Group Title: repetitive integral measurement technique for X and gamma radiation dosimetry and depth dose scanning
Title: A repetitive integral measurement technique for X and gamma radiation dosimetry and depth dose scanning
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Title: A repetitive integral measurement technique for X and gamma radiation dosimetry and depth dose scanning
Physical Description: x, 196 leaves. : illus. ; 28 cm.
Language: English
Creator: Fitzgerald, Lawrence Terrell, 1938-
Publication Date: 1974
Copyright Date: 1974
Subject: Electronic measurements   ( lcsh )
Radiation -- Safety measures   ( lcsh )
Gamma rays -- Therapeutic use   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 190-194.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098334
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000585243
oclc - 14202294
notis - ADB3876


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To my Mother and late Father who worked so hard and made

many sacrifices that I might have the

opportunity of an education.


I would like to express my appreciation to the mer.,iers of my super-

visory conmrittee for their assistance in this investitiation anJ their

support during miy graduate study. Special appreciation is given to Dr.

Walter Mauderli, my committee chairman, for his guidance in all phases

of this vxork. My committee co-chairnan, Dr. Emirett Bolch, is greatfully

acknowledged for his guidance and advise throughout my graduate study.

Sincere thanks go to M r. John Preisler for his many skills and sug-

gestions in fabrication of mechanical apparatus used in this investi-

gation. The assistance of the staff of the North East Regional Data

Center is acknowledged. My sincere appreciation goes to Mrs. Hughlene

Sadler for her assistance in typing working copies and to Mrs. Juanita

Bradley for her excellent job of typing the final manuscript.


ACKNOWLEDGEMENTS ...................................................

ABSTRACT ...........................................................


1 INTRODUCTION ..............................................

2 RADIATION DTTECTiON AND DE'TH DOSE ........................

Phantoms and Depth Dose .................................

Chemical Change .........................................

Film ..................................................
Chemical Dosimeters ...................................

Heat Production .........................................

Thermolumincsccnce ......................................

Light Production ........................................

Electrical ..............................................

Solid State ...........................................
Gas Detectors .........................................

Summary .................................................

3 THE 10NIZATION MrET OD .....................................

Ionization Chambers and Radiation Measurement ...........

Measurement of Small Currents ...........................

Measurement Methods .....................................

Depth Dose Scanning .....................................

Summary .................................................





















MEASUREMENT METHODS ...................................... 39

The Lateral Dose Function ............................... 39

Depth Dose Scanning and the Rate Measurement ........... 41

Limitations of the Rate Measurement Method ............. 46

The Scanning Speed ................................... 46
The Current Magniitude .................................. 47
The Chamber Volume ..................................... 47
The Time Constant ...................................... 48

Correction Technique ..................................... 49

The Integral Method .............................. ...... 51

The Repetitive Integral :easurerent rMthod .............. 54

Constant and Linear Current ........................... 57

Summary ...................................... ......... 58

IMEASUI'E FJ'N"T METHODS ...................................... 60

The Step Function Response .............................. 60

Point Detector Response ............................... 62
Cylindrical Detector Response .......................... 66
The Size of the Measuring Interval .................... 71

Lateral Dose Function Response .......................... 73

The Effect of Scanning Speed ............................ 79

Advantages of the Repetitive Integral
Measurement cM thod .................................... 81

Elimination of the Effect of the Time Constant ........ 81
Application to Pulsed Radiation Sources .............. 82
Elimination of Amplifier Zero Drift .................. 82
Reduction of Signal Noise ............ .................. 83
Independence of Scanning Speed ........................ 83

Summary ............................. ...................... 84


The Integration Circuit ................................ 86


The Switching Electrometer .............................. 88

The Switching Method .................................. 88
Reset Network Analysis ................................ 92

The Repetitive Integral Amplifier Circuit ............... 96

The Operational Arplifier ............................. 96
The Resetting Field-Effect Transistors ............... 98
The Compensating Pulse Level Buffer ................... 98
The Inverting Operational Amplifier ................... 98
The Input Protection Diodes ........................... 99
The Voltage-Divider Gain Adj'isLnent ................... 99

Amplifier Construction .................................. 105

Amplifier Control Logic ................................. 108

The Digital Clock ..................................... 109
The Switching Logic ................................... 110

Amplificr Testing .................................... ... 319

Linearity Testing ..................................... 119
Stability Testing ..................................... 20

Electrical Noise ........................................ 122

Power Hum ............................................. 123
iicrophonics .......................................... 123
Amplifier Drift ....................................... 124
Input Leakage ......................................... 125
Ground Loops .......................................... 125
Random Noise .......................................... 126
Amplifier Noise ....................................... 128

Summary ................................................. 133

7 THE DEPTH DOSE SCANNING SYSTEM ............................ 135

The Mechanical Scanning System .......................... 136

Stepping Motors ........................................ 136
Drive Assembly ....................................... 137
The Scanning Logic .................................... 138
The Water Phantom ..................................... 149
System Testin ......................................... 153
Adaptive Scanning Rate................................. 154

The Data Processing and Recording System ................ 155

The Analog-to-Digital Converters ..................... 156


The Shift Registers ................................... 156
The Optical Couplers .................................. 158
The Arithmetic Processing Units ....................... 159
Binary-to-Binary-Coded-Decinal Converters ............. 159
The Data Processing Circuit ........................... 159
The Magnetic Tape Recorder ............................ 162
System Testing ........................................ 163

The Detector and Amplifier System ....................... 163

Detector Construction ........... ......... ...... ....... 16',
Design Considerations ................................. 167
System Testing ........................................ 167

The Total System ........................................ 168

Computer Processing .................................... 171

Summiry .................................................. 176

8 RESULTS AND CO'CLUSIO:IS ................................... 178

Depth Dose Scanning S stemi Results ...................... 178

Conclusions ............ ................................ 184

BIBLIOGRAPHY ....................................................... 190

BIOGRAPHICAL SKETCH ...................................... .......... 195


Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy



Lawrence Terrell Fitzgerald

June, 1974

Chairman: Walter Mauderli, D. Sc.
Co-Chairman: W. Ermett Bolch, Ph. D.
Major Department: Eiviroimnental Engineering

The purpose of this study was to iL.prove measuring techniques in

depth dose scanning of a radiation treatment field with regard to in-

creasing accuracy, speed of measurement and the design of an easily

transportable system. A new measurement technique and a new detector

transport system have been developed to fulfill these objectives.

The new measurement technique, called the repetitive integral Method,

estimates the input current flowing from a radiation detector by repeti-

tive cycles of integrating and resetting over short time intervals and

has been shown theoretically to be superior to the standard rate

measurement method for the real-time dynamic current measurements re-

quired in depth dose scanning. Electronic instrumentation which

functions in the repetitive integral mode has been developed and experi-

mental results follow the theory. The repetitive integral measurement

method has the following advantages:

1. The effect of the amplifier time constant is eliminated.

2. The method is better suited for measurement of pulsed radiation

3. Long-term amplifier drift may be eliminated.

4. The integrating circuit acts to attenuate higher-frequency noise.

5. Amplifier thermal-noise output is negligible.

6. The method is independent of scanning speed.

The new detector transport system which uses stepping motors and

digital logic guarantees the accuracy and reproducibility of the new

depth dose scanning system. Digital techniques permit precise detector

positioning to within a small fraction of a millimeter and ensure

perfect correlation between detector position and amplifier measurement


Application of the repetitive integral measurement method in con-

junction with the detector transport system enables accurate and repro-

ducible measurements to be made at greater scanning speeds than previ-

ously possible. The depth dose scanning system developed is completely

self-contained, is housed in two units which are easily transported in

a small van and provides a means of rapidly determining complete depth

dose distributions for a variety of radiation therapy equipment.



Shortly after the earliest therapeutic applications of x-rays,

it became evident that some measure of absorbed energy, or dose, was

required to prevent over-treatment and to enable the compilation of

treatment results which would be transferable to other patients. As

the energies of the radiation used in x-ray therapy increased the need

developed for dose data at various depths below the skin surface.

These doses below the skin have come to be called depth doses.

Complete depth dose determination for a radiation treatment

field requires measurement at many points throughout the field.

Scanning devices which move a radiation detector through a radiation

field have been designed for obtaining depth dose data automatically.

These scanning devices have been slow in operation, limited in

accuracy and so large that transport from one location to another

has been difficult.

The development of computer techniques in x-ray treatment

planning during the 1960s has made possible the computation of

absorbed doses from very complicated treatment plans and has provided

a means of computation for individual patients. It is generally

agreed among radiation therapists that computerized treatment planning

has improved radiation therapy. Over-treatment complications may be

avoided and new treatment plans, not previously used because of

calculation complexity, may be computed. The computer techniques

now available make use of all the known physical parameters concerning

radiation absorption in tissue, with the limiting factor in dose

determination being the accuracy of the basic depth dose data for

the radiation fields used in treatment.

The aim of this work has been the improvement of measuring

techniques used in depth dose scanning. Primary consideration has

been given to increasing the accuracy and speed of measurement and to

designing a system easily transportable. This has been accomplished

with the use of digital design techniques and a new measuring method.

All testing has been limited to cobalt-60 gamma radiation, but

the results also apply to the :-rays produced by other types of

therapy equipment. The radiation detection system has been designed

to be compatible with the radiation intensities encountered in

radiation therapy equipment. All references to scanning in later

chapters pertain to depth dose scanning and the term radiation always

refers to x or gamma radiation or to both collectively.

Reviews of the development of radiation therapy and the various

methods of depth dose measurement are given in Chapter 2. Chapter 3

discusses the ionization measurement method and its limitations in

depth dose scanning. A new measurement technique is developed and

described in Chapters 4 and 5. A new electrometer amplifier is dis-

cussed in Chapter 6. Chapter 7 discusses the mechanical scanning

design and the integration of mechanical and electronic systems into

the complete depth dose scanning system. Measurement results, system

evaluation and conclusions are given in Chapter 8.



Professor Wilhelm Conrad Roentgen made his historic discovery of

x-rays on Novenber 8, 1895 and published his results soon thereafter.1

Roentgen had used his hand in some of his experiments to test the pene-

trating power of x-rays; a fact which suggested a possible application

in medicine. Just 23 days following the public announcement of

Roentgen's discovery, Grubbe,2 a businessman-inventor, performed the

first x-ray therapy on a breast carcinoma in Chicago. The treatment

was suggested by the physician treating Grubbe for x-ray dermatitis

which he had contracted in duplicating Roentgen's experiments. Grubbe

had the dubious distinction of being the first to use x-rays thera-

peutically and the first to experience the harmful effects of excessive

x-ray exposure.

In the early days of radiation therapy, skin reactions were ob-

served in both physician and patient, making it evident that some unit

of dose for specification of quantity was necessary. The dosage was at

first judged by the effect on the skin, with erythema and epilation dose

becoming the mainstay of clinical radiotherapy. No information concern-

ing the dose received at any point under the skin was available. The

skin dose was of primary importance as it was the limiting factor in

therapy. The early x-ray apparatus used no beam filtration and

operated at low voltage; so the amount of soft radiation which was

readily absorbed by the skin was quite large.

Radiation therapy is generally considered to have come of age

around 1920 when x-ra: tubes had been improved so that they could

tolerate 200 kv and the value of beam filtration had been recognized.

Beyond this point, progress was rapid in the development of higher-

voltage machines which produced radiation with greater penetration,

and the uses of x-radiation in therapy continued to grow. Already in

1936 Elward3 reported that there were over 400 different diseases

which were treated with x-ray therapy. As the uses of x-ray therapy

have expanded and as higher-energy beams have been developed, there

have been demands for more and better dose determination. The skin

dose is no longer adequate as it was in the early days because with

higher-energy beams the doses below the skin may be the limiting

factor in therapy. Doses at points throughout the treatment volume

are thus required. A most interesting review of the development of

radiation dosimetry may be found in papers by Glasser4 and Victoreen.5,6

Phantoms and Depth Dose

As no direct measurement of the radiation received at the tumor

is possible it must be determined by measurement in simulated tissue.

