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The concept of the angular differential dose of ionizing radiation and its measurement
Pergamon
Appl. Radiat. lsot. Vol. 48, No. 9, pp. 1251-1256, 1997 Published by ElsevierScienceLtd Printed in Great Britain P l h S0969-8043(97)00110-3 0969-8043/97 $17.00+ 0.00
The Concept of the Angular Differential Dose of Ionizing Radiation and Its Measurement S. KRONENBERG, G. J. BRUCKER and E. BECHTEL* US Army CECOM, NV Laboratory, Fort Monmouth, N J, U.S.A.
(Received 3 February 1997; accepted 28 March 1997) Radiation-induced effects often depend not only on the absorbed dose but also on the distribution of directions from which it is delivered. This distribution can be described by using the angular differential dose, whose integral over all angles equals the integrated dose. A directional sensor was developed to measure this quantity. The design of the sensor is based on a carbon fiber, self-reading, electrometer dosimeter. Its sensitivity to the direction of incident gamma rays or x-rays makes it possible to measure dose or dose rate as a function of the angle of incident radiation. Experiments to demonstrate the properties of this sensor (Directional Dosimeter, DD) were conducted, using point sources of 137Cs. Results show that the sensor can detect and locate multiple ~37Cssources and determine the angular differential dose or angular differential dose rate in physical units of grays (tissue) per degree or grays per degree per minute. The DD was also used to scan and image the back-scatter from a water target of monodirectionally incident 137Cs 662 keV gamma rays. Published by Elsevier Science Ltd
The Concept of Angular Differential Dose
D = ~o'~D,~(~p)dc~
Effects produced by ionizing radiation often depend not only on the absorbed dose but also on the direction or distribution of directions from which the dose is delivered to the target. In biological and medical applications, the effects in a body can depend on the direction of incident radiation. When a target material significantly absorbs the incident radiation, the different regions of the target receive different doses, depending on the direction from where the dose is delivered. In solid state devices that consist of materials with different atomic numbers, the dependence of effects on the direction of incident gamma rays or x-rays can be significant due to the p h o t o - C o m p t o n electrons and their distribution at interfaces of dissimilar materials (Wall and Burke, 1970; Frederickson and Burke, 1971; Brucker et al., 1995). To facilitate the work where radiation effects may' depend on the angular distribution of the delivered dose and to describe the radiation environment in a scientifically defined manner, we introduce here the concept of the angular differential dose. This quantity, D,, is defined for a two dimensional geometry where the sources of radiation and the point of interest are located on a plane as: *To whom all correspondence should be addressed at: US Army NBC Defense Systems, RADIAC Project Office, Attn: AMCPM-NNN-F, Fort Monmouth, NJ 07703-5211, U.S.A.
where grays For a in an
D is the dose in grays (e.g. grays (tissue) or (Si)) and the units of D~ are grays per radian. spherical distribution of sources, D~o is defined analogous manner as:
D~,o
D = •0
•0
where the units of D¢o (~b0) are grays per steradian. F o r a parallel beam of incident radiation D~ is a delta function whose integral is defined as D and in the case of isotropic radiation D~ is a constant. Similar definitions can be formulated for angular differential dose rate:with
(dO/dt)~ = D~(d:) for sources distributed on a plane:
b =
b,(4,)d(4,). 0
To measure the angular differential dose, directional sensors are required. One approach is the use of collimators combined with some type of detector which can scan the radiation field. This approach poses several problems. Collimators with a large angle of acceptance have necessarily a poor angular resolution and those with high angular resolution have a small angle of acceptance.
1251
1252
S. Kronenberg et al.
Our previously reported research (Kronenberg et al., 1996, 1997) has resulted in the development of
sensors which lend themselves very well to measuring D,. These sensors have a 47t solid angle of acceptance and simultaneously, high angular resolution that is limited only by the accuracy of the measurement of the angle. An angular resolution of approximately one second of arc was demonstrated experimentally. Those gamma ray and x-ray directional sensors can scan and generate one-dimensional images of broad and point sources of radiation. Depending on the sensitivity requirements, different sensor types can be used, such as ionization chambers, Geiger-Mueller tubes, scintillation counters, and solid-state detectors. All of those approaches provide the capability of measuring the angular differential dose.
