UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Investigation of radiation quality with differential ionization chambers Yuen, Kenneth Fei Kam 1962

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1962_A6_7 Y9 I5.pdf [ 4.43MB ]
Metadata
JSON: 831-1.0103742.json
JSON-LD: 831-1.0103742-ld.json
RDF/XML (Pretty): 831-1.0103742-rdf.xml
RDF/JSON: 831-1.0103742-rdf.json
Turtle: 831-1.0103742-turtle.txt
N-Triples: 831-1.0103742-rdf-ntriples.txt
Original Record: 831-1.0103742-source.json
Full Text
831-1.0103742-fulltext.txt
Citation
831-1.0103742.ris

Full Text

INVESTIGATION OF RADIATION QUALITY WITH DIFFERENTIAL IONIZATION CHAMBERS by KENNETH FEI KAM YUEN B. Sc., University of British Columbia, I960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1962. In presenting this thesis in pa r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia, Vancouver 8 , Canada. September 2 0 , 1962 - i i -ABSTRACT In radiotherapy, half value layer has been accepted as a practical specification of the quality of primary x-rays. For the degraded radiation in a scattering medium, however, i t i s neither an applicable nor an adequate specification of the quality. This thesis describes a practical method of investigating the radiation quality i n an irradiated medium. The method i s based essentially on differences i n emission and on differences in absorption of different materials. Two ratios were measured: (a) the ratio of the ionization current in a copper-lined ionization chamber to the ionization current in a lucite-wall chamber, (b) the ratio of the ionization current i n the copper-lined chamber to the ionization current in the same lucite-wall chamber with the latter shielded by a copper absorber. These ratios, which depend on the spectrum of the x-radiation to which the chambers are exposed, change d i f f e r -ently with change in spectrum and, therefore, give two indices of quality. For calibration purposes, the above ratios were measured for primary x-rays generated at different kilovoltages and with different f i l t e r s . To investigate the quality of radiation in a scattering medium, the same ratios were measured and were compared with the results obtained for primary spectra. Radiation quality at different depths i n water exposed to different qualities of primary x-rays was investigated. The results are in qualitative agreement with those obtained by previous workers. ACKNOWLEDGEMENTS This investigation was carried out at the British Columbia Cancer Institute while the writer was on a National Cancer Institute Fellowship. The author i s grateful to Dr. H. F. Batho for his super-vision of the research and assistance in writing the thesis. The writer also wishes to express his gratitude to Mrs. M. E. J. Young for her many useful discussions and her supervision i n the absence of Dr. Batho. The careful machine work done by Mr. J. • F. Brydle i s appreciated. - i i i -TABLE OF CONTENTS PAGE Abst rac t i i Table of Contents i i i L i s t of I l l u s t r a t i o n s i v Acknowledgements v In t roduct ion 1 Out l ine of Pro jec t 5 T h e o r e t i c a l C a l c u l a t i o n s 7 Exper imental Measurements on Primary Spectra lU Comparison between Experimental and C a l c u l a t e d Values 18 Exper imental Measurements i n Water 20 Further Work 22 Bib l iography 23 - i v -LIST OF ILLUSTRATIONS Figures To Follow Page 1-2 Calculated Spectral Distribution for Different Kilovoltages 8 3 - h Relative Ionization for Different Kilovoltages and Different F i l t e r s 12 5 Cross-Section Drawing of Ionization Chambers lU 6 Experimental Set-up of Ionization Chambers 15 Tables I - V Calculated Spectral Distribution for Different Kilovoltages 8 VI Emission Factors mP- a/s m for Lucite and Copper 9 VII Attenuation Factors e"P d for Lucite and Copper 10 VIII - XXXVII Relative Ionization for Different Kilovoltages and Different F i l t e r s 11 XXXVIII - XL Calculated Ratios of Total Ionization in Different Chambers 12 XLI - XLIII Measured Ratios of Ionization i n Different Chambers 16 XLIV - XLVI Emission and Absorption Ratios for Degraded Radiation at Different Depths in Water 20 INTRODUCTION The term "radiation quality" implies a l l the properties of x-rays or gamma rays which depend on wavelength or wavelength distribution. While this term i s qualitative only (there i s no exact definition), there are many problems in radiotherapy and radiobiology i n which i t i s significant. For example, in radiotherapy the percentage depth dose at a point at a depth i n tissue (defined as the dose at that point expressed as a percentage of the maximum tissue dose in the exposed field) i s a function of the quality of the radiation. Also in radiotherapy, the energy absorbed in tissue for a given radiation exposure depends on the quality of the radiation, i.e., the conversion from an exposure dose in roentgens to an absorbed dose in rads depends on the quality of the radiation.* More fundamental — an under-standing of the effects of radiation in tissue must take into account the physical interaction of the radiation with the medium and this depends on the quality of the radiation as well as on the physical constants of the medium. For homogeneous gamma rays the quality of the radiation may be specified either by the wavelength or by the absorption coefficient in a specified medium. For the continuous spectrum generated by an x-ray tube, * The roentgen i s defined as "the exposure dose of x- or gamma radiation such that the associated corpuscular emission per 0.001293 grams of a i r produces, in a i r , ions carrying 1 electrostatic unit of quantity of ele c t r i c i t y of either sign". The rad, on the other hand, i s defined as "the unit of absorbed dose of any ionizing radiation such that the energy imparted to matter by ionizing particles per gram of irradiated material at the place of interest i s 100 ergs". The roentgen i s a measure of the radiation exposure only, irrespective of the medium exposed, while the rad i s a measure of energy absorption in the exposed medium. - 2 -the only complete and exact specification of radiation quality i s a complete spectrum. Alternatively, the complete absorption curve i n a specified absorber can be used as a good specification of quality since i t has been shown that, on certain assumptions, i t i s possible to deduce the spectrum from an absorption curve (l , 2 ,3 ,U) . However, the spectrum determined this way is not necessarily unique as different spectra may yield identical absorption curves. Neither of the above methods of specification of quality i s practical i n the radiological f i e l d since the necessary measuring equipment i s seldom available nor can the x-ray generating equipment be tied up for long experimental procedures. In fact, a knowledge of the complete spectrum i s not required in most cases. Hence, under these circumstances an approx-imate but practical way of expressing quality i s desired. In the past, the half value layer (abbreviated H.V.L.) has been accepted as a practical specification of the quality of primary radiation. It i s defined as the thickness of an appropriate absorber required to reduce the radiation intensity to $0% of i t s i n i t i a l value, the measurement to be made in good geometry (i.e., the scattered radiation reaching the measuring device from the absorber must be negligible). In radiotherapy, the half value layer i s a reasonably satisfactory index of the quality of the primary radiation. While an x-ray beam of a particular H.V.L. may be produced either by heavy f i l t r a t i o n of low voltage radiation or lighter f i l t r a t i o n of higher voltage radiation, so long as conventional kilovoltage-filter combinations are used the spectra do not diffe r significantly. For the calibration of dosemeters the H.V.L. index has proven adequate even for spectra quite different from