The tissue-simulating material, called a phantom, should be a material

which absorbs and scatters radiation as does human tissue. Spiers7

pointed out that a good simulator of tissue should have the same

density, same atomic number, and contain the same number of electrons

per gram as tissue. Dry pressed wood of Masonite or hardboard have

been used as phantoms, but these are not reproducible from one therapy

center to another and do not absorb exactly as tissue. Several other

reports8'9 have described solid phantom materials which are tissue

equivalent. Pressed wood and other solid materials are very limited

in their usefulness since the measuring probe may not be moved from

one point to another within the medium. Water and soft tissue have

the same effective atomic number10 of 7.42, the same density and 3.34

x 1023 and 3.36 x 1023 electrons per gram respectively. The radiation

absorption of water and soft tissue is thus essentially the same and

water is usually the phantom choice since it is readily available, is

of constant consistency and allows movement of the measurement probe

within the mediur.. Water phantoms, however, require the use of probes

sealed against moisture.

Water phantoms are generally used as simulators of tissue when

the radiation dose is derived at some depth below the skin. Measure-

ments made in water are usually specified as a ratio of the recorded

value at the depth of interest to the value at some other fixed point.

Johns and Cunningham11 define the percentage depth dose at a depth d

as follows:

dose at depth d
Percentage depth dose at depth d = 100
dose at maximum buildup

At energies less than 400 kv the depth of maximum buildup is practically

zero and the surface dose is used in the definition.

Although many different instruments have been used in radiation

detection and in depth dose determination, the operating principles

are few. The basic requirement of any radiation detector is that it

interact with radiation so that its response is proportional to the

radiation dose. Table 1 classifies the primary types of radiation

detectors according to the detector medium and the effect produced

in the detector. Each of the basic types of instrumentation will be

discussed briefly, particularly for therapy applications in depth dose

determination with x and gamna radiation.

Chemical Change


Photographic emulsions have been used for radiation dosimetry

from the very discovery of x-rays. Film is a rather unique dosireter

as it allows dosimetry of ionizing radiation over dose ranges of

millirads to m.cgarads, over tine periods of microseconds to months and

over areas of square microns to square meters. The small thickness of

film makes it particularly suited to radiation dosimetry as it can be

introduced into a radiation field with a minimum of spatial distortion.

Film has a high resolution, an advantage which is used in alpha and

beta particle autoradiography.

In the dosimetry of x and gamma radiation by photographic film,

the film is exposed by secondary electrons produced by one or more of

the primary processes (photoelectric effect, Compton effect, pair

production) whereby x and gamma radiation interact with matter. Johns

and Cunningham11 and Hendee12 describe the interactions of x and gamma






Chemical Dosimeter


Thermoluminescent Dosimeter

Scintillation Counter

Solid State
Ionization Chamber
Geiger Counter
Proportional Counter

Photographic Emulsion
Solid or Liquid

Solid or Liquid


Crystal or Liquid


Chemical Change

Heat Production


Light Production

(Pulse or Current)

radiation in detail. The important fact concerning the interaction of

x and gamma radiation with the 'ilm emulsion is that the mass attenu-

ation coefficient for the photoelectric effect varies with the cube of

the atomic number. The film emulsion is made up largely of silver

bromide which has a high atomic number. Thus a large amount of the

energy deposited in the silver emulsion is from low-energy photons.

The primary defect in film dosimetry of x and gamma radiation is the

dependence of sensitivity on photon energy.

Photographic methods with plates and paper were used in the early

1900s for dose determination. Strips of photographic paper were placed

on the patient's skin in the treatment area during the time of treatment

with x-rays. The degree of blackening on the paper was determined by

comparison with a standard chart. Paper strips covered with different

thicknesses of aluminum were used to estimate depth dose. These

methods were unsatisfactory since standard paver, standard developer,

standard temperature and a standard scale were required. Also the

method gave results only after the radiation dose had been given. The

energy dependence of film was especially important at that time, as no

filtration was used, and the beam was composed largely of low-energy


The energy dependence of film has been overcome to some extent by

selective filtering and the method has again been used for depth dose

determinations. Granke et al.13 have used film dosimetry for determi-

nation of tissue doses with 2 Mev x-rays by placing sheets of film

between different sections of an Alderson14 RANDO (RAdiation ANalog

DOsimetry) phantom, a tissue equivalent phantom containing a human

skeleton. Isodose curves of depth dose values for different radiation

fields were also produced with film dosimetry. Loevinger and SpiralS

used film dosimetry in radium therapy and developed a method combining

multiple films to determine the dose for a total treatment.

Even under the best of conditions, film dosimetry presents

significant problems. Irregular emulsion thickness contributes to

varying sensitivity over different portions of the film. Variations in

film processing and storage conditions from one laboratory to another

make it difficult to exchange results with other researchers. For

these reasons and the problem, of energy dependence film dosimetry is

not the method of choice when accurate results are required. Filn

dosimetry has been most useful in personnel monitoring where highly

accurate results are not required. Film dosimetry as a method of depth

dose determination for x and gamma radiation has been replaced with

more reliable and easier techniques.

Chemical Dosimeters

With chemical dosimeters the radiation dose is determined by the

chemical change in a particular medium. Roentgen1 in his first report

of the discovery of x-rays called attention to chemical reactions

created by the rays. Very early dosimetry used crude chemical dosime-

ters which changed color on exposure to the soft x-rays then used in

therapy and diagnosis. In 1902 small discs of fused potassium chloride

and sodium carbonate which became discolored on radiation exposure were

used and various colorations were related to erythema doses. Barium

platinocyanide formed the basis of a dosimeter developed in 1904 and

was used extensively for many years. Again a color change indicated

the degree of x-ray exposure. This system was highly energy dependent

because of the high atomic number of the dosimeter material. These

early chemical systems were rather insensitive and required exposures

of 1,000 roentgens or more to produce visible changes. Due to these

problems and the rapid growth of the ionization method, interest in

chemical dosimetry waned, but was rekindled with the advent of atomic

weapons, nuclear reactors and the use of high-intensity radiation

sources. These developments created a need for dosimeters for measuring

large doses of x and gamma radiation and have provided an impetus to

further research in the area of chemical dosimetry.

The Fricke dosimeter, described by Fricke and Morse,16 is a

ferrous-ferric sulfate systtn whose principal drawbacks are a lack of

sensitivity and a dependency on linear energy transfer of the radiation.

The Fricke dosimeter is generally considered the best for 4 40 kilorad

doses of x and gamma radiation. It has been accepted as a standard in

radiation chemistry and it may be used to measure dose in absolute units

to within 1 2 percent. Methods of preparing a Fricke dosimeter are

given in the National Bureau of Standards Handbook 85.17 The Fricke

dosimeter has been recommended for calibration of high-energy electron

beams used in radiation therapy.18

Chemical dosimetry is now used principally for measuring higher

doses than those encountered in radiation therapy but has found some

clinical application in determining the doses received by interior body

structures, since the dosimeter may be inserted in body cavities. An

aqueous solution enclosed in a suitable container is excellent for

biological dosimetry since it closely approximates the density and

atomic composition of biological tissues. Chemical dosimeters have

been particularly useful for x and gamma ray dosimetry in animals

exposed in atomic field tests.

Stenstrom and Lohmannl9,20 used a chemical dosimeter derived from

methylene blue for determination of depth doses but, in general,

chemical dosimeters have found very little use for depth dose measure-

ments in radiation therapy primarily due to .their insensitivity.

However, some researchers have used the ferrous-ferric system.21

Presently chemical dosimeters, which may be used for doses as low as

400 rads,22 are available and thus are sensitive in the range of

therapy doses.

Hleat Production

Calorimetry has been employed to measure the heat produced from

the dissipation of energy by radiation. A calorimeter contains an

absorber specifically designed to convert all or part of the incident

radiation into heat. The absorber contains a temperature-sensitive

element and is thermally insulated. Calorimetry permits measurements

of radiation energy in terms of fundamental energy units thus providing

an absolute basis for evaluation and comparison of experiments or


Calorimeters have for many years been applied to many different

problems but their use with ionizing radiation has been limited due

to the small magnitude of energy involved. The calorimetric method

has a primary advantage over other dosimetric methods as it measures

the energy deposited directly whereas other methods use secondary

processes. Calorimeters also have some disadvantages. Their sensitivity

is adequate for radiation intensities and dose rates used in diagnostic

and therapy but is insufficient for use in radiation protection. Also

in some types of radiation processes energy, which should be measured,

may be lost and in some processes energy is gained from sources other

than the radiation beam. Scattering of radiation out of the calorimeter,

photonuclear reaction or the emission of a penetrating neutron,

bremsstrahlung production by secondary electrons and endothermic or

exothermic chemical reactions are such processes.

Calorimetry was used by early investigators in radiation measure-

ment. Curie and Laborde23 used the method in the first determination

of the rate of energy release by radium disintegration. Stahel24

employed the calorimetric method in measuring the energy absorbed by

water on exposure to x and gamma radiation. The skin erythema dose in

humans was related to these measurements, given in ergs per cubic

centimeter. Genna and Laughlin25 demonstrated the determination of

absorbed doses in radiation therapy with cobalt by the calorimetric

method. Rollo et al.26 have used calorimetry for measurement of total

energy deposition of Grenz rays. The calorimetric method has not played

a large role in depth dose measurement primarily because the ionization

method provides a simpler way of measurement. As more interest is

expressed in absolute units the calorimeter will surely play a role as

a primary standard for these units.


Thermoluminescent dosimeters have been classified by Fowler and

Attix27 as solid state integrating dosimeters. This broad classification

includes photographic film, solid scintillators and plastic films

containing dye. Semiconductor devices could also be included in this

classification but they shall be discussed in a separate section.

Nonelectrical solid state dosimetry systems may be further divided into

two categories: destructive readout and nondestructive readout. The

nondestructive readout systems are those in which the effect produced

by the radiation is not destroyed by measurement of the effect.

Nondestructive systems may have their radiation effect measured any

number of times. Destructive readout systems may have their radiation

effect measured only once as the method required in reading destroys

the effect.

Nondestructive systems include glasses, plastics and dyes which

change color upon radiation exposure. Other nondestructive effects

are radiophotoluminescence of phosphate glass, degradation of

luminescence of anthracene and other crystals and a change in electron

spin resonance in alanine. Most of the nondestructive system materials

are useful only for doses greater than 104 rads but some dyes, phosphate

glass and alanine are suitable for doses in the range given in radiation

therapy (100 to 400 rads). A dyed polymethyl methacrylate, called

Perspex Red 400,* which becomes black on irradiation is commercially

available. It has been found useful for x-ray and electron beam dose

for depth dose measurements in x-ray contact therapy where the dose

rate is very high. Phosphate glass has a high effective atomic number

and is thus quite energy dependent. Bradshaw et al.28 used powdered

*May be obtained from Imperial Chemical Industries Ltd., Plastics
Division, Welwyn Garden City, Herts, England.

alanine, an amino acid, for depth dose measurements in animals and

satellites. This method is difficult due to the very small electron

spin resonance signals produced. Nondestructive readout systems for

radiation dosimetry are in general not suitable for routine depth

dose measurements in the range of therapy doses.

Destructive readout systems include the thermoluminescent

materials and infrared-stimulated luminescence. Many of these systems

are suitable for measurement from below 10 rads to 104 rads. The

thermoluminescent materials have had the greatest impact of the two

systems on radiation dosimetry methods.

Many materials are thermoluminescent but only a few have been

found useful for therapeutic dosimetry applications. The ideal thermo-

luminescent phosphor must have a strong light output and be able to

hold trapped electrons for some period of time at a temperature suit-

able for the particular dosimetry application. The three most impor-

tant phosphors used in radiation dosimetry in the range of therapy

doses and lower are calcium sulfate, calcium fluoride and lithium


Calcium sulfate was used in depth dose measurement in body cavi-

ties of experimental animals as early as 1954. This phosphor has the

remarkable ability to measure exposures in the microroentgen range.

