or non-isotropic and they emit either 
 or heterogeneous photon beams. The most common photon 
in radiation oncology are X ray machines, teletherapy radio-
s and linacs.
pic photon source produces the same photon fluence rate in all 
s, while the photon fluence rate from a non-isotropic source 
on the direction of measurement.
 number of photons per energy interval versus photon energy is 
to as a photon spectrum. Photon spectra for a monoenergetic 
terogeneous photon beam are shown in Figs 6.1(a) and (b), 
ely. The area under the curve in Fig. 6.1(b) represents the total 
f photons in the beam:
Ë ¯ airR r
y
 ab
air
medm
r
ÊËÁ ˆ˜¯
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
(6.21)
● All photons in a monoenergetic photon beam have the same energy hn
(Fig. 6.1(a)). Photons in a heterogeneous X ray beam form a distinct 
spectrum, with photons present in all energy intervals from 0 to a 
maximum value hnmax, which is equal to the kinetic energy of electrons 
striking t
● In Fig. 6
photons, 
bremsstr
● g ray sou
beams, w
neous ph
● Narrow m
half-value
other han
HVL: lar
hardening
beam soft
6.4. INVERS
In extern
point sources 
schematically i
and a square fi
df
dhn
0
FIG. 6.1. Typic
f
f n
n
n= ( )Ú d d dhh h 
167
he target (Fig. 6.1(b)).
.1(b) the two spikes in the spectrum represent characteristic 
while the continuous spectrum from 0 to hnmax represents 
ahlung photons.
rces are usually isotropic and produce monoenergetic photon 
hile X ray targets are non-isotropic sources producing heteroge-
oton spectra.
onoenergetic photon beams will have identical first and second 
 layers (HVLs). In narrow heterogeneous photon beams, on the 
d, the second HVL will be either larger or smaller than the first 
ger in the superficial and orthovoltage range because of beam 
 effects and smaller in the high megavoltage range because of 
ening effects.
E SQUARE LAW
al beam radiotherapy, photon sources are often assumed to be 
and the beams they produce are divergent beams, as shown 
n Fig. 6.2. Let us assume that we have a photon point source S 
eld with side a (area A = a2) at a distance fa from the source. At 
hn
(a)
hn
df 
dhn
(b)
0 hnmax
al spectra for (a) monoenergetic and (b) heterogeneous photon beams.
CHAPTER 6
168
a distance fb we then have a square field with side b (area B = b
2), and the two 
fields are geometrically related as follows:
or (6.22)
where b is the
edge.
The phot
distance fa and
A
Area B = b
FIG. 6.2. Div
from the sourc
tg
a
f
b
fa b
b = =/2 /2 
a
b
f
f
a
b
= 
 angle between the beam central axis and the geometric beam 
on source S emits photons and produces a photon fluence fA at 
 a photon fluence fB at distance fb. Since the total number of 
Photon
source
S
fa
fb
rea A = a2
2
b
a
b
Central
axis
ergent photon beam originating in a photon point source. At distance fa
e S the field size is A = a2, at distance fb the field size is B = b
2.
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
photons Ntot crossing area A is equal to the total number of photons crossing 
area B (assuming no photon interactions take place in air between area A and 
area B), we can write:
Ntot = fAA = fBB
and
The phot
distance from 
will be exactly
Since at 
(Kair)air and ‘do
to the photon
quantities X, (
6.5. PENETR
PHANTO
A photon
inverse square
on the other ha
attenuation an
These three e
complicated pr
A direct
essentially im
treatment it is 
known precise
several functio
the known dos
f
f
A
B
B
A
=
X f
X f
a
b
( )
( )
=
169
(6.23)
on fluence is thus inversely proportional to the square of the 
the source. For example, if fb = 2fa then the photon fluence at B
 1/4 of the photon fluence at A (i.e. fB = fA/4).
a given point P in air the exposure in air X, air kerma in air 
se to small mass of medium in air’ D′med are directly proportional 
 fluence at point P, it is reasonable to conclude that the three 
Kair)air and D′med all follow this inverse square law behaviour:
(6.24)
ATION OF PHOTON BEAMS INTO A 
M OR PATIENT 
 beam propagating through air or a vacuum is governed by the 
 law; a photon beam propagating through a phantom or patient, 
nd, is affected not only by the inverse square law but also by the 
d scattering of the photon beam inside the phantom or patient. 
ffects make the dose deposition in a phantom or patient a 
ocess and its determination a complex task.
 measurement of the dose distribution inside the patient is 
possible, yet for a successful outcome of patient radiation 
imperative that the dose distribution in the irradiated volume be 
ly and accurately. This is usually achieved through the use of 
ns that link the dose at any arbitrary point inside the patient to 
e at the beam calibration (or reference) point in a phantom.
b
a
b
a
f
f
= =2
2
2
2
 
K f
K f
D f
D f
fa
b
a
b
( ( ))
( ( ))
( )
( )
= ¢¢ =air airair air medmed bbafÊËÁ ˆ˜¯ 2
CHAPTER 6
170
The functions are usually measured with suitable radiation detectors in 
tissue equivalent phantoms, and the dose or dose rate at the reference point is 
determined for, or in, water phantoms for a specific set of reference conditions, 
such as depth, field size and source to surface distance (SSD), as discussed in 
detail in Section 9.1.
A typical dose distribution on the central axis of a megavoltage photon 
beam striking a patient is shown in Fig. 6.3. Several important points and 
regions may be
delivers a cert
rapidly, reache
exponentially 
techniques fo
Section 6.13.
0
Ds
Dmax = 100
Dex
FIG. 6.3. Dose d
dose at the beam
dose maximum o
percentage depth
referred to as the
 identified. The beam enters the patient on the surface, where it 
ain surface dose Ds. Beneath the surface the dose first rises 
s a maximum value at depth zmax and then decreases almost 
until it reaches a value Dex at the patient’s exit point. The 
r relative dose measurements are discussed in detail in 
Source
0
Patient
zmax zex
zmax Depth (z) zex
eposition from a megavoltage photon beam in a patient. Ds is the surface 
 entrance side, Dex is the surface dose at the beam exit side. Dmax is the 
ften normalized to 100, resulting in a depth dose curve referred to as the 
 dose (PDD) distribution. The region between z = 0 and z = zmax is 
 dose buildup region.
EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS
6.5.1. Surface dose 
For megavoltage photon beams the surface dose is generally much lower 
than the maximum dose, which occurs at a depth zmax beneath the patient’s 
surface. In megavoltage photon beams the surface dose depends on the beam 
energy and field size.
The larger the photon beam energy, the lower the surface dose, which for 
a 10 × 10 cm2 f
cobalt beam, 1
For a given bea
The low 
the skin sparin
beams over ort
tumours.
Orthovol
since their dos
equal to the m
The surfa
chambers for 
positive and 
Section 6.13).
The surfa
● Photons 
● Photons 
● High ene
shielding
6.5.2. Buildu
The dose
megavoltage p
from the rela
(electrons and
interactions (p
deposit their k
● In the re
CPE doe
collision 
reached 
171
ield typically amounts to some 30% of the maximum dose for a 
5% for a 6 MV X ray beam and 10% for an 18 MV X ray beam. 
m energy the surface dose increases with the field size.
surface dose compared with the maximum dose is referred to as 
g effect and represents an important advantage of megavoltage 
hovoltage and superficial beams in the treatment of deep seated 
tage and superficial