conventional ones (£). - 3 -For specification of the quality of radiation in a scattering medium, the half value layer i s neither an applicable (since the measurement cannot be made i n good geometry) nor an adequate specification of quality. The spectra of degraded radiation i n a medium have been measured by s c i n t i l l a t i o n spectrometry (6,7,8,9,10) and, also, attempts have been made to describe the quality of the radiation by analysis of absorption curves ( l l , 12). These methods are subject to the same limitations as for the primary radiation. The Monte Carlo method has been used by Bruce and Johns (13) to calculate the spectrum of scattered radiation (i.e., excluding the f i l t e r e d primary radiation) in a medium but again this cannot be con-sidered as providing a practical method of specifying radiation quality for radiological purposes. With one exception to be noted later, only one method of measuring radiation quality i n a scattering medium, which could be described as practical i n the radiological sense, has been attempted ( lU,1^,16). This may be described as the "differential emission method" and i s based on the fact that the charge liberated in a small ionization chamber depends upon the material of which the wall of the chamber i s constructed and that the ratio of ionization currents in two chambers of different wall materials depends upon the wavelength distribution of the incident radiation.* Since i t gives only a single index the method cannot give an adequate specific-ation of quality in a scattering medium where the shape of the spectra may * The authors using the differential emission method have specified the radiation quality in terms of "equivalent wavelength". The equivalent wavelength of a continuous spectrum i s defined as the wavelength of monochromatic radiation which has the same half value layer as the contin-uous spectrum. In order to use equivalent wavelength to describe the - h -be very different i n different circumstances. In addition, as w i l l be shown in a later section, the method loses i t s sensitivity for soft radiation. The purpose of the present paper i s to describe an improved, practical method of specifying radiation quality using two indices instead of a single one. The method requires only relatively simple measurements with equipment which i s available or can be made available in a radiological physics department. Moreover, i t i s applicable to radiation of the quality used in diagnostic radiology and in superficial x-ray therapy (i.e., x-radia-tion generated at 12£ kilovolts or less) as well as to the harder radiation used in deep x-ray therapy. The method proposed does not give a complete specification and must be considered as giving essentially a qualitative description of radia-tion quality. In fact, no practical method can give a complete specification of the very different spectra encountered in a scattering medium. It i s believed, however, that the proposed method provides an improved description of quality of radiation. quality of radiation in a scattering medium, i t was necessary for the authors to determine emission ratios with their ionization chambers for primary spectra of known equivalent wavelengths. The equivalent wave-length of degraded radiation i n a medium was determined from the measured emission ratio, assuming the same relationship between equivalent wave-length and emission ratio as for the primary spectra. OUTLINE OF PROJECT The two indices which have been used in the present method are based on "differential emission" and on "differential absorption". The basic idea of the differential emission method has already been stated. The differential absorption method, on the other hand, i s based on the fact that i f two ionization chambers are shielded by different absorbers the ratio of the ionization currents w i l l depend on the wavelength distribu-tion of the incident radiation. Apart from some preliminary measurements by Clarkson and Mayneord (which they did not feel were very promising) ( i i i ) , the di f f e r e n t i a l absorp-tion method has not been used in conjunction with the dif f e r e n t i a l emission method as a method of "measuring" quality of radiation. In fact, they attempted to use differential absorption measurements to confirm differen-t i a l emission measurements. In the present project the two measurements have been considered to provide complementary rather than alternative indices of quality, the two providing a better description of quality than either one alone. The actual work may be subdivided under several headings: Theoretical calculations — to serve as a guide in planning the experimental work and as a qualitative confirmation of experimental results Experimental measurements on primary spectra Experimental measurements on radiation i n a scattering medium. While the method was developed primarily to investigate and the quality of radiation in an irradiated medium, i t was necessary, (a) (b) (c) describe - 6 -f i r s t , to determine how differential emission and differential absorption change with change in known primary spectra. Much of the work to be described is , therefore, concerned with calculation and measurement of these ratios for primary spectra generated at known kilovoltage and filtered by different filters. - 7 -THEORETICAL CALCULATIONS It i s adequate for the present purpose to assume Kramer's equation (17) for the continuous unfiltered x-ray spectrum from a thick target, namely, where I e i s the intensity per unit energy interval at photon energy e <C E, E i s the constant x-ray potential and k i s a constant. In fact, the measurements to be described in following sections were made on x-rays produced by pulsating potentials but i t may be shown that this does not change the shape of the primary spectrum significantly. For the present calculation, i t i s convenient and adequate to use the spectrum generated at constant potential. Kramer's equation gives the intensity distribution of the radiation generated in an x-ray target. The radiation emerging from an x-ray machine is modified by f i l t r a t i o n and i s described by the equation where the attenuation factor includes the effect of both inherent and added ( i f any) f i l t e r s , u i s the effective total linear absorption coefficient for quantum energy e and d is the effective thickness of the total f i l t e r . Since the inherent f i l t r a t i o n i s usually small and seldom accurately known i t has been adequate and convenient in these calculations to use a single attenuation factor which includes the effect of both inherent and added f i l t e r s . The intensity distribution I e for unfiltered spectra have been I e = k (E - e) (1) I e - k (E - e) e"Md (2) - 8 -calculated directly from equation ( l ) . To calculate the intensity distribu-tion in the f i l t e r e d spectra, values of the total linear absorption co-efficients U of the various materials were taken from National Bureau of Standards Circular 583. To convert mass absorption coefficients to linear absorption coefficients the following densities xvere used: Al : 2.70 gm/cm3, Cu: 8.89 gm/cm3, Sn: 7.29 gm/cm3. Total absorption coefficients rather than real coefficients were used since the f i l t e r i s always placed so that l i t t l e of the radiation scattered from the f i l t e r i s present i n the emergent beam. Data calculated for different spectra are given in Tables I to V. The figures in the body of the tables are the relative ordinates for the quantum energies shown i n the f i r s t column of each table. Each column is for different f i l t r a t i o n with the TOTAL (i.e., inherent plus added) f i l t e r shown at the head of the column. The absolute values for the unfiltered spectra are arbitrary and cannot be compared from one kilovoltage to another. Spectra