Its main disadvantage is significant "fading" at room temperature, a

factor which apparently is dependent upon the method used in phosphor


Calcium fluoride has a linear response to gamma radiation from

a few milliroentgens to 500 roentgens. This phosphor does not have

significant problems of "fading" but its response is energy dependent

at energies below 0.1 Mev.

Lithium fluoride dosimeters may be found in a number of shapes

and sizes and are widely used in clinical dosimetry. Lithium fluoride

dosimeters are approximately tissue equivalent and are of sizes that

may be placed in body cavities or in phantoms for depth dose studies.

Vacirca ct al.29 have reported a film-thermoluminescence system for

determining body doses in diagnostic radiography. Thermoluminescent

dosimeters have been used by Puite et al.30 for the purpose of

intercalibration of x-ray units at many different institutions so that

experimental results may be transferrable. The dosimeters were ideal

for this purpose as they could be sent from one institution to another

through the postal service.

The search for other useful thermnolurminpscent materials continues

with the hope that dosimeter "fading," which is currently a problem,

may be overcome.

Dixon and Watts31 have reported on barium fluoride as a thermo-

luminescent dosimeter which exhibits good characteristics, but "fading"

is still a serious problem. Jayachandran32 reports that lithium

borate is more tissue equivalent than other thermoluminescent dosime-

ters and should be evaluated for clinical use. Scarpa33 has suggested

that beryllium oxide may be a useful thermoluminescent material.

Light Production

One of the earliest means of radiation detection was by scin-

tillation counting. Rutherford in his experiments with alpha particles

used a zinc sulfide crystal as a primary detector and visibly observed

the light flashes produced by the alpha particles striking the crystal.

This was very tedious and with the development of gas-filled detectors

the scintillation method fell into disuse. Interest in the method was

revived in the late 1940s and phenomenal development has taken place.

Many solid and liquid substances emit light when exposed to x,

alpha, beta or gamma radiation. Photomultiplier tubes have made it

possible to detect light flashes that correspond to the absorption of

a single quantum or a single charged particle and stimulated the search

for better scintillators. Scintillators may be classified as organic

crystals of the hydrocarbon type, inorganic crystals and powders of

the alkali halide.and zinc sulfide types, liquid and plastic solutions

in hydrocarbon solutes, noble gas types and glass types. Murray3 has

listed the various scintillators available and describes the important

characteristics of each.

Two methods of measurement are used with scintillation detectors.

With the first method individual particles or quanta are counted. In

the second method the average DC current is measured as the total

light output of the scintillator. The DC output of the photomultiplier

tube is proportional to the rate at which radiation energy is absorbed

in the scintillator if the light output of the scintillator is propor-

tional to the absorbed energy. The inorganic crystals are of partic-

ular importance for measuring x and gamma radiation. The alkali

halides are most often used since they can be grown into large crystals

of good transparency, a requirement for efficient detection of x and

gamma radiation. The inorganic crystals are activated by addition of

certain metals to make them highly efficient scintillators. Sodium

iodide activated with thallium is the most useful scintillator for

x and gamma radiation detection.

For purposes of x and gamma ray dosimetry it is desirable to have

a scintillator whose output per roentgen is constant over the entire

range of energies for which the detector is to be used. The output

per roentgen is a comparison between the scintillator measurement and

the results obtained from the standard free-air ionization chamber.

All inorganic scintillators contain elements with atomic numbers

higher than that of air and thus have a greater output per roentgen

at low energies due to the photoelectric effect. At high energies

a larger output is expected due to pair production. With organic

crystals the output per roentgen at low energies is determined by the

photoelectric absorption of carbon which is less than with air. The

output per roentgen of a scintillator wil1 be constant only if it has

the same effective atomic number as air, that is, the scintillator must

be air equivalent. The most efficient scintillator with the closest

effective atomic number to air is anthracene with an effective atomic

number of 5.8. The effective atomic number for air is 7.64. Plastic

and liquid scintillators have atomic numbers similar to air and thus

should be suited for biological dosimetry. The inorganic scintillators

such as sodium iodide may be used to determine depth dose for high-ener-

gy radiation but the effects of low-energy scatter must be considered.

Simple pulse-counting methods cannot provide a useful measure of x

or gamma ray exposure unless pulse-height discrimination is used.

Scintillation detectors may be used for direct measurement of depth

dose in body cavities but calibration is required with radiation of

the same energy.


Solid State

Electrical solid state detectors or semiconductor detectors are

solid state analogs of the ionization chamber. The ionizing particle

or x or gamma ray reacts with the sensitive volume of the detector to

produce ionization. The ionization produces a conductivity through

the solid which is a function of absorbed dose rate in the material.

In some materials'the induced conductivity change is permanent due to

radiation damage and is thus a measure of total absorbed dose.

A semiconductor consists of a p-n junction where the p-region is

deficient in electrons and the n-region has an excess of electrons.

When an electric field is connected across the semiconductor the

region in the vicinity of the junction becomes depleted of ions. The

presence of ionizing radiation in this region causes a current to flow

which is a measure of the amount of radiation. The size of the voltage

pulse produced is proportional to the energy lost in the detector by

the incident radiation.

The energy required to produce an ion pair in most gases is 30-40

ev whereas it is only 3.5 ev for a silicon semiconductor. Thus many

more ions are produced in a semiconductor detector than in a gas

detector of the same mass for the same amount of energy absorbed. This

means that the pulse from a semiconductor detector is about ten times

larger than that from a gas detector. Semiconductor detectors have

a linear response, excellent resolution, a fast rise time and are

small in size. They are practically 100 percent efficient for partic-

ulate radiation but are much less sensitive to x and gamma radiation

due to the small depletion region. Thicker depletion layers may be

obtained by applying a higher bias voltage or by the use of silicon

with higher specific resistance. Increased bias voltage increases

noise and thus methods of increasing the resistivity of silicon have

been developed. In the "lithium drifted" silicon detector lithium is

diffused into the silicon; a process which increases the resistivity

about 1,000 times. Thick junctions may be obtained with this technique

which improves sensitivity to x and gamma radiation.

Semiconductor detectors have been used in clinical dosimetry for

depth dose measurements.35 Silicon detectors are particularly useful

for measuring depth dose distribution in bone since the atomic number

of silicon (14) is near that of bone (13.8).

Gas Detectors

Roentgen reported in his second report36 that positive and negative

charged bodies in air were discharged when placed in an x-ray beam and

that the rate of discharge was proportional to the intensity of the

beam. This remarkable observation has provided the basis for gas-filled

radiation detectors used today.

All gas-filled detectors operate on the principle of collection of

the ions produced in the gas by particulate, x or gamma radiation. The

detectors consist of a gas-filled tube with a center electrode. The

chamber wall forms a second electrode. With the proper potential

difference electrons are collected on the center electrode. The

operation of the gas detector depends on the voltage difference. As

the voltage difference increases, the current collected increases

until it approaches asymptotically the saturation current for the

radiation intensity being measured. All ions produced in the chamber

are collected at the saturation voltage and thus the current is pro-

portional to the total ionization produced, which is proportional to

the amount of radiation striking the chamber. If the voltage is

increased much beyond the saturation voltage, secondary ionization,

caused by collision of the original ions formed by the radiation with

other gas molecules, begins. As soon as secondary ionization occurs

a rapid multiplication of ions in the cha-ber takes place and the total

current depends very strongly on the applied voltage. A detector

operating in the region of the saturation voltage in which secondary

ionization is not taking place is called an ionization chamber, or

simply an ion chamber. Such a chamber is said to be working in the

ionization chamber region, indicating operation at saturation voltage

with no secondary electron emission. The current produced in an ion

chamber is very small and requires amplification before measurement.

The Geiger counter, a gas-filled counter operating in the ion

multiplication region, is not a precise instrument for measurement

of absorbed dose because its response is not directly proportional

to the energy absorbed in its sensitive volume. It has a detection

efficiency of nearly 100 percent for alpha and beta particles and is

sensitive to x and gamma radiation, but to a much smaller degree.

Geiger counters have been used for the measurement of low-dose rate

radiation fields. In this case the recorded counts are related

indirectly to dose by considering the efficiency with which secondary

electrons are ejected from the cathode walls as a function of x or

gamma ray flux. These results are then related to the dose rate

measured with an air-wall ion chamber. Counter response in terms of

dose rate is a function of the energy of the x or gamma radiation.

Geiger counters are not suitable for measurement of low-energy radia-

tion due to the photoelectric interaction in the chamber wall. Neither

are they suitable for depth dose measurement in a scattering medium

because of the mixture of energies present at different depths.

Sinclair37 has discussed the use of Geiger counters in the measurement

of radiation fields and the problems involved.

Proportional counters have not been used for measurement of

radiation fields due to the complex instrumentation required to ensure

higher-stability high-voltage power supplies and amplifiers of great


Because of the many difficulties in making both direct and indirect

measurement of radiation as indicated in previous sections, the prin-

cipal method of dosimetry has been based on the ionization of gases,

particularly ionization of air. Although air ionization is only an

indirect measure of energy absorption in other media it has proven to

be of the greatest value in medical radiology. The effective atomic

number of both soft tissue and water is 7.42 which is quite close to

that of air (7.64). Thus the absorption of ionizing radiation per gram

of air is almost the same as the absorption in tissue or water, and

ionization in air offers an accurate and reproducible method of depth

dose dosimetry in water phantoms. The unit of radiation exposure, the

roentgen, was defined in 1928 at the Second International Congress of

Radiology in terms of ionization in air. The definition of the unit

of exposure was modified slightly in 193738 but is still essentially

as originally defined. The acceptance of air ionization as the means

of defining and measuring x or gamma ray exposure was due largely to

the simplicity and reproducibility of the method. Another important

consideration was the fact that the measured energy absorption, al-

though not in tissue, is in an approximate tissue-equivalent material.

Air is a particularly suitable gas to use in ionization chambers

because of its effective atomic number, its availability and its

constancy of composition.

Air ionization chambers operate in the saturation voltage region,

where the output signal is proportional to the energy deposited in the

chamber by the impinging radiation. Air ionization chambers are used

routinely in equipment calibration and in depth dose measurements with

water phantoms.


Many methods of radiation detection are available and all have

been used at one time or another for determination of depth dose. The

principal method of depth dose determination has been based on ion-

ization of air. This method is simple to implement and is easily

reproducible from one therapy center to another. The method is partic-

ularly suited to measurement of data to be used in treatment planning

for x-ray therapy patients since the output of an ionization chamber

is proportional to the energy absorbed in the air medium. Air has

essentially the same effective atomic number as soft tissue and water

and thus absorbs radiation as these two media. It is because of

these many advantages that air ionization is the method applied in

depth dose measurement in this research.

Further details of the air ionization method and its limitations

as applied in depth dose scanning are presented in the following




The physical phenomenon of air ionization has formed the basis

of the most widely used and reliable method of measurement of x and

gamma radiation. The ionization of air by x-rays was observed by

Roentgen immediately after the discovery of the rays and was discussed

in his early publications. The Curies also observed air ionization by

gamma rays from radium and noted that the time required to discharge a

gold-leaf electroscope was proportional to the intensity of the radia-

tion incident upon it. The electroscope may be considered as the first

ionization chamber. Many refinements have been made to ionization

chambers over the years, but the principle of operation remains the


Ionization Chambers and Radiation Measurement

By 1925 ionization measurements had become standardized to the

extent that agreement had been reached as to what quantity should be

measured. Serious problems of wavelength dependence due to wall effects

were, however, still present. The early ionization chambers designed

for dose measurements in radiation therapy were made of various materi-

als, usually metal, and were quickly discovered to be unsatisfactory


because of photoelectrons emitted from the walls. The wall effects

were a particular problem because ionization chambers fabricated at

different therapy centers did not produce the same results due to

different materials and wall thicknesses. Most radiation physicists

were already at this time using the unit which was later defined as

the roentgen as a means of comparing results. This unit called for

measurement of "the associated corpuscular emission per cubic centi-

meter of air at standard temperature and pressure," which meant that

the measurement must depend only on air ionization with no ionization

resulting from wall interactions included.

Duane39 realized that in order to measure the ionization in 1

cubic centimeter of air correctly it should be surrounded by a large

volume of air. Duane constructed a large free-air chamber but Glasser"0

pointed out that the chamber was still too small for correct measure-

ment. Failla~1 and several European physicists independently developed

several different types of free-air chambers which were large enough.

Taylor,42 after studying these chambers, developed the American stand-

ard free-air chamber. The development of the standard free-air chamber

provided a means of standardized air ionization measurement and set the

stage for the definition of the unit of radiation exposure in 1928.

In 1932 Taylor43 reported agreement between the standard free-air

chambers of several national laboratories to within 1 percent. This

meant a standard of radiation exposure was defined on an international

basis and it then became possible to exchange, internationally, results

of radiation therapy. A vast body of knowledge of dose-effect re-

lationships has been built up over the years since the establishment

of the standard ionization measurement.


Standard free-air ionization chambers are large, bulky and very

sensitive instruments and are not suited for routine radiation measure-

ment. The purpose of a free-air ionization chamber is to provide a

primary standard which can be used to calibrate other instruments which

may be used routinely. A dosimeter used in dose determination in

radiation therapy must respond like tissue to radiation ex-osure and

must be small enough to *determine the dose in a small volume. First

attempts to produce small ionization chambers, called "thimble chambers"

because of their size and shape, were not very successful. The

chambers were highly wavelength dependent and thus did not respond as

tissue to the radiation. Fricke and GlasserL concluded that a cham-

ber having a wall with effective atomic number of 7.69 would have the

same effective atomic number as air and would thus produce the same

ionization per cubic centimeter as a standard free-air chamber. This

conclusion was however not borne out in practice. The first successful

thimble chamber was developed by Victoreen in 1927 and is discussed in

his review5 of the development of thimble chambers. His chamber was

fabricated from carbon with an aluminum electrode and was designed to

give the same output per cubic centimeter as a free-air chamber. Each

chamber was balanced to the proper response by calibration with a

free-air chamber. The Victoreen chamber was attached to a condenser

which was charged prior to the radiation measurement. The loss of

charge during irradiation was proportional to the dose. This type of

cavity or thimble chamber has been made available commercially* and

*This instrument is available from Victoreen Instrument Company,
Cleveland, Ohio.

has been the primary instrument for dose determination in radiation

therapy for many years. The instrument is commonly called today the

"condenser r-meter" or simply the "r-meter."

The design requirements of ionization chambers used in depth

dose scanning are not quite as rigid as those discussed above. Thimble

chambers are used to measure absolute values of radiation exposure and

thus must provide the same result as would a standard free-air chamber.

The definition of depth dose given earlier involves the ratio of the

measured result at the depth in question to the measured result at the

depth of maximum buildup. Since a ratio is involved it is not essential

that the ionization chamber used in depth dose scanning produce the

same result as would a standard free-air ionization chamber. In depth

dose scanning both primary and scattered radiation are measured and

so the ionization chamber walls should be made of a material which will

not produce significant wall effects.

The Victorecn r-meter used the voltage drop on a condenser as a

measure of radiation exposure. Later, ionization chambers were devel-

oped which operated at constant potential supplied by a power supply

and the ionization current was measured directly by an electrometer

during the time of irradiation. The constant potential ionization

chamber is the type used in depth dose scanning.

Measurement of Small Currents

Ions produced by radiation interactions are collected in ionization

chambers under the influence of a polarizing voltage. The collection

of charge over a period of time constitutes a current flow. The

currents of interest in radiation measurement are very small, ranging

from 10-~ to 10-16 amperes with l0-10 to 10-!2 amperes typical of

those encountered in depth dose scanning. These small currents place

severe restrictions upon circuit design and make electrometers manda-

tory. An electrometer is an instrument with very high input impedance

and is used to measure small currents.

One of the earliest electrometers to be used in radiation measure-

ment was the quartz fiber electrometer, whose operation depends upon

the attractive or repulsive force existing between two conductors, one

of which is charged by the signal to be measured and the other by a

polarizing voltage. The original Victoreen r-meter used this type of

electrometer. These electrometers are sensitive to shock and vibration

and have been largely replaced by vacuum tube electroneters which are

more rugged and less sensitive to damage. Vacuum tube electrometers

are however prone to drift. In an effort to overcome the drift prob-

lem, the vibrating-capacitor electrometer was developed. This electrom-

eter is extremely stable and highly sensitive so that currents down to

10-15 to 10-16 amperes may be measured. These excellent instruments

are however rather bulky and expensive.

Solid state electrometer devices were developed slowly because

solid state components with high input resistances were not available.

The field-effect transistor has now solved this problem. Mauderli and

Bruno45 developed the first solid state electrometer amplifier using

field-effect transistors. This amplifier has good sensitivity and is

extremely stable. It is small and may be placed in small probes in

close proximity to the ionization chamber.

The small currents produced in ionization chambers present some

measurement problems not encountered with larger currents. The sensi-

tivity of an electrometer makes it particularly susceptible to insu-

lation difficulties not present in less sensitive current measurement

devices. The input to the electrometer must be highly insulated from

its support. The insulation must be stable with time and should be

impervious to water. The electrometer is placed as near the ionization

chamber as possible and thus must be ionization-proof. No air spaces

should surround the electrometer or a second source of ionization and

collection may occur. The electrometer must be surrounded by some

highly insulating material to exclude all air spaces. Ceresin wax is

often used due to.its high insulating properties and low melting point.

Measurement Methods

Electrical current measurements are performed by one of two

methods, the IR-drop method or the loss-of-charge method, also called

the rate-of-drift method. Figure 1 illustrates a circuit typical of

small current measurement. The ionization chamber operates at constant

potential supplied by a power supply, a battery in this case. The

collection of ions at the center electrode causes a current flow which

is measured by the electrometer. The resistance R and the capacitance

C include the total resistance and capacitance present in the circuit.

If all circuit capacitance is ignored, that is, C = 0, the essential

characteristics of the IR-drop method are easily seen. The resistor R,

in this case, is the load resistor and is an added resistance used only






in the IR-drop circuit. When a polarizing voltage sufficient to cause

saturation in the chamber is applied, the magnitude of the ionization

current is proportional to the rate of ion production which in turn

is proportional to the radiation intensity. If I is the constant

ionization current, then the voltage drop, as a function of time,

apparent at the electrometer is, by Ohm's law,

V(t) = I R (1)

and the origin of the name of the method becomes quite clear.

The loss-of-charge method of current measurement may be demon-

strated from Figure 1 if the total circuit resistance is made infinite.

The definition of capacity C, is

C = (2)

where C is the capacity in farads, q is the charge, in coulombs, stored

in the capacitor and V is the potential, in volts, at the terminals of

the capacitor. The current I is defined as

I = dq (3)

that is, the rate of change of charge with time. Differentiating

equation (2) with respect to time t, and substituting in equation (3)


dV(t) I (4)
dt C

Integrating equation (4) the voltage at time t is

i It
V(t) = dt = C (5)

assuming the capacitor has no charge at time zero and the ionization

current I is constant. The term loss-of-charge is used because the

current flow is in the direction to neutralize the charge placed on

the chamber by the polarizing voltage.

The actual current measurement circuit is neither of the two

idealized circuits just discussed but is a combination of the two

as shown in Figure 1. In the real case C represents the total

capacitance of the circuit including that of the ionization chamber

and R is the total resistance including any load resistance. Applying

Kirchhoff's law to the circuit in Figure 1

C dV(t) + V(t) I=0 (6)
dt R

and a differential equation relating voltage and current results.

For constant current I the solution is easily shown to be

V(t) = I R [1 exp (-t/RC)] (7)

if the capacitor has no initial charge. If the current is not constant

but a function of time the solution of equation (6) is

V(t) = [exp (-t/RC)/C) exp (x/RC) J(x) dx (8)
J 0

if the capacitor has no initial charge. Equations (7) and (8) express

the voltage change at the electrometer.

Both the IR-drop method and loss-of-charge method are used

routinely in radiation measurement, depending on the particular

application. With the idealized IR-drop circuit, it is clear from

equation (1) that the voltage output of the electrometer is pro-

portional to the ionization current at any instant of time. The

voltage produced at a particular time is in no way affected by any

changes in the ionization current, which occur before that point in

time. If the method is used to sample the ionization current at

prescribed points in time, the measured values when plotted may not

come even close to approximating the true current function.

The loss-of-charge circuit in its ideal realization will result

in a measurement value which is the area under a curve describing

the input signal. The measurement is made over some time interval as

opposed to an instantaneous measurement with the IR-drop method. In

this case, the signal change at every instant of time, during the

measuring interval, is considered in the total measurement and hence

this method is inherently the most sensitive and contains the most

information about the signal. It will later be shown that noise is

negligible compared to the signal with the loss-of-charge method.

The method cannot give exact information concerning the signal at any

instant of time but the measurement value is proportional to the

average of the input signal over the measurement interval. The IR-drop

method and the loss-of-charge method are often referred to as the rate

method and integral method, respectively.

The two measurement methods have been discussed up to this point

in terms of the idealized circuits. However, no matter which of the

two methods is chosen for a radiation measurement, the actual electrom-

eter circuit is that shown in Figure 1 where both a capacitance and

resistance are present.

The capacity of the ionization chamber and other components is

always present and the circuit can never have infinite resistance.

When a rate measurement (IR-drop) is desired a load resistor is added

and the capacity is that inherent to the circuit. When an integral

measurement (loss-of-charge) is desired additional capacity is added

and the load resistance is removed, although some circuit resistance

is still present. In either case both the R and the C components of

Figure 1 are present and thus the circuit has an associated RC time

constant. Equation (7) clearly shows the effect of this time constant

for constant current. The output from the actual current measuring

circuit reaches the value of the idealized IR-drop circuit only after

a certain time period depending on the value of the time constant. The

output voltage reaches 99 percent of its final value after a time of

4.6 time constants. The measured value differs from the final value by

less than 10-5 only after a time of more than 12 time constants has

elapsed. If the input current varies with time, equation (8) expresses

the measurement result for the circuit in Figure 1.

It would be desirable to have C in Figure 1 equal to zero when

making rate measurements, in which case equation (8) reduces to

equation (1). Likewise it would be desirable to have R in Figure 1

equal to infinity when making integral measurements, in which case

equation (8) reduces to equation (5). These ideal conditions are

impossible to achieve. When a rate measurement is desired the value

of the time constant is made as small as possible but is limited by

the size of the load resistor which must be used and the circuit stray

capacitance. When an integral measurement is desired the value of

the time constant is made as large as possible but this is again

limited by the size of the capacitor which must be used and the leakage


The rate method has always been used in depth dose scanning

because the value of the ionization current must be approximated at

many points in time. The integral method has never been used in depth

dose scanning due to the nature of the measurement. The presence of

a finite nonzero time constant makes it impossible to make measurements

in a radiation field instantaneously. If the radiation field is constant

during the time of measurement the proper measured value may easily be

obtained by waiting an appropriate length of time until the instrument

has reached its final value. However, if the radiation field is

changing, as is the case when depth dose scanning is performed, the use

of the rate method may lead to significant errors particularly in the

region where the radiation field is changing most rapidly.

Depth Dose Scanning

In the 1920s and early 1930s x-ray equipment had reached a stage

of development such that the equipment was reliable and capable of

delivering doses which were reproducible. The value of beam filtration

had been recognized and x-ray equipment was able to operate at higher

voltages. With beam filtration and higher-energy operations, skin and

air doses did not correlate with observed tumor reactions and thus the

need for dose measurements beneath the skin became apparent.