for two different kilovoltage are plotted i n Figures 1 and 2. In each figure, two curves are given, one for light f i l t r a t i o n and the other for heavier f i l t r a t i o n . These curve i l l u s t r a t e the dependence of the shape of the spectrum on kilovoltage and f i l t e r . The ionization produced i n an ionization chamber exposed to x-rays can be calculated from the Bragg-Gray equation ( l8,19) Jra - A - (3) s m W where J m i s the ionization produced per unit mass of the gas i n the cavity (usually a i r ) , E m is the primary x-ray energy converted to energy of secondary TABLE I CALCULATED SPECTRAL DISTRIBUTION OF kO KV X-RAYS Quantum Energy, KeV" Total F i l t e r None 1.0 ram A l 2.0 mm A l 3.5 » i A l 0.5 mm Cu + 1.0 mm A l 0.20 mm Sn + 0.25 ram Cu + 1.0 mm A l 10 15 20 30 iiO 30 25 20 10 0 2.k3 x 10" 3 3.01 8.1k 7.56 0 2.0k x 10"* 0.365 3.32 5.70 0 Neg. 1.52 x lO" 2 0.860 3.7k 0 Neg. Neg. 2.12 x 10-o 6.21 x 10" 0 Neg. Neg. 3.76 x 10-J 1.60 x lO" 3 0 TABLE II CALCULATED SPECTRAL DISTRIBUTION OF 60 KV X-RAYS Total F i l t e r Quantum Energy, KeV None 1.0 mm A l 2.0 mm A l 3.5 mm A l 0.5 mm Cu + 1.0 mm A l 0.20 mm Sn + 0.25 ram Cu + 1.0 mm A l 10 15 20 30 UO 50 U5 Uo 30 20 U.1U x 10~2 5.U2 16.3 22.7 17.U 3.U1 x 10-5 0.657 6.6U 17.1 15.2 Neg. 2.7U x 10-2 1.72 11.2 12.U Neg. Neg. U.2U x 10~6 0.186 2.0U Neg. Neg. 7.52 x 10"t| U.80 x 10~3 0.392 50 60 10 0 9.16 0 8.39 0 7.35 0 3.08 0 1.20 0 TABLE I I I CALCULATED SPECTRAL DISTRIBUTION OF 100 KV X-RAYS Total F i l t e r Quantum Energy, KeV None 1.0 mm A l 2.0 mm A l 3.5 ram A l 0.5 mm Cu + 1.0 mm A l 0.20 mm Sn + 0.25 ram Cu + 1.0 mm A l 10 15 20 30 ho 90 85 80 70 60 7.kk x 10-2 10.2 32.6 52.9 52.3 6.13 x 10-5 1.2k 13.3 39.9 k5.7 Neg. 5.17 x lO" 2 3.kk 26.2 37.2 Neg. Neg. • 8.k8 x 1 0 " 6 0.k35 6.12 Neg. Neg. 1 1.50 x 10-3 1.12 x lO" 2 1.18 50 60: 80 100 50 ho 20 0 k5.8 37.k 19.0 0 k2.0 35.0 18.1 0 36.8 31.6 16.8 0 I5.k 19.1 13.7 0 6.00 10.7 10.6 0 i-3 O TABLE IV CALCULATED SPECTRAL DISTRIBUTION OF lUO KV X-RAYS Total F i l t e r Quantum Energy, KeV None 1 . 0 mm A l 2 . 0 mm Al 3 . 5 mm A l 0 . 5 mm Cu + 1 . 0 mm A l 0 . 2 0 mm Sn + 0 . 2 5 mm Cu + 1 . 0 mm A l 1 0 1 5 2 0 3 0 UO 1 3 0 1 2 5 1 2 0 1 1 0 1 0 0 0 . 1 0 8 1 5 . 1 U 8 . 8 8 3 . 1 8 7 . 2 8 . 8 5 x 10"* 1 . 8 3 19.9 6 2 . 7 76 .1 Neg. 7 . 6 0 x 1 0 - 2 5.16 U l . l 6 2 . 0 Neg. Neg. 1 . 2 7 x 1 0 - 5 0 . 6 8 3 10.-2 Neg. Neg. 2 . 2 6 x 1 0 - 3 1 . 7 6 x lO" 2 1 . 9 6 5 0 6 0 80 1 0 0 90 8 0 6 0 . Uo 8 2 . U 7 U . 8 5 7 . 1 3 8 . 3 7 5 . 5 7 0 . 0 5 U . 2 3 6 . 7 6 6 . 2 6 3 . 3 5 0 . 3 3 U . U 27 .7 3 8 . 2 U l . 2 3 1 . 7 1 0 . 8 21. U 3 1 . 9 27 . 6 1 U 0 0 0 0 0 0 0 To Follow Page 8 9 PQ CO >i X o CM CM Cn O o M pq a p i O CO o w o eg 3 o rH O XA OJ CM o • • • o o H CO -P rH •H &4 H C(! -P O En 3 O XA rH <! XA C A rH CM CO c +3 bo C(J CO > 3 C CO C3>W « C A I O rH • • X bo bo CO CO NO S 53 r-CM I O rH C A X in _=f C A O -Cf C — l A • • • O CM _=t C M r-C \ . ON O C M ON r— CO XA rH C A C A XA I O • • X bO bO CO CO CM 53 55 rH • CM OO rH -=T rH CO XA CM O NQ H O CM NO NO XA r— ON XA rH OO ON NO rH XA CM O • H O r l bO • • • CO O CO 55 rH CM X A r— r— CM CM rH r-i H rl t - 0 \ 0 • • C A rH O-O NO H rH I O H ON X ON C M • • OA CM OA oo r— _=r CA O CA OA O C— 3 3 3 rH C— O O XACO rH NO rH r-rH r—_d-• • • O -=f rH C-CM OO _=tXA H rH NO O OA XAXA CA XA_d-0 X A r- ON rH NO H H O XA O O O rH O O ON oo CM CM CM rH rH O O O C--NO _=t H H H O O O O CM O- CM O XAO o o rH rH CM CA _=i O O O XANO OO o p o o O XA O CM H rH CM CM To Follow Page 8 + + C 3 • rH CO O H -a! • O ^ O IA ^ M \ > 1—t H 0) rH O CM CM O • • • * r-1 O O rH Curve a: Curve b: Data froj Curve a: Curve b: Data froj •j (rt o vO o o CM rH O O rH O OO O MO o O CM fc> CO' >» CD W c o b CO I X > O o r-H O O r-H E-t 1=) « r-H PS 13 I—! « - H EH O OH CO Q W E-i 3 H P=H o O CM o rH - 9 -electrons (i.e., photo electrons and rec o i l electrons) per unit mass of the wall which surrounds the cavity, W i s the average secondary electron energy dissipated per ion pair produced i n the gas, % i s the mass stopping power of the wall material relative to the gas in the cavity (i.e., the electron energy dissipated per gm per cm2 of wall relative to the energy dissipation per gm per cm2 of gas). This equation i s valid for a small gas cavity surrounded by a solid wall thick enough that essentially a l l secondary electrons producing ionization in the cavity arise in the wall. E m i s pro-portional to the real mass absorption coefficient m u a of the wall material and, therefore, the Bragg-Gray equation can be rewritten as J m = ^ • 1 (U) where I i s the energy flux of the incident x-rays. It i s evident from the above equation that, provided the conditions under which the Bragg-Gray equation holds are satisfied, the ionization pro-duced in an ionization chamber is proportional to the ratio m u a / s m for the wall material. Values of raua/sm for lucite and for copper for different quantum energies are tabulated i n Table VI. These w i l l be referred to as "emission factors". Values of myxa for lucite were taken directly from Nat-ional Bureau of Standards Handbook 78 while the values for copper were obtain-ed by adding the real Compton absorption to values of the photoelectric coefficient given in NBS Circular 583. A i l values of the relative stopping power, s m, were derived from data given in NBS Circular 577. The relative mass stopping power of each material was calculated by dividing the absolute mass stopping power of the material for electrons of given energy by the corresponding absolute mass stopping power of a i r . Circular 577 gives To Follow Page 9 TABLE VI EMISSION FACTORS raPa/sm FOR LUCITE AND COPPER Lucite Copper Quantum Energy sm m^ m U / S itv a / m KeV cm^ /gm cm2/gm cm2/gm cm2/gm 10 2.92 1.15 2.5U 22U 0 .682 328 15 0.788 1.15 0.685 75.9 0.695 109 20 0.311 l.iU 0.273 3U.0 0.708 U8.0 30 0.0892 l.lU 0.0782 10.6 0.72U 1U.6 Uo 0.0U26 l.iU 0.037U U.50 0.732 6.15 50 0 .0288 l.lU 0.0253 2.30 0.738 3.12 60 0.02U3 1.13 0.0215 1.37 0.7UU 1.8U 86 0.0226 1.13 0.0200 0.587 0.7U8 0.785 100 0.0235 1.13 0.0208 0.310 0.756 0.U10 150 0.0267 1.13 0.0236 0.106 0.76U 0.139 200 0.0289 1.13 0.0256 0.0588 0.767 0.0767 300 0.0311 1.12 0.0275 0.0365 0.778 0.0U69 "-10-directly the absolute mass stopping powers of copper and a i r for electrons of different energies. The absolute mass stopping powers of lucite (Cr; Hg 0 2) were calculated from the mass stopping powers of i t s atomic constituents. In calculating the ratio m u a / s r a for any given quantum energy, the value of s m used should be that for the average energy* of the electrons produced by quanta of the specified energy. In fact, the value of s m for electron energy equal to the quantum energy has been used i n each case. While the average electron energy i s much less'than the quantum energy, the error introduced i s not great since s m changes slowly with electron energy. Table VII contains the attenuation factors required in the cal -culation of the tables in the next section. For an absorber adjacent to the cavity (i.e., on the inside of the wall or the wall i t s e l f ) , approximately half the scattered radiation w i l l contribute to ionization in the cavity. For this case i t has been assumed that u 1 = u a + I ^ s where u 1 i s the effective absorption coefficient, u a i s the coefficient of real absorption and c r s i s the Compton scatter coefficient. For an absorber placed around the chamber (i.e., relatively remote from the cavity) much less of the scattered radiation w i l l contribute to the ionization and, there-fore, i t has been assumed that u' = u (total) Obviously, these assumptions are approximations only but any errors introduced are too small to change the qualitative dependence of relative ionization on kilovoltage and f i l t e r . * The appropriate method of averaging i s discussed i n Hine & Brownell: Radiation Dosimetry, Page 29. TABLE VII ATTENUATION FACTORS e'P* FOR LUCITE AND COPPER Quantum Energy Lucite Copper n» -e - u ' x 0.2k u« -e - u ' x 0.005 (Total) e-u x 0.015 e-u x 0.03 KeV cm~i 10 15 20 30 LO 3.606 1.057 O.L855 0.2155 0.15U8 0.U21 0.776 0.890 0.950 0.96k 1991 676 303.1 95.12 k0.63 k.73 x 10" 5 0.03k0 0.220 0.622 0.816 1991 676 303.1 -96.01 kl.3k 3.95 x 10-5 1.06 x 10 - 2 0.237 0.538 2.06 x 10"8 1.12 x 10"L 5.61 x 10-2 0.289 50 60 80 100 0.13U1 0.12L6 0.1151 0.1100 0.969 0.971 0.973 0.97k 21.07 12.80 5.779 3.272 0.900 0.938 0.972 0.98k 21.78 13.1*2 6.k99 3.796 0.721 0.818 0.907 0.9k5 0.520 0.669 0.823 0.892 150 200 300 0.1019 0.0958 0.0869 0.976 0.977 0.980 1.387 0.9130 0.6kl0 0.993 0.996 0.997 1.831 1.307 0.960 0.972 0.981 0.986 0.9k7 0.962 0.972 - 11 -In Table VII, the choice of the effective absorption coefficient used has been based on the position of the absorber as indicated in the next paragraph. Relative ionization produced in an ionization chamber has been calculated for air-cavity chambers of the following wall characteristics: (A) 2 . 1 ; mm thick lucite wall (B) 2 . 1 ; mm thick lucite wall surrounded by a 0 . 1 5 mm thick copper absorber (C) 2 . 1 ; mm thick lucite wall surrounded by a 0 . 3 0 mm thick copper absorber (D) 2.h mm thick lucite wall lined with 0 . 0 5 nun of copper. (Practi-cally a l l secondary electrons producing ionization in the ai r cavity arise in the copper l i n i n g . ) * The calculated values of the relative ionization i n the different chambers for different spectra are shown i n Tables VIII to XXXVII. The kilovoltage and the f i l t e r of each spectrum are shown at the head of each table. The figures in the four columns A, B, C and D of each table are the calculated relative ionizations in the respective chambers per unit energy interval at the quantum energy shown at the l e f t of the table. Values i n column A were obtained by multiplying the spectral ordinates from the appropriate table of Tables I - V by the corresponding emission factors of * For a l l the ionization i n the cavity to be produced by secondary electrons from copper i t would be necessary that the thickness of copper be greater than the maximum range of the secondary electrons. Theorectically, this would require a thickness of copper about 0.15 mm for radiation generated at 300 KV. In fact, about one-quarter of this thickness i s enough to ensure that practically the maximum ionization due to secondary electrons from copper i s obtained. To Follow Page 11 TABLE VIII RELATIVE IONIZATION FOR 1|0 KV X-RAYS, NO FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 15 20 30 ho 32.1 13.3 U.9 0.7 0 Neg. 0.001 0.052 0.176 0 Neg. Neg. 0.0005 0.0U17 0 Neg. 72 188 86 0 Total Ionization 5U.U 0.515 0.0852 5U8 Ratio of D/A = 10.1 Ratio of D/B - 106 0 Ratio of D/C - 6U30 TABLE IX RELATIVE IONIZATION FOR LO KV X-RAYS, 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 15 20 30 UO Neg. 1.60 1.98 0.56 0 Neg. Neg. 0.021 0.133 0 Neg. Neg. ' Neg. 0.0315 0 Neg. 8.7 76.5 65.2 0 Total Ionization 5.50 0.357 0.069U 270 Ratio of D/A = U9.1 Ratio of D/B - 756 Ratio of D/C = 3890 To Follow Page 11 TABLE X RELATIVE IONIZATION FOR UO KV X-RAYS, 2.0 MM AL TOTAL FILTER Quantum Relative Ionization Per Unit Energy Interval Energy, KeV Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 10 0.19U Neg. Neg. 1.0 20 0.807 0.009 0.0001 31.0 30 O.U23 0.100 0.0238 U9.2 Uo 0 0 0 0 Total Ionization 2.26 0.2U6 0.05U3 157 Ratio of D/A = 6 9 . 5 Ratio of D/B - 638 Ratio of D/C = 2890 TABLE XI RELATIVE IONIZATION FOR UO KV X-RAYS, 3.5 MM AL TOTAL FILTER Quantum Relative Ionization Per Unit Energy Interval Energy, KeV Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.008 Neg. Neg. Neg. 20 0.209 0.0022 Neg. 8.1 30 0.278 0.0659 0.0156 32.3 Uo 0 0 0 0 Total Ionization 0.931 0.152 0.0380 82.1 Ratio of D/A =88.2 Ratio of D/B = 5U0 Ratio of D/C = 2160 To Follow Page 11 TABLE XII RELATIVE IONIZATION FOR 1*0 KV X-RAYS, 0.50 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 15 20 30 ho Neg. Neg. Neg. h.6l x 10-3 0 Neg. Neg. Neg. 1.09 x 10-3 0 Neg. Neg. Neg. 2.59 x 10-U 0 Neg. Neg. Neg. 0.536 0 Total Ionization 13.6 x 10-3 U.55 x 10-3 16.8 x 10~h 1.72 Ratio of D/A = 126 Ratio of D/B =378 Ratio of D/C = 1020 TABLE XIII RELATIVE IONIZATION FOR UO KV X-RAYS, 0.20 MM SN + 0.25 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 15 20 30 ho Neg. Neg. 9.1 x 10-5 11.9 x 10-5 0 Neg. , Neg. 1.0 x lO-o 28.2 x lO" 6 0 Neg. Neg. 1 x 10-° 667 x 10-8 0 Neg. Neg. 3.5 x 10-3 13.8 x 10-3 0 Total Ionization 713 x 10-5 1110 x 10" 6 22700 x l O - 8 636 x 10-3 Ratio of D/A - 89.2 Ratio of D/B = 573 Ratio of D/C = 2800 To Follow Page 11 TABLE XIV RELATIVE IONIZATION FOR 60 KV X-RAYS, NO FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 53.5 Neg. "Neg. Neg. 15 23.9 0.001 Neg. 129 20 9.7 0.103 0.001 376 30 2.2 0.528 0.125 259 UO 0.7 0.388 0.208 97 50 0.3 0.177 0.128 27 60 0 0 0 0 Total Ionization 96.0 2.L9 0.922 1L60 Ratio of D/A » 15.2 Ratio of D/B = 586 Ratio of D/C = 1580 TABLE XV RELATIVE IONIZATION FOR 60 KV X-RAYS, 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 0.0k Neg. Neg. Neg. 15 2.88 Neg. Neg. 16 20 3.96 0.0U2 Neg. 153 30 1.69 0.L00 0.095 196 ho 0.63 0.337 0.181 8U 50 0.22 0.162 0.117 25 60 0 0 0 0 Total Ionization 13.7 1.97 0.797 889 Ratio of D/A = 6k.9 Ratio of D/B = U5l Ratio of D/C - 1120 To Follow Page 11 TABLE XVI RELATIVE IONIZATION FOR 60 KV X-RAYS, 2.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.35 Neg. Neg. 2 20 1.61 0.017 Neg. 62 30 1.27 0.301 0.071 1U8 ko 0.55 0.295 0.158 7k 50 0.21 0.1L8 0.107 23 60 0 0 0 0 Total Ionization 6.85 1.56 0.68k 603 Ratio of D/A =88.0 Ratio of D/B = 387 Ratio of D/C = 882 TABLE XVII RELATIVE IONIZATION FOR 60 KV X-RAYS, 3.5 MM AL TOTAL FILTER Quantum Relative Ionization Per Unit Energy Interval Energy, KeV Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.015 Neg. Neg. 0.1 20 0.kl8 0.00k Neg. 16.2 30 0.832 0.197 0.0L7 96.6 ko 0.UU7 0.2k0 0.129 60.0 50 0.180 0.130 0.09k 20.0 60 0 0 0 0 Total Ionization 3.65 1.16 0.552 38k Ratio of D/A - 105 Ratio of D/B = 331 Ratio of D/C = 696 To Follow Page 11 TABLE XVIII RELATIVE IONIZATION FOR 60 KV X-RAYS, 0.$0MMCU+1.0MMAL TOTAL FILTER Quantum Relative Ionization Per Unit Energy Interval Energy, KeV Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 Neg. Neg. Neg. Neg. 20 Neg. Neg. Neg. Neg. 30 0.0138 0.0033 0.0008 1.60 h.0 0.0735 0.0396 0.0213 9.87 50 0.0755 0.05U5 0.0393 8.38 60 0 0 0 0 Total Ionization 0.332 : 0.197 0.12k ko.7 Ratio of D/A = 123 Ratio of D/B - 207 Ratio of D/C - 328 TABLE XIX RELATIVE IONIZATION FOR 60 KV X-RAYS, 0.20 MM SN + 0.25 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 15 20 30 ko Neg. Neg. 0.0002 0.000k O.Olkl Neg. Neg. Neg. 0.0001 0.0076 Neg. Neg. Neg. Neg. O.OOkl Neg. Neg. 0.01 o.ok 1.90 50 60 0.029k 0 0.0212 0 0.0153 0 3.27 0 Total Ionization 0.102 0.0585 0.0380 11.7 Ratio of D/A = 115 Ratio of D/B = 200 Ratio of D/C - 308 To Follow Page 11 TABLE XX RELATIVE IONIZATION FOR 100 KV X RAYS, NO FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 96.2 Neg. Neg. 1 15 U5.2 Neg. Neg. 2UU 20 19.U 0.21 0.002 752 30 5.2 1.23 0.292 60U Uo 2.2 1.16 0.625 290 50 1.2 0.88 0.638 136 60 0.8 0.68 0.559 67 80 o.U 0.35 0.320 15 100 0 0 0 0 Total Ionization 192 10.6 6.07 3690 Ratio of D/A = 19.2 Ratio of D/B = 3U8 Ratio of D/C = 608 TABLE XXI RELATIVE IONIZATION FOR 100 KV X-RAYS, 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 0.08 Neg. Neg. Neg. 15 5.U2 Neg. Neg. 29 20 7.92 0.09 0.001 306 30 3.93 0.93 0.220 U56 . Uo 1.89 1.01 0.5U5 253 50 1.12 0.83 0.58U 125 60 0.78 0.6U 0.522 63 80 0.37 0.3U 0.30U 1U 100 0 0 0 Total Ionization 35.5 9.26 5.78 2U20 Ratio of D/A » 68.2 Ratio of D/B - 261 Ratio of D/C = Ul9 To Follow Page 11 TABLE XXII RELATIVE IONIZATION FOR 100 KV X-RAYS, 2.0 MM AL TOTAL FILTER Quantum Energy, - KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.66 Neg. Neg. u 20 3.23 0.03U Neg. 125 30 2.96 0.703 0.166 3UU Uo 1.65 0.886 O.U76 221 50 1.03 0.7U3 0.536 11U 60 0.73 0.598 O.U89 59 80 0.35 0.319 0.290 13 100 0 0 0 0 Total Ionization 20 .7 8.10 5 .27 1790 Ratio of D/A » 86.5 Ratio of D/B = 221 Ratio of D/C = 3U0 TABLE XXIII RELATIVE IONIZATION FOR 100 KV X-RAYS, 3 .5 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.03 Neg. Neg. Neg. 20 0.8U 0.009 Neg. 32 - -30 1.95 0.U61 0.109 226 Uo 1.3U 0 .721 0.388 180 50 0 .90 0.651 0.U69 100 60 0.66 o.5Uo 0.UU1 53 80 0.33 0.297 0.269 12 100 0 0 0 0 Total Ionization 13.3 6.78 U .60 1280 Ratio of D/A = 9 6 . 