The first depth dose measurements were made using Victoreen

condenser ionization chambers embedded within various tissue-simulating

phantom materials. This method was very cumbersome and extremely time

consuming. With solid phantom materials it was difficult to position

the chamber precisely at the desired depth making it necessary to use

water phantoms. The use of water presented still another problem, that

of waterproofing the condenser ionization chamber. Depth dose measure-

ments performed in this manner were limited to the central beam axis

because of the great amount of time required in charging the chamber,

waterproofing it, placing it in the phantom and reading the chamber.

Central-axis depth dose measurements did not adequately describe radia-

tion fields used in therapy, particularly for isotope machines with

large penumbra. The lack of sharp beam edges due to large source size

in isotope machines made it imperative that entire radiation distribu-

tions be determined in the form of isodose curves.

Kemp46 developed an automatic method of scanning a radiation field

with a direct-reading ionization chamber. The scanner plotted isodose

curves during the measurement through a selsyn motor arrangement and

a balancing circuit. His device though automatic was very slow, moving

at a speed of only 3 centimeters per minute. An entire set of 10

isodose curves for 1 radiation field required about 2 hours. Several

other researchers47-50 later used depth dose scanners which were

essentially the same as that developed by Kemp. In 1954 Mauchel and

Johns51 developed an automatic scanner capable of measuring a set of

isodose curves in 10 minutes. Berman et al.52 reported a scanner using

a ratio circuit to eliminate variations in response due to variations

of output from an x-ray source.

In 1966 Fitzgerald et al.53 reported the first digital scanner

capable of recording data at discrete points during scanning. This

scanner, rather than plot isodose curves, measured data at 5 millimeter

intervals so that a dose matrix was formed representing the dose dis-

tribution. The dose values were recorded automatically on punched

cards, a form suitable for use in radiation treatment planning computer

programs. This scanner was the first which recorded data suitable for

immediate computer processing. If required, standard isodose curves

could be produced from the measured data by a digital plotter attached

to a computer. A complete radiation field distribution could be re-

corded in digital matrix form in about 15 minutes. This scanner used

a solid state electrometer amplifier45 and a small constant-potential

ionization chamber. In 1969 King54 reported a similar scanning device

which produced isodose curves during the scan. Glenn et al.55 developed

a computer-controlled scanner which plotted isodose curves during meas-

urement and collected data in digital form for treatment planning.

A number of depth dose scanners* are now available commercially.

There are many different features available on these scanners but they

all have one thing in common, the measurement method. All use the rate

method of measurement, a distinct disadvantage.


The ionization method of radiation measurement had become the

method of choice by 1925. The development of the standard free-air

ionization chamber paved the way for the definition of the roentgen

as the unit of radiation exposure and established a means of standard

measurement so that transfer of radiation therapy results was possible

on an international basis.

The currents produced in an ionization cha-ber on exposure to

radiation are small and an electrometer is required to measure them.

Current measurements are nade by either the rate (IR-drop) method or

the integral (loss-of-charge) method. The rate method has always been

used in depth dose scanning and the RC time constant associated with

the measuring circuit has posed a problem in this application.

The limitations of the rate method and the development of a new

measuring technique based on an integral measurement method is discussed

in the following chapter.

*Depth dose scanners are available from:
Victoreen Instrument Company, Cleveland, Ohio
Artronix Medical Systems, St. Louis, Missouri
SHM Nuclear Corporation, Sunnyvale, California
Scanditronix, Uppsala, Sweden



The Lateral Dose Function

A radiation detector moving across a typical symmetric teletherapy

radiation field should produce a response, which when plotted against

detector position, results in a curve of the type shown in Figure 2.

This curve is representative of all symmetric radiation fields and is

the idealized response of the detector, that is, no time constant error

is present.

Daniel and Wood,56 in a review of functions producing certain

basic shapes, include the function

h(x) =
A + BCx

For A and B positive, this function takes values between zero and a

maximum of 1/A. The range of x required to produce values from zero

to the maximum depends on the values of B and C. This function may be

used to approximate as closely as desired the radiation detector re-

sponse as the detector moves into a radiation field. By properly

0 0 0 0 O
cO (D !

2S00 Hi d30 %

- C)




choosing the values of A, B and C, the function h(x) can closely

approximate that portion of the curve shown in Figure 2 corresponding

to abscissa values ranging from 0 to 10 centimeters. The detector

response may be approximated only as it moves from outside the radi-

ation field into the field since once h(x) reaches the maximum value

of 1/A it remains at this value for all larger values of x. The

other one-half of the response curve, representing the change as the

detector moves from inside to outside the field, may be approximated

by subtracting a function of the same type as h(x) from h(x).

A new function was defined by combining two functions of the type

given by h(x). The new function, f(x), may be used to approximate the

entire detector response as it moves across the radiation field. This

function is given by

1 1
f(x) = for x > 0 (9)
A + BC(-D) A C(x-E)

The function f(x) has been defined as the lateral dose function and

was developed for use in mathematical analyses of detector response.

The curve in Figure 2 may be reproduced with this function with

A = 0.01, B = 2.0, C = -14.0, D = 1.0, and E = 6.0.

Depth Dose Scanning and the Rate Measurement

Depth dose scanners have greatly improved over the years. The

mechanical scanning apparatus has been improved in order to increase

the scanning speed, automate the scanning, and ensure the reproduc-

ibility of positioning of the ionization chamber. It is generally

agreed that the present limitation on scanning speed is the amplifier

time constant. This limitation was recognized by the developers of

early scanners and was responsible for the long measuring times.

In the author's53 experience of depth dose scanning, the amplifier

time constant is normally a problem in that area of the radiation field

where a large intensity gradient exists. Figure 2 shows a plot repre-

sentative of a single lateral scan across a radiation field and corre-

sponds to a curve which would be determined by an idealized rate

measurement. It is clear that a rapid change of signal occurs as the

detector moves into the radiation field. The change from almost zero

signal to the maximum signal occurs within a few millimeters. A

reverse change occurs at the other field edge as the ionization chamber

moves out of the beam. It is in these two regions that the amplifier

time constant presents a problem.

The curve in Figure 2 is expressed in normalized units as a func-

tion of detector (ionization chamber) position. The curve represents

the voltage output of an electrometer capable of making idealized rate

measurements or the ionization current at the electrometer input. When

the curve represents the ionization current, the response of a nonideal-

ized rate-measurement circuit to this input current, given by equation

(9), may be mathematically computed by evaluation of equation (8).

The dotted and dashed curves in Figure 3 are the computed responses

of a rate-measuring circuit, with a finite time constant, to the input

current given by equation (9) and correspond to scans across a radiation

field in opposite directions at the same depth. Equation (9) is eval-

uated with A = 0.01, B = 2.0, C = -14.0, D = 1.0, and E = 6.0. The




o oo

L "- az
C) 0 UJ

0n a
0) "5 Q < <2 2
< n En U-

<. Z
c UI I

., v


/ O.

I < F
/ -u


or u)

u O
U 0



0 o (oD .o 1C
SO %

0 0 0 0 0 0
0 D a,0 ,, c',

3SO Hld30 %

dotted and dashed curves are obtained by numeric integration* of

equation (8) with the time constant equal to 300 milliseconds and a

scanning speed of 2.54 centimeters per second. Because of the nonzero

time constant, the curves show displacement toward the direction of

the scan in areas of rapid signal change. The curves correspond with

each other and with the solid curve, which represents the ideal

response, in the plateau areas since the input does not change and

the output reaches its final value in these regions. If no time

constant error were present the scans made in opposite directions

would be identical and would lie on the solid curve in Figure 3.

The deviations of the dotted and dashed curves from each other

and from the correct response, given by the solid curve, are greater

in Figure 3 than would be encountered in depth dose scanning due to

the long time constant and fast scanning speed chosen to more clearly

demonstrate the problem of the time constant. Figure 4 shows two

scans, in opposite directions, of a 10 x 10 centimeter cobalt treatment

field performed with the digital depth dose scanner53 previously

mentioned. The time constant in this case was about 100 milliseconds

and the scanning speed was just over 1 centimeter per second. The

shifting effect, indicative of time constant error, is still clearly

evident which shows that the rate measurement method, as applied in

depth dose scanning, has severe limitations.

*The method of numeric integration was three-point quadrature,
generally known as Simpson's Rule and described in all texts of
integral calculus.


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Limitations of the Rate Measurerent Method

The accuracy of the rate measurement method, as applied in depth

dose scanning, is limited by the effect of the nonzero amplifier

time constant. The synergistic effect of several factors produces

this problem. The most important of these factors are the scanning

speed, the magnitude of the measured currents and the volume of the

ionization chamber used.

The Scanning Speed

The inaccuracy introduced by the nonzero time constant may be

completely eliminated by sufficiently reducing the scanning speed.

If scanning is so slow that the amplifier output reaches its final

value in a small enough time interval such that the ionization chamber

movement is insignificant, the nonzero time constant ceases to effect

the measuring accuracy. Slow scanning, however, defeats the very

purpose for which depth dose scanners were developed. If adequate

computer treatment planning is to be done, radiation depth dose data

of several hundred different treatment fields are required. A slow

scanner would be very impractical in view of the man-hours required

for depth dose measurements. If a scanning ionization chamber is to

move no more than 0.5 millimeter during the period of amplifier output

buildup to 99 percent of its final value, the maximum scanner speed

is approximately 0.11 centimeter per second when the amplifier time

constant is 100 milliseconds. In this case the complete scan of one

radiation field would require almost 3 hours. Such a long scanning

time is impractical particularly with linear accelerators since the

generating tubes have limited operational life.

The Current Magnitude

The magnitude.of the current produced by the radiation-induced

ionization in an ionization chamber is directly related to the

intensity of the radiation and the volume of the detecting chamber.

A cobalt teletherapy unit typically has a radiation output of about

80 roentgens per minute at a treatment distance of 100 centimeters.

This radiation output would produce a charge of 80 electrostatic

units per minute per cubic centireter in an ionization chamber. The

collected ions result in a current I expressed by

I 80 esu/min/cc = 4.44 x 10-10 C/sec/cc
[3 x ]09 esu/C] [b0 sec/min]

= 4.44 x 10-10 A/cc

The ionization current may be made as large as desired, depending on

the chamber volume.

The Chamber Volume

The volume of an ionization chamber used in depth dose scanning

must be kept as small as possible to ensure good resolution. The

chamber response is a measure of the average ionization occurring in

the chamber in that portion of the radiation field covering the

sensitive volume and with a smaller chamber volume a smaller radiation

gradient is present across the chamber. Cylindrical ionization

chambers are most often used in depth dose scanning. The cylinder

axis is perpendicular to the direction of scanning and the radiation

beam axis so as to minimize the radiation gradient across the chamber.

The scanning chamber used in this study has an inside diameter of

3.8 millimeters and is 26.5 millimeters in length. The sensitive

volume is 0.21 cubic centimeter. The current delivered to the

electrometer from the ionization chamber is 9 x 10-11 amperes with a

radiation output of 80 roentgens per minute.

The Time Constant

The amplifier time constant T is defined as

T = RC

where C is the total circuit capacitance and R is the feedback

resistance in the circuit. The value of C may be 1 picofarad in a

typical rate-measuring circuit. With a rate circuit, the voltage

developed at the electrometer amplifier is the product of the input

current in amperes and the feedback resistance in ohms. This means,

that with the ionization current calculated above, a resistor of about

1011 ohms is required to produce a 10 volt output at the amplifier

output. The required selection of R completely determines the value

of T since C is fixed. The value of the time constant under these

conditions is

r = RC = [1 x 1011 ] [1 x 10-12 f] = 0.1 sec = 100 msec

This value of T is fixed by the desired output voltage and may not be


Correction Technique

Since the time constant limitation of the rate measurement method

cannot be eliminated in a satisfactory way, a means of correcting the

measured scan data was developed. Equation (6) is a differential

equation relating -current and voltage in an electrometer amplifier and

has the form

C dV(t) V(t I(t) = 0
dt R

This may be rewritten as

I(t) R = V(t) + RC dV(t) = V(t) + T dV(t)
dt dt

This equation relates the final output voltage (I(t) R) to the

electrometer output voltage and its derivative. The derivative of

the output voltage may be approximated from output voltage values.