2 Ratio of D/B = 189 Ratio of D/C = 278 To Follow Page 1 1 TABLE XXIV. RELATIVE IONIZATION FOR 1 0 0 KV X-RAYS, 0 . 5 0 MM CU + 1 . 0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 1 5 Neg. Neg. Neg. Neg. 20 Neg. Neg. Neg. Neg. 3 0 0.032 0.008 0.002 3.8 1*0 0.221 0.119 0.061* 29.6 5 0 0 . 3 7 8 0.272 0.196 1*1.9 60 0.399 0.326 0.267 32.0 80 0.267 0.2k2 0.219 10.2 100 0 0 0 0 Total Ionization 3.79 2.99 2.1*2 298 Ratio of D/A = 7 8 . 6 Ratio of D/B - 9 9 . 7 Ratio 0 f D/C = 123 TABLE XXV RELATIVE IONIZATION FOR 1 0 0 KV X-RAYS, 0 . 2 0 MM SN + 0 . 2 5 MM CU + 1 . 0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 1 0 Neg. Neg. Neg. Neg. 1 5 Neg. Neg. Neg. Neg. 2 0 Neg. Neg. Neg. Neg. 30 0 . 0 0 1 Neg. Neg. 0 . 1 l+o 0 . 0 U 3 0 . 0 2 3 0 . 0 1 2 5.7 5 0 0.11*7 0.106 0.077 1 6 . 3 6 0 0 . 2 2 3 0 . 1 8 3 0.11*9 17.8 8 0 0.206 0.187 0 . 1 7 0 7.9 1 0 0 0 0 0 0 Total Ionization 2.2-3 1 . 7 8 1.1*8 1 5 2 Ratio of D/A = 6 8 . 2 Ratio of D/B = 85.b Ratio of D/C = 1 0 3 To Follow Page 11 TABLE XXVI RELATIVE IONIZATION FOR llt0 KV X-RAYS, NO FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 139 Neg. Neg. Neg. 15 66 Neg. Neg. 360 20 29 0.31 Neg. 1130 30 8 1.9U 0.U6 9U9 Uo U 1.9U l .oU U8U •50 2 1.59 1.15 2U5 60 2 1.37 1.12 13U 80 1 1.06 0.96 U5 100 1 0.77 0.72 16 lUo 0 0 0 0 Total Ionization 29U 25.2 17.5 6100 Ratio of D/A = 20.7 Ratio of D/B. = 2U2 Ratio of D/C - 3U9 TABLE XXVII RELATIVE IONIZATION FOR lUO KV X-RAYS, 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 0.1 Neg. Neg. Neg. 15 8.0 Neg. Neg. U3 20 11.6 0.13 Neg. U59 30 6.2 1.U6 0.35 717 Uo 3.1 1.69 0.91 U22 50 2.0 1.U6 1.05 22U 60 1.6 1.28 1.0U 125 80 1.1- 1.01 0.91 U2 100 0.8 . 0.73 0.69 15 lUo 0 0 0 0 Total Ionization 62.9 22. U 16.2 U110 Ratio of D/A = 65.3 Ratio of D/B = 183 Ratio of D/C « 25U TABLE XXVIII To Follow Page RELATIVE IONIZATION FOR lhO KV X-RAYS, 2.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.97 Neg. Neg. 5 20 k.8k 0.05 0.001 187 30 k.66 1.10 0.261 5ki UO 2.7)4 l.k8 0.793 368 50 1.85 1.33 0.963 205 60 1.L6 1.20 0.978 117 80 1.05 0.96 0.868 ko 100 0.7k 0.70 0.663 lk mo 0 0 0 0 Total Ionization ko.5 20.2 15.1 3120 Ratio of D/A - 77.0 Ratio of D/B - 15k Ratio of D/C = 207 TABLE XXIX RELATIVE IONIZATION FOR lkO KV X-RAYS, 3.5 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 o.ok Neg. Neg. Neg. 20 1.25 0.01 Neg. k8 30 3.05 0.72 0.171 355 ko 2.23 1.20 o.6L6 300 50 1.62 1.17 0.8kk 180 60 1.32 1.08 0.88k 106 80 0.98 0.89 0.806 37 100 0.70 0.66 0.622 l k lko 0 0 0 0 Total Ionization 28.5 17.6 13.6 2310 Ratio of D/i  - 81.1 Ratio of D/B =* 131 Ratio of D/C - 170 TABLE XXX T o F°llow Page 11 RELATIVE IONIZATION FOR lhO KV X-RAYS, 0.50 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 Neg. Neg. Neg. Neg. 20 Neg. Neg. Neg. Neg. 30 0.051 0.012 0.003 5.9 ko 0.368 0.198 0.106 U9.3 50 0.679 0.U90 0.353 75.k 6o 0.798 0.652 0.53k 6k. 0 80 0.802 0.727 0.660 30.6 100 0.6k2 0.607 0.573 12.5 lkO 0 0 0 0 Total Ionization 12.3 10.5 9.18 663 Ratio of D/A =53.9 Ratio of D/B =63.1 Ratio of D/C =72.2 TABLE XXXI RELATIVE IONIZATION FOR lkO KV X-RAYS, 0.20 MM SN + 0.25 MM CU +1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 Neg. Neg. Neg. Neg. 20 0.001 Neg. Neg. Neg. 30 0.001 Neg. Neg. 0.2 ko 0.071 0.038 0.020 9.5 50 0.265 0.191 0.138 29.k 60 o.kk7 0.366 0.299 35.9 80 0.621 0.563 0.511 23.7 100 0.559 0.529 0.k99 10.8 lkO 0 0 0 0 Total Ionization 8.66 7.57 6.76 385 Ratio of D/A = kk.5 Ratio of D/B - 50.9 Ratio of D/C = 57.0 To Follow Page 11 TABLE XXXII RELATIVE IONIZATION FOR 220 KV X-RAYS, NO FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 22U Neg. Neg. Neg. 15 109 Neg. Neg. 590 20 1*9 0.52 0.01 1880 30 lk 3.35 0.79 16U-1 Uo 6 3.U9 1.88 870 50 U 3.01 2.17 U60 6o 3 2.73 2.2U 270 80 3 2.U7 2.2U 100 100 2 2.30 2.17 50 150 2 1.57 1.53 10 200 1 0.U9 0.U8 Neg. 220 0 0 0 0 Total Ionization 513 7U.2 59.7 11000 Ratio of D/A - 2 1 . U Ratio of D/B = II48 Ratio of D/C = 186 To Follow Page 11 TABLE XXXIII RELATIVE IONIZATION FOR 220 KV X-RAIS, 1.0 MM AL TOTAL FILTER Quantum Energy, KeV R e l a t i v e I o n i z a t i o n Per U n i t Energy I n t e r v a l Chamber A Chamber B Chamber C Chamber D 10 0.2 Neg. Neg. Neg. 15 13.1 Neg. Neg. 70 20 19.8 0.21 Neg. 770 30 10.7 2.5U 0.60 12U0 Uo 5.7 3.0U 1.6U 760 50 3.8 2.76 1.99 U20 60 3.1 2.56 2.10 250 80 2.6 2.35 2.13 100 100 2.3 2.20 2.08 50 150 1.6 1.51 1.U7 10 200 0.5 0.U8 0.U7 Neg. 220 0 0 0 0 T o t a l I o n i z a t i o n 139 67.9 55.8 7630 R a t i o of D/A » 5U.9 R a t i o of D/B = 112 R a t i o o f D/C = 137 To Follow Page 11 TABLE XXXIV RELATIVE IONIZATION FOR 220 KV X-RAYS, 2.0 MM AL TOTAL FILTER Quantum Relative Ionization Per Unit Energy Interval Energy, KeV Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 1.59 Neg. Neg. 9 20 8.07 0.09 Neg. 312 30 8.02 1.90 0.U5 932 UO U.9U 2.66 1.U3 663 50 3.51 2.53 1.82 389 60 2.92 2.39 1.96 235 80 2.U7 2.2U 2.03 9U 100 2.23 2.11 1.99 U3 150 1.50 1.U6 1.U2 9 200 0.U7 0.U6 0.U5 1 220 0 0 0 0 Total Ionization 99.2 63.1 52.7 592 Ratio, of D/A =59.7 Ratio of D/B = 93 .9 Ratio of D/C = 112 To Follow Page 11 TABLE XXXV RELATIVE IONIZATION FOR 220 KV X-RAYS, 3.5 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 0.07 Neg. Neg. Neg. 20 2.09 0.22 Neg. 81 30 5.28 1.25 0.30 613 1*0 U.OU 2.17 1.17 51*2 50 3.07 2.21 1.59 31*0 60 2.65 2.17 1.77 213 80 2.28 2.07 1.87 87 100 2.09 1.97 1.86 1*0 150 1.1*2 1.38 1.35 8 200 0.1*5 0.1*1* 0.1*3 1 220 0 0 0 0 Total Ionization 77.0 57.1 l*8.k 1*1*70 Ratio of D/A = 58.0 Ratio of D/B = 78.0 Ratio of D/C = 92.3 To Follow Page 11 TABLE XXXVI RELATIVE IONIZATION FOR 220 KV X-RAYS, 0.50 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 Neg. Neg. Neg. Neg. 20 Neg. Neg. Neg. Neg. 30 0.09 0.02 0.01 10 ho 0.66 0.36 0.19 89 50 1.28 0.93 0.67 1U3 60 1.60 1.31 1.07 128 80 1.8? 1.70 1.51* 71 100 1.92 1.82 1.72 37 150 1.1*2 1.38 1.3U 8 200 0.1*5 o.hh O.hh 1 220 0 0 0 0 Total Ionization 1*7.1 1*3.0 39.6 1500 Ratio of D/A = 31.6 Ratio of D/B = 3I4.8 Ratio of D/A - 37.8 To Follow Page 11 TABLE XXXVII RELATIVE IONIZATION FOR 220 KV X-RAYS, 0.20 MM SN + 0.25 MM CU + 1.0 MM AL TOTAL FILTER Quantum Energy, KeV Relative Ionization Per Unit Energy Interval Chamber A Chamber B Chamber C Chamber D 10 Neg. Neg. Neg. Neg. 15 Neg. Neg. Neg. Neg. 20 Neg. Neg. Neg. Neg. 30 Neg. Neg. Neg. 0.3 1*0 0.13 0.07 o.ou 17.1 50 0.50 0.36 0.26 55.5 60 0.89 0.73 0.60 71.6 80 1.1*5 1.31 1.19 55.3 100 1.68 1.59 1.50 32.6 150 1.37 1.33 1.30 8.0 200 0.1*5 O.IJ* 0.1*3 1.3 220 0 0 0 0 Total Ionization 38.8 35.9 33.7 91*9 Ratio of D/A - 21*. 5 Rs itio of D/B = 26.1* Ratio of D/C = 28.2 - 12 -l u c i t e from Table VI and by the at tenuat ion f a c t o r s o f the l u c i t e w a l l from Table VI I . Each value i n column B or C was c a l c u l a t e d by m u l t i p l y i n g each value i n A by the at tenuat ion f a c t o r f o r 0.15 mm copper or 0.30 mm copper, as the case may be . F i n a l l y , values under D were obtained by m u l t i p l y i n g the appropr iate s p e c t r a l o rd inates by the emission f a c t o r s o f copper, by the a t tenuat ion f a c t o r s of the l u c i t e w a l l and by the at tenuat ion fac to rs of the 0.05 mm copper l i n i n g . The data from Tables XXI and XXXVII are p l o t t e d i n F igures 3 and I*. These graphs i l l u s t r a t e the r e l a t i v e importance of d i f f e r e n t quantum energies i n the spectrum i n producing i o n i z a t i o n i n the d i f f e r e n t chambers. For each spectrum the t o t a l r e l a t i v e i o n i z a t i o n produced i n each chamber i s shown a t the bottom of the t a b l e . These values were computed by numerical - in tegrat ion by adding the ord inates shown, each weighted by a f a c t o r dependent on the i n t e r v a l between o r d i n a t e s . Where necessary f o r reasonable accuracy , more ord inates were read from curves s i m i l a r to those shown i n F igures 3 and it. For each spectrum, the r a t i o s o f the t o t a l i o n i z a t i o n s o f chambers D to A, D to B, and D to C are given a t the bottom of the respec t i ve t a b l e . The r a t i o s were obtained by d i v i d i n g the t o t a l i o n i z a t i o n i n chamber D by that i n each of the other three chambers. ( I t i s to be noted that the absolute values of the i o n i z a t i o n i n any tab le are a r b i t r a r y and cannot be compared from tab le to t a b l e ) . The three r a t i o s c a l c u l a t e d are c o l l e c t e d f o r a l l spectra i n Tables XXXVIII to XL. The r a t i o s tabulated i n Tables XXXVIII to XL are the r a t i o s which k 0 Chamber A: Multiply ordinate scale by 10 Chamber D: Multiply ordinate scale by 1000 Data from Table XXI B A / C -f / / / M 0 20 kO 60 80 100 120 Photon Energy (KeV) FIGURE 3 RELATIVE IONIZATION FOR 100 KV X-RAYS, 1.0 MM AL TOTAL FILTER TABLE XXXVIII CALCUIATED RATIO OF TOTAL IONIZATIONS OF CHAMBERS D TO A Kilovoltage Total Filter 0.20 mm Sn None 1.0 mm Al 2.0 mm Al 3.5 rnm Al 0.50 mm Cu T 0.25 mm Cu < 1.0 mm Al 1.0 mm Al hO 10.1 19.1 69.5 88.2 126 89.2 60 15.2 61*.9 88.0 105 123 115 100 19.2 68.2 86.5 96.2 78.6 68.2 1U0 20.7 65.3 77.0 81.1 53.9 1*1*. 5 220 21.1* Sk.9 59.7 58.0 31.6 21*. 5 TABLE XXXIX CALCULATED RATIO OF TOTAL IONIZATIONS OF CHAMBERS D TO B Kilovoltage Total F i l t e r 0.20 mm Sn None 1.0 mm A l 2.0 mm Al 3 . 5 mm Al 0.50 mm Cu 0.25 mm Cu f 1.0 mm A l 1.0 mm A l UO 1060 756 638 5U0 378 573 60 586 U51 387 331 207 200 100 3U8 261 221 189 99.7 85.U lhO 2U2 183 15U 131 63.1 50.9 220 LU8 112 93.9 78.0 3U.8 26.h TABLE XL CALCULATED RATIO OF TOTAL IONIZATIONS OF CHAMBERS D TO C Kilovoltage Total Filter 0.20 mm Sn None 1.0 mm Al 2.0 mm Al 3.5 mm Al 0.50 mm Cu + 0.25 mm Cu 1.0 mm Al 1.0 mm A l ho 6U30 3890 2890 2160 1020 2800 60 1580 1120 882 696 328 308 100 608 hl9 31+0 278 123 103 l h o 3h9 2$h 207 170 72.2 57.0 220 186 137 112 , 92.3 37.8 28.2 - 13 -have been selected as indices of quality in the experimental work of the next section. No one of these ratios is a differential emission ratio or a differential absorption ratio but each depends on both differential emission and differential absorption. The ratio of the ionization in chamber D to that in chamber A depends primarily on differential emission but is modified by absorption in the copper lining of the chamber. The other two ratios depend strongly on both differential emission and differential absorption. Despite these facts, for simplicity, the ratio of D/A wil l be referred to in the remainder of this report as an "emission ratio" and the other two ratios as "absorption ratios". Normally, the ratios of D/A and D/C wil l be used as the indices but under some conditions (to be noted later) the ratio of D/B is more useful than the ratio of D/C. The ratios chosen as indices of quality have been selected because (a) they vary with kilovoltage and f i l ter in quite a different manner and, therefore, provided two distinct indices of quality and (b) they could be measured very conveniently with the equipment to be used (more conveniently than some other indices that would have been equally significant). It wi l l be noted from Table XXXVIII that the emission ratio loses its sensi-t ivity as a "measure" of quality for soft radiation, as already pointed out in the "Introduction". For this reason an additional index is needed. The ratios chosen appear to give as significant a description of quality as is possible with two indices. Two different qualities of radi-ation may yield identical values for one ratio but the values of the other ratio will be quite different for the two spectra. - l U -EXPERIMENTAL MEASUREMENTS ON PRIMARY SPECTRA Two ionization chambers were used. The construction of these chambers is shown in Figure They differ only in the fact that the inside of the lucite wall of the first chamber is coated with a thin layer of colloidal graphite (Aquadag) to provide a conducting electrode whereas the second chamber is lined with 0 . 0 0 mm of copper. The central electrode in each case is a thin aluminium wire. In use the central electrode is maintained near zero potential and the outer electrode is at either plus or minus 60 volts. The lead to the outer electrode through the insulating stem of the ionization chamber is surrounded by a grounded shield. The potential difference between the central electrode and this shield never exceeds a fraction of a volt (about 0 . 0 5 volts maximum). Therefore, any ions produced in the insulator or in air gaps in the insulation wil l not be collected. The entire ionization chamber is shielded by a grounded conductor. Copper caps 0.15 mm and 0 .30 mm thick were also made to f i t over the first ionization chamber. The ionization chambers were used with a dose comparator which has been previously described ( 2 0 ) . This comparator is capable of measuring directly the ratio of the ionizations produced in two ionization chambers.* * The comparator consists of essentially two stable, linear, D.C. amplifiers whose outputs are balanced in a ratio bridge in which the balance point is found by null detection. It is designed to compare the ionization currents in two ionization chambers. The ionization current from each chamber flows through a very high resistance (lOlO to 1012 ohms) in the grid lead of an electrometer tube. The high negative feedback amplifier develops an a l -most equal voltage across a much lower resistance in the output circuit (A) LUCITE CHAMBER A , i i i i J 0.05 MM COPPER \ ) i i j 1 1 1 1 / J I t 1 I 1 1 1 1 1 / 1 / 1 I 1 f i i i i i i /\ • ' Y ' i i i i i i 1—7—7 7 7 7 f / / / I t i i J i ) i i i i i i J i i t / / / J / I i i i n (B) COPPER—LINED CHAMBER FULL SCALE V / A ALUMINIUM |v-' • ] LUCITE 1 POLYSTYRENE FIGURE 5. CROSS-SECTION DRAWING OF IONIZATION CHAMBERS - 15 -By selection of suitable input resistances for the two ionization chambers and by selection of circuit in the ratio bridge the comparator can be used to measure directly ratios up to one thousand. Provided the intensity to which the chambers are exposed is sufficient these ratios may be measured with an accuracy of 1% or better. To measure ionization ratios two ionization chambers were clamped side by side in a wooden block (Figure 6) and were exposed to x-rays of known kilovoltage and known added fi ltration. The ratio of the ionization currents was determined by means of the comparator. The wooden block was than rotated 180° to interchange the positions of the chambers and the ratio of ionization currents was again determined. The average of these two readings was taken as the true ratio of the ionization currents in the chambers. The interchanging of the two chambers eliminates errors due to non-uniformity over the radiation field. For each primary radiation three ratios.were measured: (1) The ratio of ionization current in chamber D to that in chamber A (see page 11) (2) The ratio of ionization current in chamber D to that in chamber B (3) The ratio of ionization current in chamber D to that in chamber C. The experimental measurements for (2) and (3) were identical with that for (l) except that for (2) the 0.15 mm copper cap was placed over the lucite chamber and for (3) the 0.3 mm copper cap was used. of the amplifier. The