If Vi and Vi + 1 are two values of the electrometer output voltage

at two sampling points separated by a distance AX, the derivative of

the output voltage midway between the two measuring points may be

approximated by

Vi + 1 Vi

where v is the scanner speed.

The value of the output voltage at the point midway between the two

sampled points may be approximated by

Vi + 1 + V.

The approximation to the correct output voltage is given by

Vi = I(t) R Vi + 1 + Vi + T Vi + 1 Vi (10)
2 AX

where T is the time constant of the amplifier.

This correction technique was applied to each sampled point in

each depth dose scan performed with the previously described digital

scanner. The correction greatly reduced the effect of the time constant

and produced scans which were essentially symmetric in both directions.

This correction technique was particularly attractive since the

measured data could be corrected after measurement with no increase

in scanning time required. Over 700 different radiation fields were

scanned and corrected as above. Many of the isodose curves plotted

from these data are included in the International Atomic Energy Agency

Dosimetry Catalog57 and have had worldwide distribution.

The correction technique provides only an approximation to the

correct chamber response since the differential equation is evaluated

using discrete data points. This correction technique then becomes

less satisfactory as the scanning speed increases. The fact that the

rate measurement method is unsuitable for the rapid sampling required

in depth dose scanning and the need for faster depth dose scanners

has promoted a search for a new measurement technique.

The Integral Method

An integral method of measurement is used in radiation therapy

when the total dose administered over some time period is desired.

The Victoreen r-meter, developed in the 1920s and still the primary

instrument for equipment calibration, is such an integrating device.

The loss of charge on the ionization chamber capacitor is the measure

of total accumulated dose during the time of exposure. The time of

exposure in this case is determined by a separate timing device.

Integrating dosimeters have been used primarily in dose monitor

devices which turn off the x-ray unit after a preset dose is delivered.

These monitors have used both electromechanical and electronic methods

of integration. Wheatly58 and Farr59 reported the use of a small motor

driven by an amplifier whose output voltage was proportional to the

ionization current. The motor speed varied linearly with applied

voltage and the number of motor revolutions-made in a period of time

was proportional to the integral of the ionization current. After

a preset number of revolutions the x-ray unit was turned off. This

electromechanical means of digital integration has not been widely

used because the motor speed was not quite linear with voltage at low

voltage levels and primarily because better techniques became available.

When integration is performed electronically the integrating

capacitor is charged by the ionization current and the voltage present

after some time is proportional to the integral of the current. Inte-

gration may also be accomplished by initially charging the capacitor to

some fixed voltage and letting the capacitor be discharged by the

ionization current. The charge lost during the measuring time is pro-

portional to the integral of the current. Both methods have been used

in dose monitors to turn off an x-ray unit when the voltage on the

capacitor reached a preset voltage level. The dose monitor had to

work over a wide dose range from just a few roentgens to several hundred.

It was difficult to cover the entire required dose range with a single

integrating capacitor and thus a method of digital integration was


A single integrating capacitor may be used in a dose monitor,

operating over a wide dose range, if the capacitor can be recharged

when the voltage on the capacitor drops to a preset voltage or, with

the other method of integrating, if the capacitor can be reset to zero

when it reaches a preset voltage. The number of times the capacitor

goes through its voltage excursion and recharge or discharge cycles is

a digital measure of the integral of the ionization current. Farmer60

developed a measuring circuit of this type which used an electrostatic

relay to actuate a counter and at the same time recharge the integrating

capacitor. This device was limited to measuring dose rates of less than

40 roentgens per minute due to the recharge time of the capacitor.

Watson61 used a neon tube, which flashed after a particular voltage

built up on the capacitor, to discharge the capacitor. This method

was used in a Geiger-counter type personnel monitor worn by persons

working in radiation therapy. This device could be adjusted to operate

over a dose range of 0.1 milliroentgen to 10 roentgens per minute.

Watson62 also developed a dose monitor for use in radiation therapy.

In his design, a moving-coil relay operated to reset the capacitor.

The device produced one count for every 10 roentgens and could operate

at up to 30 cycles per minute. Naylor,63 in a similar circuit, used

a cold cathode trigger tube to discharge the capacitor. Kemp et al..64

and Kemplay65 have used solid state electronics to reset the capacitor

with cycle repetition rates of 100 or more per minute. Lorenz and

Mauderli66 reported a similar solid state system for use with cobalt

teletherapy units.

Neither the electromechanical nor the electronic methods of

digital integration discussed above are applicable to depth dose scanning

for several reasons. Electromechanical methods are not sufficiently

accurate because of nonlinear motor response to voltage. The best of

the electronic methods has a repetition rate of just over a hundred

per minute which is too slow for measuring while scanning. The magni-

tude of the ionization currents measured in the dose monitor devices

is of the order of 10-6 amperes, with 10-7 amperes minimum. These

currents are 1,000 to 10,000 times greater than those encountered in

depth dose scanning. The methods of recharging or discharging the

capacitor involve switching at the input to-the electrometer amplifier.

Switching transients and leakage currents become quite important when

currents below 10-7 amperes are measured and these problems have

limited the presently used digital integration techniques to measure-

ment of large currents. Furthermore, the digital integration tech-

niques discussed above are not sufficiently accurate for depth dose

scanning since the measurement may be in error by as much as one com-

plete cycle.

The Repetitive Integral Measurement Method

A new method of measurement based on repetitive integrate-reset

cycles has been developed. Significant modification of the techniques

used previously in dose monitors allows the new method to be applied

to depth dose scanning. The method has been named the "Repetitive

Integral Measurement Method."

The details of the new method may best be described by reconsider-

ation of some of the results developed in Chapter 3. The general

solution of the differential equation (6), relating ionization current

to the voltage output of the electrometer amplifier, is given by

equation (8) as

V(t) = [exp(-t/RC)/C] j exp(x/RC) I(x) dx

when RC becomes large this becomes

V(t) 1 I(x) dx (11)

showing that the voltage output of the electrometer is proportional

to the integral of the input current from time zero to time t. The

average current I(0, t) in the interval [0, t] is

1(0, t) = I(x) dx
t O


tI(O, t) = I(x) dx (12)

Substituting equation (12) into equation (11)

V(t) = tI(0, t)


I(0, t) = C V(t) (13)

and it is seen that V(t), the voltage present at the electrometer

output at time t, is a measure of the average current over the time

interval [0, t].

The integral measurement is a sum of all values of the input

current over the interval of integration and thus the value of the

integral can give no information concerning the variation of the input

current at any particular time. As nothing can be said concerning the

actual value of the input current at a specific time, it is reasonable

to estimate the value of the input current at the center of the interval

of integration by the average current 1(0, t). This may be expressed,

using equation (13), as

I(t/2) ~ I(0, t) = 0 V(t) (14)

Equation (14) shows that the voltage V(t) at the electrometer output

at time t is a measure of the input current at the center of the

measuring interval.

An input current may be approximated over a total time t by

estimating the current value at the center of each of m measuring

intervals by the average current in each of the intervals. The input

current function may be approximated by the average current in each of

m equal intervals as indicated by

p (n + 1) At
I[(n + 1/2) At] 1 I(x) dx = V[(n + 1) At]
At f At

n = 0, 1, 2, .. m 1

where At = t/m is the length of each of the m intervals. In the above

expression, the value of the input current at time (n + 1/2) At is

approximated by the average current in the interval [nAt, (n + 1) At]

which is, as shown by equation (14), proportional to the output voltage

of the electrometer at time (n + 1) At.

The voltage V[(n + 1) At] in the above equation is a measure of

the average current in the interval fnAt, (n + 1) At] only if the

integrating capacitor was in a reset state prior to start of the inte-

gration at time nAt. The value of the integral over each of the m

intervals must be independent of the value in any other interval.

The relationship between output voltage and the average current

in an interval may be shown by combining equation (11) and equation


J (n + 1) At
V[(n + 1) At] = 1 I(x) dx = At I[nAt, (n + 1) At]
C nAt C

The output voltage at time (n + 1) At is proportional to the average

current in the interval [nAt, (n + 1) At] when the voltage at time

nAt is zero. If the capacitor is not reset at time (n + 1) At and

integration continues until (n + 2) At then

I (n + 2) At
V[(n + 2) At] -= I(x) dx = t I[nAt, (n + 2) At]

and V[(n + 2) At] is proportional to the average current over the

interval [nAt, (n + 2) At]. The necessity of resetting the capacitor

prior to integration in each interval is clear. Without resetting,

the output voltage reflects the average current from the time inte-

gration began and not the average current in each separate time inter-


In summary, the repetitive integral measurement method approxi-

mates an input current through repetitive cycles of integrating and

resetting. The output voltage generated in each integration cycle

is proportional to the average current over the interval and is used

to approximate the value of the input current at the center of the

measuring interval.

Constant and Linear Current

When the input current function is constant (I(x) = IO) the

average current in any interval [nAt, (n + 1) At] is given by

1 j (n + 1) At
I[nAt, (n + 1) At] = -A I dx = IO

and in this case the current value in the middle of the measuring

interval is equal to the average current.

Likewise for a linear function (I(x) = kx, for k constant) the

average current in any interval [nAt, (n + 1) At] is given by

f(n + 1) At
I[nAt, (n + 1) At] kx dx = k(n + 1/2) At

and again the value of the average current over the measuring inter-

val is equal to the current at the midpoint of the interval.

These results show that the repetitive integral measurement

method will give exact results with a constant or linear function of

current. This also implies that if it is possible to choose the inte-

gration intervals so small that the function is essentially constant

or linear within the interval then the repetitive integral measurement

method will result in very good approximations to the actual values of

the input function at the center of the measuring interval.


The rate measurement method is limited in depth dose scanning

by the time constant of the amplifier. The time constant is determined

by the magnitude of the current to be measured and is of the order of

100 milliseconds with the currents encountered in depth dose scanning.

With a time constant of this magnitude, measurement values suffer

significant signal lag in regions where there is rapid change in the

input function. Correction techniques must be applied to measured

data, if scanning speeds exceeding a few millimeters per second are


A new measurement technique based on integral measurement has

been developed for use in depth dose scanning. The method is called

the repetitive integral measurement method and approximates an input

current through repetitive cycles of integrating and resetting over

short time intervals. The output voltage at the end of each inte-

gration cycle is proportional to the average current over the interval

and is used as an approximation of the input current at the center

of the interval of integration.

A comparison of both measurement methods is made in the following




The Step Function Response

The rate measurement method has been shown to present a problem

in those parts of the radiation field where rapid changes occur. When

the input signal increases or decreases rapidly the amplifier output

is late in increasing or decreasing due to the nonzero time constant.

The unit step function has the value zero up to a prescribed

point at which the function value becomes unity. It is an example of

a function with the most rapid change possible and is useful in

evaluating the response of an amplifying system to a changing signal.

The unit step function has been used to compare the responses of the

rate measurement and repetitive integral measurement methods.

The step function may be defined as a function of time in the

following way

f! t T
j(t) = t where T is a fixed time
iL t <

The responses of both methods of measurement to the above step function

are determined by evaluating the expressions

R(t) = [exp(-t/T)/C] exp(x/T) j(x) dx (15)

for the rate measurement, where i = RC, and

(n + 1) At
S[(n + 1/2) At] ={exp[-(n + 1) At/T]/C} exp(x/) j(x) dx (16)

n = 0, 1, 2,

for the repetitive integral method. The time unit in the above

equations is arbitrary. Equation (16) produces a value which is pro-

portional to the amplitude of the step. For a meaningful comparison

with .the rate measurement this result must be normalized so that

equation (16) will produce a value equal to the step amplitude for

any measuring interval fully inside the step. This normalization is

performed by dividing the result of equation (16) obtained in each

measuring interval [nAt, (n + 1) At] by the result obtained in any

one interval contained entirely within the step.