output from one amplifier is read directly as a percentage of the output from the other amplifier. The electrometer tube and the high input resistance of each amplifier are placed in a housing at the end of a cable. The ionization chambers plug into sockets in the preamplifier housings and the connecting cables in turn plug into the main amplifier cabinet. FIGURE 6 EXPERIMENTAL SETUP OF IONIZATION CHAMBERS - 16 -For each measurement the field size selected was large enough to provide a reasonably uniform exposure dose over the region occupied by the ionization chambers. The x-ray tube current was selected to provide suit-able intensity. However, for low voltages and heavy filtrations i t was not possible to get sufficient intensity for accurate measurements of ionization ratios. (This wil l be discussed later.) The three ratios specified, in the above paragraph were measured for a number of different kilovoltage-filter combinations. The experimental results are shown in Tables XLI to XLIII. For each kilovoltage and f i l ter in each table, four values are shown. The two values on the same line are the two readings obtained by interchanging the two chambers. The values in the two lines are results for two independent measurements. Differences in the two values in the same line may be interpreted as due to (a) non-uniformity in the radiation field or (b) lack of sensi-t iv i ty . Differences between the values obtained in the two independent measurements must be explained as due to (a) a failure to duplicate the experimental conditions exactly or (b) lack of sensitivity. Measurements for H4.O KV and higher were made with a 220 KV x-ray machine. This machine has better voltage control, provides a larger field and, for a l l f i lters used, gives adequate intensity. The readings for 120 KV and less were measured with a superficial x-ray machine. With this machine the intensity is relatively low, the field size is small and i t is difficult to control kilovoltage closely. The variations between the four readings for a given spectrum are greatest for low kilovoltage, particularly for the ratio of chambers D to 0 . Part of this variation may be due to TABLE XLI MEASURED RATIO OF IONIZATION OF CHAMBERS D TO A Kilovoltage Added Filter 0 . 2 0 mm Sn None 0 . 5 mm Al 1 . 0 ram Al 3 . 0 mm Al O.50 mm Cu _i_ 0 . 2 5 + mm Cu 1 . 0 mm Al 1 . 0 mm Al liO 1 5 . 6 15 . 3 lit.3 1U.U 18 .3 17 .2 1 7 . 2 17 . 0 2U .L 26.8 2 2 . 0 23.9 6 0 16.6 1 6 . 6 16 . 7 16.7 2 1 . U 21 . 5 20.9 21 . 0 2 5 . 0 2U.8 2k.k 2k.k 32.8 33.6 31 . 5 3 2 . 3 80 20.h 2 0 . 3 2 0 . 0 2 0 . 2 2 5 . 0 2 5 . 3 2k. 6 2U .7 28.7 28 .5 28.1 28.2 36.7 3 6 . 6 35 .U 36 . 0 100 2 2 . 5 2 2 . 5 2 2 . 3 22.3 27.5 27.3 26.9 26.8 3 0 . 7 3 0 . 3 3 0 . 1 3 0 . 0 3 7 . 2 3 7 . 3 3 7 . 2 3 6 . 6 120 23.9 23.8 23-8 23 .3 2 8 . k 28. U 28.1 27.9 31 .3 3 1 . 1 31 . 0 37.h 3 7 . 3 37 . 2 36.6 lliO 3 6 . 5 3 6 . 5 36.1i 3 6 . 6 3 U . 2 3U.U 33 . 8 3U.U 30.8 30.9 30.2 30.lt 160 35.9 3 6 . 2 3 6 . 1 3 6 . 5 3 2 . 1 3 2 . 3 31.9 32.1 2 8 . 1 28.2 27.8 28 . 0 180 3 5 . 5 3 5 . 5 35 .8 3 6 . 0 36.1* 36.7 36 .U 36.9 3 0 . 3 3 0 . 6 30.3 3 0 . k 2 6 . 5 26.2 2 6 . 0 26.2 200 3k.9 3U-6 3 5 . 0 3 5 . U 28.6 28.7 28.3 28.6 2U.2 2U.2 2h.2 2U.2 220 3 U . 2 33.9 3 U . 3 3 U . 6 3k.k 3 5 . 0 3 U . 0 3)4.6 26.6 26.8 26.5 26.8 22.7 22.6 22.3 22.3 TABLE XLII MEASURED RATIO OF IONIZATION OF CHAMBERS D TO B Added Filter Kilovoltage 0.20 mm Sn t None 0.5 ram Al 1.0 mm Al 3.0 mm Al 0.50 mm Cu 0.25 mm Cu 1.0 mm Al 1.0 mm Al ho 116 11+6 125 1U6 110 11*1 116 129 111 123 110 133 95.5 100 95.5 116 60 98 117 109 119 93.h 103 111; 110 92.3 108 97.6 108 82.3 92.6 86.7 9k.2 80 87.8 107 95.9 105 81;. 5 100 91.2 98 82.0 9k.6 87.1 93.8 73.2 81.6 77.1 81.3 100 79.3 93.5 86.1 92.6 76.8 89.3 81.6 86.8 73.9 83.8 78.1; 83.5 66.6 73.2 70.1 73.0 120 73. h 85.1* 79.5 8k.5 71.8 81.0 75.7 81.0 69.1 76.7 72.9 77.8 61.8 67.2 6U.6 68.0 IliO 6k. 5 61.3 65.7 61.6 39.5 38.5 39.2 38.3 33.8 33.1 33.6 32.6 160 60.6 57.3 61.2 57.5 36.6 35.9 36.6 36.2 31.1 30.1* 30.6 30.3 180 56.U 51;. 5 57.3 5k. 8 53.7 52.7 U8.U U8.8 33.8 33.7 31*. 1 33.1 28.6 27.9 28.2 27.6 200 5k.3 51.3 5U.8 52.0 31.7 31.1; 31.U 31.1* 26.2 26.0 25.9 25.7 220 50.6 U8.5 51.5 k8.9 U7.5 U7.6 1*3.1 1*3.8 29.1; 29.0 29.1 28.9 2U.5 21*. 1 23.6 23.5 TABLE XLIII MEASURED RATIO OF IONIZATION OF CHAMBERS D TO C Kilovoltage Uo 60 80 100 120 1U0 160 180 200 220 Added Filter None 7 3 8 5 1 7 U92 272 223 195 17U 1 5 5 1U7 1 3 2 9 0 . 7 85.U 81.7 7 5 . 7 7U.U 7 1 . 8 6 8 . U 6U.U 6 3 . 1 6 0 . 0 6U6 688 313 3 0 U 211 209 168 16U 1U2 139 92.3 86.0 82.6 77.9 7U.9 72.0 68.6 66.3 6U.0 61.0 0.5 mm Al 688 U70 3 1 0 2U9 2 0 7 1 7 7 160 1U2 135 1 2 2 5U3 5U3 2 7 9 272 199 1 9 0 1 5 7 1 5 0 1 3 3 1 3 2 1 . 0 mm Al 607 516 U30 U70 279 258 225 252 190 16U 1U8 133 183 176 1 U 3 1 U 2 1 2 5 123 1 1 5 1 2 1 6 5 . 9 6 5 . 7 5 6 . 3 5 6 . 6 3 . 0 mm Al 382 UU8 2 6 5 2 1 5 U31 U13 2 6 5 199 1U8 1U8 1 5 0 lUo 1 1 8 1 1 5 1 2 0 l iU 1 0 1 1 0 0 1 2 3 97 5 7 . 9 5 7 . 2 5 0 . 8 5 0 . 3 0 . 5 0 mm Cu + 1 . 0 mm Al 0 . 2 0 mm Sn + 0 . 2 5 iron Cu + 1 . 0 mm A l U 5 . 2 U 3 . 8 U i . 5 Uo.5 3 8 . 1 3 6 . 9 3 5 . 1 3 U . 1 3 2 . 0 31.U U 5 . 6 U 3 . 8 U l . 5 U 0 . 2 3 8 . 1 3 6 . 8 3 5 . 3 3 U . 1 3 2 . 2 3 1 . 2 37.6 36.8 3 U . 1 3 3 . 3 3 1 . 2 3 0 . 9 28.6 27.6 2 6 . 1 2 5 . 2 3 7 . 2 3 6 . U 3 3 . 5 3 2 . 9 3 0 . 8 3 0 . 2 2 8 . 0 27.5 2 5 . 3 2 5 . 1 - 17 -failure to maintain a constant kilovoltage since i t is in this range that the ratios are most dependent on kilovoltage. Part is due to lack of sensitivity resulting from low intensity. In this case the ratio of the ionization in chamber D to that in chamber B may be more useful than the ratio of chambers D to C. - 18 -COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED VALUES The experimental results are qualitatively in agreement with calculated values. Quantatively, however, the experimental values are, in general, smaller than the calculated ones and, further, they show less change with change in kilovoltage and with change in f i l ter . For a given kilovoltage and a given total f i ltration, the two sets of values differ for two reasons: (a) The use of an aluminium centre electrode in both chambers reduces the experimental emission ratio since the emission in the lucite chamber is increased and the emission in the copper-lined chamber is decreased by the aluminium. (b) For the lowest quantum energies, the air cavity is not small enough to satisfy the Bragg-Gray principle, i . e . , appreciable ionization is produced by secondary electrons arising in the cavity. This tends to reduce the emission ratio s t i l l further. Further, i t should be noted that in the theorectical calculations total fi ltration is stated while in the experimental measurements added f i l ter is given. The inherent filtration in an x-ray machine is commonly equivalent to about 0.5 to 1.0 mm of aluminium. In comparing experimental results with calculated values, allowance must be made for this extra f i l t ra -tion. For example, the experimental emission ratios for no added fi lter should be compared with the corresponding calculated values for 0.5 mm to 1.0 mm aluminium total f i l ter . The apparent discrepancy in the experimental measurements with no added f i l ter can be accounted for by the fact that the 220 KV unit used for measurements at lkO KV and higher has appreciably greater - 19 -inherent filtration than the superficial therapy unit used for measurements at lower voltages. While the experimental ratios change less rapidly with changing kilovoltage and f i l ter than do the calculated values, they s t i l l provide a sensitive description of quality. - 20 -EXPERIMENTAL MEASUREMENTS IN WATER To test the usefulness of the method for investigating the quality of radiation in a scattering medium measurements of the emission and absorp-tion ratios were made in water exposed to x-rays of