Suppose the interval [kAt, (k + 1) At] lies entirely within the

step (kAt T) then the result of equation (16) in this interval is

(k + 1) At
S[(k + 1/2) At] = {exp[-(k + 1) At/T]/C} exp(x/T) dx

= (l1 exp(-At/T)]

The normalized values are given by

S[(n + 1/2) At]
N[(n + 1/2) At] = + 1/2) At]
Sj(k + 1/2) At]

(n + 1) At
exp[-(n + 1) At/T] (n + 1
= T[1 exp(-At/T)] exp(x/t) j(x) dx (17)

n = 0, 1, 2,

where the interval [kAt, (k + 1) At] lies entirely within the step.

Equation (17) gives values which may be compared directly with the

results produced by equation (15). The values resulting from evalu-

ation of equation (17) in each of the intervals is interpreted as the

value of the input function j[(n + 1/2) At] in the middle of the

measuring interval. Equation (15) is evaluated at corresponding

points so that comparison is possible. It is to be noted that

equations (16) and (17) contain exponential terms not present in

equation (11), the equation on which the definition of the repetitive

integral measurement method is based. The exponential terms are

included so that the effect of the time constant T on the repetitive

integral method may be observed. When T becomes large the exponential

terms reduce to unity as in other discussions of the measurement method.

Point Detector Response

Figure 5 shows a series of results for each measurement method

for several values of the time constant and several positions of

measurement points relative to the step location. The figure repre-

sents the response of a point detector to a time-dependent step input




r*TE A

0 6 0 10 12

T-0 01

S T.O0 5

0 04 06 0


1.0 I 2

T T0 I

02 04 06 0 10 12

TT5 0

Point Detector Response to Step Function Input.



rTI 0
TIM4 0




0.2 0.4 0 6 0. 10 1.2

Figure 5.

when measurements are made at equally spaced time intervals. All

points are determined at time intervals separated by 0.2 units and

straight lines connect each series of points. For example, the

calculated values at time 0, 0.2, 0.4, 0.6, 0.8, 1.0 and 1.2 correspond

to the same series of measurements and are connected by a straight

line. Likewise the calculated values at time 0.04, 0.24, 0.44, 0.64,

0.84 and 1.04 correspond. It is emphasized that each value determined

with the repetitive integral measurement method is the normalized

result of an integration over a time interval. The value is plotted

at the center of the integration interval. In each interval of

measurement At = 0.2. The integral expressions in both equations (15)

and (17) were evaluated by three-point quadrature. Equation (15) was

evaluated at points corresponding to the center of the interval of

integration for equation (17).

Figures 5a and 5b show the results of the two measurement methods

with a time constant T = 0.01. From equation (8) it is seen that the

basic integral expression evaluated for the two methods is identical

when T is the same. There is a significant difference however in the

way the integral expression is evaluated in each method. When a rate

evaluation is made the integral in equation (8) is determined by

integration from time zero to the time of sampling. When a repetitive

integral evaluation is made the integral is determined by integration

from time nAt to time (n + 1) At and the result is normalized as

discussed above. Figures 5a, 5b, 5c and 5d show that even with the

same value of the repetitive integral method reaches the step value

sooner than the rate method. The repetitive integral method overesti-

mates the step in Figure 5b and rises too quickly due to integration

over an interval At. The rate method also overestimates the step

when measurements are made at the same interval At apart and the output

is represented by a straight line between points. This area where

overestimation of the step occurs is directly dependent upon the time

interval between sampling with the rate measurement and the time

interval over which integration is performed in the case of the

repetitive integral method. The repetitive integral method is clearly

superior to the rate method when T = 0.5, although again the step is


Figure 5e shows the response of the repetitive integral method

to the step input when T > 5.0. It was found that Figure 5e did not

change for values of T > 5.0, which means that the exponential term

in equation (16) is essentially unity and thus a simple integration of

the input function is performed. The response when T > 5.0 is then

that which is produced by the repetitive integral method as it was

originally defined, that is, a measure of the average of the input

function over the interval of measurement. The response to the step

input of the repetitive integral method when T < 5.0, as shown in

Figures 5b and 5d, is not a measure of the average of the input function

but an average of the product of the exponential function for the

appropriate T and the input function over the interval of measurement.

Only with T > 5.0 does the repetitive integral method produce an output

which is proportional to the average input current. As the average

input current is the only reasonable estimator of the input within the

interval, the repetitive integral method would in practice always use

a T > 5.0.

The repetitive integral method, as shown in Figure 5e, responds

most quickly to the step when the step occurs at the beginning of the

integrating interval in which case the step value is reached within

one measuring interval. The worst case in response is when the step

occurs in the middle of the integrating interval. In this case, two

intervals are required to reach the step value. Results which have

been obtained with values of T not shown in Figure 5 indicate that

the repetitive integral method with T > 5.0 always reaches the value

of the step before the rate method with T > 0.02. The repetitive

integral method with T > 5.0 reaches the step value at least two

intervals earlier than the rate method with T > 0.05.

All the results shown in Figure 5 and the above discussion of the

figure pertain to measurements made with a perfect point detector,

which is physically impossible to achieve. The dimensions of the

detector become important when evaluating its response to a changing

signal. Ionization chambers are most often cylindrical because of

certain electrical characteristics and because of simplicity of

fabrication. The response of the chamber is proportional to the volume

irradiated or if a two-dimensional cross section is considered, the

response is proportional to the area irradiated. It is sufficient to

consider the two-dimensional case since the entire length of the

sensitive volume is equally irradiated and the cross-sectional area

irradiated is then proportional to the volume irradiated.

Cylindrical Detector Response

Figure 6 shows a cross-sectional view of a cylindrical ionization

chamber of radius R. The shaded section represents that portion of the

chamber irradiated. The dividing line between the irradiated and the









unirradiated portions forms a chord of distance x from the center of

the cylinder. The response of the chamber is proportional to the area

irradiated and the fraction of full response is the ratio of the shaded

area to the total area. The area of the shaded section is given by the


x R2 X 2
A() = [x 2 x2 + R Arcsin (x/R)]

for x in the interval [-R, R]. The ratio of the shaded area to the

total area is

A(x) 1
F(x) = = 0.5 [(x/R) /R)V ( R)2 + Arcsin (x/R)]

for x in the interval [-R, R]. The response of the cylindrical detector

is described by F(x) as the chamber moves across an irradiation step.

If the step occurs at time ts and the chamber moves at a rate of k

distance units per time unit

0 t < ts R/k

g(t) = F(t) ts R/k < t < ts + R/k

1 t > ts + R/k

is the expression of the chamber response to a step input. The function

g(t) is used in equations (15) and (17) to compare the results of the

two measurement methods for the cylindrical detector.

Figure 7 shows the response of the cylindrical detector to a

step input. The chamber diameter in this example was taken to be the


ATE 0 01

.0O 01

04 06 0 10 12


rT* 5

0 6 0 10 1 2





T> 0

TIME 0 0.2 04 06 0 10 1.2

Figure 7. Cylindrical Detector Response to Step Function Input.

T-0 5

. . . v -

distance transversed during one measuring interval or, in time units,

it corresponds to the time between individual measurements. When

Figures 5a and 7a are compared, it is seen that the cylindrical

detector is delayed in reaching the step value and in the worst case

requires three intervals to reach the step amplitude whereas the point

detector requires only two intervals. The repetitive integral method

response shown in Figure 7b reaches the step value sooner than the rate

method, but overestimates the step more than the rate method. With

the large value of T = 0.5 in Figures 7c and 7d, the response is quite

similar to that with the point detector, but both methods anticipate

the step before it arrives due to the finite size of the detector. The

response of the repetitive integral method with T > 5.0 is shown in

Figure 7e. In the worst case, three intervals are required to reach

the step amplitude and in the best case, two intervals are needed.

As the cylindrical chamber is made smaller, the response will

become closer to that of the point detector. If a larger chamber is

used, the number of measuring intervals required to reach the step

value increases. The dimensions of the cylindrical ionization chamber

used in depth dose scanning are approximately the same as those used in

the example in Figure 7 and thus its response is well described by

Figure 7.

Figure 7e shows that the repetitive integral method, with T > 5.0,

is superior to the rate method in approximating the step input except

for the rate method with T = 0.01, and it is almost as good in that case


The results shown in Figures 5 and 7 and some similar results,

which are not plotted, with other values of T indicate that the

repetitive integral method with T > 5.0, which is really a measure of

the average input, is far superior to the rate method with T > 0.02 in

responding to a rapidly changing signal.

The Size of the Measuring Interval

The closeness of approximation of the step by both methods depends

on two factors, the time interval between measurements and the diameter

of the detector. The effect of reducing the measuring interval is

easily seen with the point detector. Figure 8 shows the result of

reducing the measuring interval by ten times. Figures 8a and 8b show

the response of both methods of measurement for T = 0.1 for the rate

method and T > 5.0 for the repetitive integral method. Figure 8a

shows the best case when the step occurs at the beginning of the

interval. Figure 8b illustrates the worst case when the step occurs

in the middle of the interval of measurement. Figures 8c and 8d show

the same results for T = 0.01 for the rate method. Comparisons of

Figures 8 and 5 show the improvement in approximating the step. It

is possible to approximate the step as closely as desired with the

repetitive integral method and a point detector by choosing a suf-

ficiently small interval of measurement.

In the case of the cylindrical detector, the closeness of approxi-

mation of the step is limited by the detector diameter. Reducing the

measurement interval improves the approximation but no matter how small

the interval becomes, the step amplitude is first reached at a point

inside the step by a distance equal to the detector radius.




0---- .2 0.4 06
O 0.2 0.4 0.6

0.2 04



0.8 1.0



0.6 08 1.0



0.6 0.8

0 02
0 0.2 0.4



06 0.8 1.0

Point Detector Response to Step Function Input with
a Tenfold Reduction in the Size of the Measuring


p-~----- I





Figure 8.

I - T- -i 1 -





Lateral Dose Function Response

The lateral dose function given by equation (9) represents the

input current expected at the electroaeter during a scan across a

radiation field. This function provides a means of evaluating both

measurement methods as they would be applied in depth dose scanning.

Equations (15) and (17) were evaluated, by numeric integration, using

the lateral dose function as the input function. The solid curve in

Figure 9 shows a plot of the lateral dose function. The dotted and

dashed curves are the result of evaluating equation (15) and correspond

to scans across the field in opposite directions. The amplifier time

constant was taken as 0.1 seconds, a value typical in depth dose

scanning, and the scanning speed was 2.54 centimeters per second. The

curves for the scans in opposite directions show the shifts from the

true value which are characteristic of the rate-measurement method.

The repetitive integral measurement method was applied to the

lateral dose function under the same conditions as with the rate method

except that the time constant for the repetitive integral method was

chosen equal to 50 seconds so that the electrometer amplifier output

was proportional to the average current. Figure 10 shows a plot of

the lateral dose function and the results of the evaluation of equation

(17) for scans in opposite directions. The three curves superimposed

show no deviation greater than the line width.

Figure 10 shows that the repetitive integral measurement method

produces identical results for scans in opposite directions, completely

eliminating the shift introduced by the rate method. The results shown

in Figure 10 were determined with a scanning speed of 2.54 centimeters

per second and At = 0.125 seconds.

0 0o
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The accuracy of the repetitive integral measurement method in

reproducing the lateral dose function was evaluated by consideration

of two types of errors, the function error and the displacement error.

Figure 11 shows a diagram of a function F, over interval [nAt, (n + 1)

At], the integral approximation of the midpoint and the two types of

errors. The repetitive integral method approximates the function value

at the midpoint of the interval by the integral of the function over

the interval. Only rarely does the function value at the midpoint

equal the integral value and, thus, the integral value lies above or

below the function value. The difference between the function value

and the integral value is denoted by AF and is called the function

error. The distance from the midpoint of the interval to the point

on the abscissa, where the function value and integral value are equal,

is denoted by AX and is called the displacement error.