known kilovoltage and known added f i l ter . For these measurements the two chambers were coated with beeswax to waterproof them and placed in a tank of water at a measured depth below the surface on which an x-ray beam was incident. The two chambers were placed one on either side of the central axis of the x-ray beam and about equidistant from i t so that they were exposed to radiation of approximately the same intensity and quality. Two measurements were made with the chambers interchanged in position as in the measurements of primary spectra. The ratios were measured at several different depths. The physical arrangement of the chambers prevented measurements at a depth of less than 1.3 cm; the maximum depth of measurement was limited by intensity. The results are given in Tables XLIV - XLVI for three different qualities of primary radiation. The kilovoltage and the added f i l ter of the incident x-rays are shown at the head of each table. The values shown are the average of at least two and sometimes four measurements. The results for large depths are less reliable than for smaller depths because of low intensity at large depths. For primary radiation generated at 80 KV, (Tables XLIV and XLV) the change of quality with change of depth in water cannot be determined with certainty from the emission ratio alone but when the absorption ratios are taken into account i t is evident that the radiation is getting harder To Follow Page 20 TABLE XLI? EMISSION AND ABSORPTION RATIOS FOR DEGRADED RADIATION AT DIFFERENT DEPTHS IN WATER Incident Radiation: Field Size: 80 KV, 7.5 cm 1.0 mm Al Added Filter Diameter Depth (cm) Emission Ratio (D/A) Absorption Ratios D/B D/C 1.3 29.1 93.7 195 2.0 31.0 91.9 187 3.0 33.0 89.U 179 5.0 35-7 86.7 16U 7.0 36.9 80.9 151 10.0 37.2 7U.U 135 15.0 35.U 62.8 103 TABLE XLV EMISSION AND ABSORPTION RATIOS FOR DEGRADED RADIATION AT DIFFERENT DEPTHS IN WATER Incident Radiation: Field Size: 80 KV, 7.5 cm 2.0 mm Al Added Filter Diameter Depth (cm) Emission Ratio (D/A) Absorption Ratios D/B D/C 1.3 3U.8 86.0 169 2.0 35.6 85.5 165 3.0 36.5 8U.0 161 ll.O 37.0 82.3 5.0 37.U 81.2 152 7.0 37.8 77.7 1U3 10.0 37.1 72.ii 129 i5.o 33.0 59.3 103 To Follow Page 20 TABLE XLVI EMISSION AMD ABSORPTION RATIOS FOR DEGRADED RADIATION AT DIFFERENT DEPTHS IN WATER Incident Radiation: 220 KV, 0.20 mm Sn + 0.25 mm Cu + 1.0 mm Al Added Filter Field Size: 10 x 10 cm Depth (cm) Emission Ratio (D/A) Absorption Ratios D/B D/C 1.3 27.9 31.9 35.3 2.0 28.3 32.U 36.2 3.0 28.6 33.1 36.8 U.o 28.8 33.5 37.6 5.o 28.9 33.8 38.3 6.0 29.1 3U.1 38.5 7.0 29.1 3U.1 38.9 8.0 29.1 3U.1 39.0 , 9.0 29.1 10.0 28.8 3U.2 39.3 11.0 28.9 .12.0 28.7 3U.0 39.2 i5.o 28.2 33.3 38.1 17.0 27.U 31.9 36.8 18.5 26.li 30.6 3U.9 21 -with increasing depth. It is interesting to note that the quality of the radiation at 1$ cm depth is practically independent of the added f i l ter used in the primary beam. For radiation generated at 220 KV (Table XLVI) i t can be seen that even at 1.3 cm depth, the radiation is considerably softer than the incident primary radiation and gradually becomes s t i l l softer to a depth of 8 or 10 cm. Beyond this depth i t becomes gradually harder. This is in qualitative agreement with results obtained by Clarkson & Mayneord (lk). The quality at 18 cm is very similar to that at 1.3 cm. When radiation is transmitted through a medium, so far as change of quality with increasing depth is concerned, there are two competing processes: (a) The primary radiation is "filtered" by the medium (b) Scattered radiation is introduced into the beam. The first process tends to harden the radiation while the second tends to soften i t . For the 80 KV radiation investigated i t is evident that the filtering action was predominant. For 220 KV radiation, for small depths the second effect obscured the first while at greater depths the reverse was true. - 22 -FURTHER WORK While the emission and absorption ratios measured in this work appear to give a useful and practical description of radiation quality, i t i s possible that with further work more sensitive and more significant ratios might be found. In particular, i t may be possible that for very soft radiation an aluminium-lined chamber would be more useful than a copper-lined chamber. With the present experimental set-up of the two ionization chambers, i n which they are separated by about U cm, i t is not possible to use the method to determine quality in regions i n which the quality or intensity changes rapidly with position in the f i e l d . For example, i t i s not possible to use the present set-up to investigate the change in quality near or at the edge of the irradiated f i e l d . A more compact and preferrably coaxial arrangement of chambers such as has been used by other workers (llj.,13>>l6) would be desirable. - 23 -BIBLIOGRAPHY SILBERSTEIN, L . F . , "Determination of Spectral Composition of X-ray Radiation from Filtration Data". Opt. Soc. Amer., XXII, 265, 1932 JONES, D.E.A. , "The Determination from Absorption Data of the Distribution of X-ray Intensity in the Continuous X-ray Spectrum". Brit . Journ. Rad., XIII, 95, 191+0 GREENING, J .R. , "The Determination of X-ray Energy Distributions by the Absorption Method". Brit . Journ. Rad., XX, 71, 19U7 GREENING, J .R. , "The Determination of X-ray Wavelength Distribution from Absorption Data". Proc. Phys. Soc. A, LXIII, 1227, 1950 PROCTOR, N.M. and GREENING, J .R. , "On the Adequacy of Half-Value Layer as a Criterion of X-ray Quality in the Calibration of Dosemeters". Brit . Journ. Rad., XXXIII, 321, I960 CORMACK, D.V., GRIFFITH, T . J . and JOHNS, H . E . , "Measurement of the j Spectral Distribution of Scattered 1+00 KVp X-rays in a j Water Phantom". Brit. Journ. Rad.,. XXX, 129, 1957 DIX^N, W.R., "Angular Energy Flux of Secondary Gamma Rays in Matter: Small-Angle Scattering from a Point Isotropic Source". Can. J . Phys., XXXVI, 1+19, 1958 CORMACK, D.V., DAVITT, W.E., BURKE, B.E. and RAWSON, E . G . , "Spectral Distributions of 280 KVp X-rays". Brit. Journ. Rad., XXXI, 565, 1958 HETTINGER, G. and STARFELT, N. , "Energy and Angular Distribution of Scattered Radiation in a Water Tank Irradiated by X-rays". Arkiv. for Fysik, XIV, 1*97, 1959 MAK, S. and CORMACK, D.V., "Spectral Distributions of Scattered X-rays at Points Lying Off the Beam Axis". Brit . Journ. Rad., XXXni, 362, I960 QUIMBY, E.H. and McNATTEN, R .F . , "The Change in Quality of Roentgen Rays on Passing Through Tissue". Amer. Journ. Roentgenol., XXVIII, 236, 1932 GREENING, J .R. , "A Method of Determining the Wavelength Distribution of the X-radiation at a Point in a Scattering Medium". Brit . Journ. Rad., XXIV, 20U, 1951 BRUCE, W.R. and JOHNS, H.E . , "The Spectra of X-rays Scattered in Low Atomic Number Materials". Brit . Journ. Rad., Supplement No. 9, I960 - 2h -lh . CIARKSON, J.R. and MAYNEORD, W.V., "The 'Quality' of High Voltage Radiations: Part II 'Quality' within a Scattering Medium". Brit . Journ. Rad., XII, 168, 1939 15. WILSON, C.W., "Estimation of the 'Quality' of Depth Radiations in Gamma-Ray Therapy by Means of the Ionization Produced in Chambers with Wall Materials of Different Atomic Numbers". Brit . Journ. Rad., XII, 231, 1939 16. GREENING, J.R. and WILSON, C.W., "The Wavelength of the X-radiation at a Depth in Water Irradiated by Beams of X-rays". Bri t . Journ. Rad., XXIV, 605, 1951 17. KRAMERS, H.A., "On the Theory of X-Ray Absorption and of the Continuous X-Ray Spectrum". Phil. Mag., XLVI, 836, 1923 18. BRAGG, W.H., "Studies in Radioactivity". Macmillan, London, 1912 19. GRAY, L . H . , "An Ionization Method for the Absolute Measurement of y-ray Energy". Proc. Roy. Soc. A, CLVT, 578, 1936 20. MIBUS, S.A., "An X-ray Dose Comparator". Unpublished Master's Thesis, the University of British Columbia, 1956 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0103742/manifest

Comment

Related Items