Both AF and AX were determined for both measurement methods, as

applied to the lateral dose function. These errors were determined

from the same data used in plotting Figures 9 and 10. The time constant

was taken as 0.1 second for the rate method, as this corresponds to

the minimum value used in depth dose scanning. These errors were

determined for each measuring interval, as the lateral dose function

increased from 0 to 100 percent. In the case of the repetitive

integral method, the value of the integral in each interval [nAt, (n + 1)

At] was normalized to a 100 percent maximum by dividing each integral

value by the integral value obtained when the input function remained

at its maximum during the entire measuring interval. This corresponds

to normalization to the value obtained at the central axis.

Table 2 gives the values of AF and AX for both the repetitive

integral method and rate method, as applied to the lateral dose

function. All errors are the difference between the actual value

and the experimental value. With the rate method, the function error

AF exceeds 21 percent in the region where the function is increasing

rapidly. The displacement error AX continually increases, a fact

observed in Figure 9. Both the function errors and the displacement

errors are large with the rate method showing the unsuitability of

the method in this application. Both the function errors and dis-

placement errors with the repetitive integral method are quite small

showing that the method very closely approximates the lateral dose


The Effect of Scanning Speed

It has been noted, from experience in depth dose scanning, that

the rate measurement results are directly dependent upon the speed

of scanning. The effect of scanning speed may be observed by consider-

ation of equation (8), which may be rewritten as

V(t) = exp[(x t)/T] I(x) dx (18)

where T = RC.

The above equation gives the results of measuring the current I(x)

under the influence of a time constant T. If the scanning speed is

increased m times, the current function in equation (18) becomes I(mx)

and a larger range of function values is included in the integral. If

the measurement of the current is performed at time t/m, then

V(t/m) = C exp[(x t/m)/] I(mx) dx (19)

In order to compare the results of equations (18) and (19), it is

convenient to make a simple change of variable in equation (19) by

letting y = mx, then

V(t/m) = exp[(y t)/mT] I(y) dy (20)
f 0

Equation (20) shows that the expression under the integral sign is

identical with that in equation (18), except that the time constant is

effectively increased by m times. When the rate measurement method is

used, the effect of increasing the scanning speed m times is an increase

in the time constant by m times, relative to V(t), as given by equation


With the repetitive integral measurement method, the value pro-

portional to the average current over a single measuring interval is

given by

I (n + 1) At
V[(n + 1) At] = C I(x) dx (21)

If the scanning speed is increased m times, the current function

becomes I(mx), as above. If the measuring interval At is divided by m


(n + 1) At
V[(n + 1) t] = I (mx) dx (22)
m C t

Again changing variables by letting y = mx and substituting into

equation (22)

(n + 1) At
V[(n + 1) At= I I(y) dy (23)
m mC |
m nAt

Comparing equations (23) and (21), it is seen that the only effect of

increased scanning speed on the repetitive integral method is a

reduction of the magnitude of the output voltage by 1/m. Theoretically,

this is of no consequence, since all the results of the repetitive

integral method are normalized and, thus, this factor disappears. It

is of practical importance, however, since the magnitude must be large

enough to be distinguishable from noise. It may be said that the

repetitive integral method is independent of scanning speed as only

the signal magnitude changes.

Equations (18) through (23) apply equally well in describing

the effect of reduced scanning speed on both measurement methods.

Advantages of the Repetitive Integral Measurement Method

The previous results in this chapter indicate certain advantages

of the repetitive integral measurement method, when compared to the

rate measurement method. These advantages, which are summarized below,

are of particular importance in depth dose scanning and provide the

basis for the development of a totally new approach in scanning.

Elimination of the Effect of the Time Constant

When the rate method is applied in depth dose scanning, the lag in

output response, a result of the nonzero time constant, causes the

plot of output voltage versus detector position to be shifted away

from the correct response toward the direction of the scan. The

magnitude of the shift is directly dependent upon the value of the

time constant. Figure 9 shows results typical of those obtained in

depth dose scanning with the smallest possible time constant employed.

The results of scans in opposite directions show the lack of symmetry

about the central axis, which leads to a zig-zag effect when the

recorded data are plotted. Figure 10 and Table 2 show that the

repetitive integral method applied to the same input data produces

much smaller displacement and function errors and reproduces the plot

of the input function so well that no deviations are evident. Figures

5 and 7 show the superior response of the repetitive integral method

applied to a step input.

Application to Pulsed Radiation Sources

Pulsed radiation sources such as betatrons and linear accelerators

pose a particular problem in radiation measurement because the radiation

output is not constant, as with cobalt, but appears in short pulses of

microsecond duration and, thus, determination of the dose rate is

uncertain. The most reasonable measure of the dose rate would be the

average dose rate over some interval. The repetitive integral method

is ideally suited for this type measurement, since the integral result

is proportional to the average input current.

Elimination of Amplifier Zero Drift

This advantage of the repetitive integral method does not result

from the theoretical development of the method but becomes evident

when the electrical analog of the repetitive integral procedure is

developed. All DC amplifiers have a certain amount of drift from

zero, which is included as part of the value measured by the rate

method. The repetitive integral method can completely eliminate all

long-term zero drift (drift over a period much longer than the measuring

interval). Amplifier zero drift may be eliminated by making two

measurements during integration, the first soon after the start of

integration and the second at the end of the measuring interval, and

using the difference of the two measurements as the integral value over

the interval. Any zero drift, which has occurred prior to the interval

of measurement, is eliminated. Drift occurring during the interval of

measurement is not eliminated by this method.

Reduction of Signal Noise

It is well known that the RC circuit shown in Figure 1 has a

certain filtering effect on the input signal. When the value of T is

large the circuit functions as an integrator and produces a filtering

effect which severely attenuates high-frequency signals while passing

low-frequency signals. The integrator forms what is called a low-pass

filter. The filtering effect attenuates high-frequency noise components

superimposed on the input and reduces total signal noise. A further

discussion of noise is included in the next chapter.

Independence of Scanning Speed

The repetitive integral method is theoretically independent of

scanning speed, as only the magnitude of the output is reduced. The

practical realization of the method by electronic means, however, is

limited by the minimum signal which may be distinguished from noise.

The method is, then, practically limited by the magnitude of the output

which is dependent upon speed. The rate method is quite dependent

upon speed, as the time constant is effectively increased. The effective

increase in time constant is proportional to the increase in speed.


The repetitive integral measurement method has been shown to be

superior to the rate method in responding to a step input and to-the

lateral dose function, which simulates the input current expected

during depth dose scanning.

The repetitive integral method, when applied in depth dose scanning,

has the following advantages:

1. The effect of the time constant is eliminated.

2. It is better suited for measurement of pulsed
radiation sources because the result produced is
proportional to the average current over the
measuring interval.

3. Amplifier long-term zero drift may be eliminated
by taking the difference of two measurements during

4. The integrating circuit acts as a low-pass filter,
thus attenuating high-frequency noise components.

5. It is theoretically independent of scanning speed
as only the magnitude of the signal is reduced.

The actual implementation of the repetitive integral method by

electronic means is presented in the following chapter.



The magnitudes of the currents produced in small ionization

chambers such as those used in depth dose scanning are of the order

of 10-12 to 10-10 amperes, and thus sensitive amplifying devices are

required for their measurement. Amplifiers used for current measure-

ment in this range are usually called electrometer amplifiers or simply

electrometers. The voltage output of the electronic electrometer

amplifier is usually proportional to the input current.

Frequently, operational amplifiers are used in the construction

of electrometers. An operational amplifier is simply a high-gain,

direct-coupled amplifier. The operational amplifier often has a

differential input and is used with external feedback networks. The

ideal operational amplifier is represented by the symbol

+ -K- eo

where el and e2 are the input voltages, e0 is the output voltage and K

is the gain of the amplifier. The idealized amplifier properties

usually assumed are

Gain (K) =

e0 = 0, when el = e2

Input impedance =

Output impedance = 0

Bandwidth =

No temperature drift.

These properties can never be realized in practice but the assumption

of idealness is useful in the analysis of feedback circuits.

The Integration Circuit

The electrical analog of the mathematical operation of integration

can be easily obtained with the use of the inverting input of an

operational amplifier with the addition of a feedback capacitor. The

integration circuit is diagrammed below

R ei

+ >i 'o 0

Since the input impedance is assumed infinite, no current flows into

the amplifier. Applying Kirchhoff's law at the junction at the amplifier


el ei d(e0 ei)
+ C =
R dt

The output-voltage may be expressed as e0 = -Kel. Hence, el K

As K in the ideal case is infinite, ei = 0 and

de0 el
dt RC

e0 = el dt + e0(t = 0) (24)

where e0(t = 0) is the voltage across the capacitor at the start of

integration. The output voltage is seen to be proportional to the

integral of the input. In this discussion, the noninverting amplifier

input is connected to voltage common so the amplifier acts as a single

input device. This technique of integration has been used for many

years with analog computers for the solution of differential equations.

The repetitive integral measurement method described in Chapters

4 and 5 approximates the input function by a series of integration

performed over short time intervals. Each of the individual inte-

grations is independent of any other integration, which means the

feedback capacitor is discharged to zero voltage before integration

begins in each interval. In the case of depth dose scanning, the

ionization current is approximated at n points across the radiation

field by repetitively integrating in n time intervals whose length is

is At with the integrating capacitor being reset to zero before inte-

gration begins in each interval. An operational amplifier with feedback

capacity is utilized to perform the integration with the repetitive

integral electrometer.

The Switching Electrometer

The repetitive integral measurement method demands that the

integrating capacitor be reset to zero and held at zero until inte-

gration of the input is to begin, at which time the capacitor must

be allowed to charge. Therefore, the electrometer must be switched

at the appropriate time in order that the amplifier output and input

are shorted and the integrating capacitor discharged. This procedure

is simple to describe but poses quite a problem to accomplish with an

electrometer. Switching at the input of such a sensitive electrometer

is quite difficult since transients accompanying both making and -

breaking of the switch may send the operational amplifier into immediate

saturation. Leakage currents through the switch during integration

are also a problem with a sensitive electrometer.

The methods60-65 of digital integration discussed in Chapter 4

employed switching at the input of the electrometer, but the currents

involved were 1,000 to 10,000 times larger than those encountered in

depth dose scanning. Switching at the electrometer input is easily

accomplished with these large currents since leakage currents through

the switching apparatus, even though present, cause no problems due to

the low sensitivity of the amplifier.

The Switching Method

The connection of an electrometer output to input for the purpose

of resetting may be accomplished by either mechanical or electronic

means. Mechanical resetting using relays was tried and immediately

abandoned because the switching noise drove the amplifier into saturation.

A method of resetting by electronic switching was successful and has

been used in the construction of the repetitive integral electrometer.

The reset network is illustrated in Figure 12.

The switching of the integrator to the reset mode is accomplished

with a pair of p-channel enhancement-type metal oxide silicon field-

effect transistors (MOSFET). These transistors, indicated as A and B

in Figure 12, are normally nonconducting with zero gate voltage and

become conducting when a negative voltage is applied at the gate. The

integrating capacitor is reset during the conducting phase when the

electrometer output is connected to the input through the transistors.

The first requirement of such a switching arrangement is that the

leakage through the switch be so small as to produce a negligible

effect on the integration. It was shown in a previous chapter that

an ionization current of 10-10 amperes, which is typical in depth dose

scanning, will produce 10 volts at the output of the electrometer

when a feedback resistor of 1011 ohms is used. A leakage of just 1

picoampere into the input will result in an output of 100 millivolts

which is 1 percent of the value measured.

Two transistors are used together as shown to reduce leakage

problems. The drain of one transistor is connected to the source of

the other and this junction goes to voltage common over a small

resistance keeping the junction point of the two transistors essentially

at zero volts during integration. The source of transistor A in

Figure 12 goes to the input of electrometer F. The input voltage to

F never exceeds a fraction of a millivolt so the voltage across

transistor A is very small during integration. Furthermore during

the integration cycle the gate voltage on both transistors is zero,

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