Principle of Directional Sensor Operation For the convenience of the readers, the principle of operation of those sensors (from Kronenberg et al., 1996) is repeated here. A planar detector (e.g. a layer of scintillator) which is thin compared with the applicable ranges of the photo-Compton electrons is sandwiched between plates of low and high Z (atomic number) materials. For quantum energies of gamma rays greater than 0.6 MeV, the number of electrons emitted from the surfaces of the two layers into the detector is greater when the gamma rays enter through the low Z-layer than when they enter through the high Z-layer (Dellin et al., 1975). For lower quantum energies the emission effect is reversed, but now the incident gamma rays are attenuated more by the high Z-layer than the low Z-layer. Thus the signal is again greater when the gamma rays enter through the low Z-material as compared to the signal when the gamma rays enter through the high Z-layer. Those directional sensors produce response functions that look like step functions when the detectors are rotated in the fields of gamma ray or x-ray photons generated by point sources, and the incident radiation is parallel to the surfaces of the layers. It has been shown (Kronenberg et al., 1997) that the first derivative of the output of such a sensor versus angle is proportional to the incident intensity versus angle, thus, it is proportional to D~. To express the output in correct units, for example, D s in grays per minute per degree, the output function of the sensor must be normalized. To accomplish this, the sensor output that is the integral of the angular differential dose rate taken between its maximum (i.e. q~ = 0 °) and its minimum (i.e. q~ = 180 °) must be made equal to the dose rate obtained from an independent measurement made at the location of the sensor with a dosimeter that is calibrated in the desired units, e.g. grays (tissue) (hereafter Gy (T)). A new version of the directional sensor was used in experiments described here. The sensor was
fabricated from a carbon fiber, self-reading electrometer type of dosimeter. Figure 1 shows a drawing of the Directional Dosimeter (DD) and its dimensions. It performs on the same basic principle as the other previously described sensors, but is operable from intensities of 100 nGy (T) h -~ to 104 Gy (T) h -~. This performance range can be accomplished by the addition of capacitors to reduce the instrument's basic sensitivity. The capacitors can be connected in parallel between the electrometer chamber and ground.
Examples of Measurements of D, Scanning two point sources
Two sources of 137Cswere arranged to irradiate the DD sensor from different locations and planes relative to the detector. The geometry of the setup is described by the drawing in Fig. 2. The exposure times were 1.0 min. Sensor scans were made for an angular range of 0-360 ° with the detector rotating on the horizontal plane. The dose at the detector per one minute exposure was measured by a special 20 laGy (T) full-scale, self-reading dosimeter constructed in a similar manner to the DD sensor, except that there was no layer of lead in the ionization chamber, and it was cylindrically shaped with a chamber diameter and height of 5.1 cm. This device was calibrated by Shonka-Wyckoff (Far West Technology, Inc., Santa Barbara, CA) air ionization chambers __+5%, traceable to NIST (National Institute of Standards and Technology). The absorbed dose rates produced by the two sources at the detector location were: source 1, 7.10 laGy (T) min - ~; source 2, 12.65 laGy (T) min-
~ ) Axis of ~'-~/rotation Occular Lens c"~ tl/ ["--1 I Top part of a 200 mr l ~ I Range All Plastic Readout ctra) Dosimeter ~ i r o s c o p e ~
~ '
Carbon F i b e r / Electrometer
/ Charging
~
Objective
Pb Plate 1.7 mm
I,..LJr'~Insulator (Cerex 250 i-'~ Pr~eferredFormula) Switch
Bottom Part of the 200 mr Dosimeter
Plastic Body Made of 5 mm Thick Plates on Top and Bottom and 3 mm Thick Plates on the Sides Conductive Carbon Paint on the Inside Air Tight, Filled With Dry Air at Standard Pressure Fig. 1. Drawing of the Directional Dosimeter (DD)
sensor.
Angular differential dose of ionizing radiation Plane of Sensor's Rotation
1253
0o
..s"
45 °
Source I
136.9 cm
40.1
/
/
Source 2 Fig. 2. Experimental setup for scanning the radiation from two mCs sources with the DD sensor.
Figure 3 shows the mean values of two independent scans generated by the D D sensor. The data represent the responses of the detector as it rotated from 0 to 360 ° in the gamma ray fields from the two ~3~Cs sources. To convert the arbitrary scale readings per minute of the DD sensor to units of Gy (T) rain- ~, the difference in the maximum and minimum scale
L°-°.o.o.o,q
260
readings of the sensor response (range of angles from 0 to 180°) in Fig. 3, namely, 95 scale units rain - ~were set equal to the 20 I~Gy full-scale, tissue-equivalent, dosimeter measurement of 19.75 ttGy (T) minThis yielded a calibration factor of 0.2079 ~tGy (T) per scale reading per minute. The left hand y-axis in Fig. 3 is in arbitrary scale units rain - ~ (as measured)
One Scale Unit min-I = 0.2079 ~Gys (T) rain-t
50
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320 340 360
Arbitrary A n g l e O f Rotation, deg
Fig. 3. DD scan results showing the sensor's responses as a function of ~37Csgamma ray incident angles for the range 0-360 ° . The four direct and mirror images representing each of the two source locations are indicated in the plot.
S. Kronenberg et al.
1254 12 - -
One Scale Unit min-1 = 207.9 nGys (T) min-1 deg-! 11
2400
--
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-2000
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Arbitrary Angle Of Rotation, deg Fig. 4. Derivatives of the DD scan data as a function of radiation incident angles. These derivatives represent the angular differential dose rate measured by the sensor. Normalization of the DD's arbitrary scale units to physical units of nGy (tissue) min - ~ deg - ' is indicated by the right hand y-axis of the plot.
whereas the right hand y-axis is in laGy ( T ) m i n - ~ . Application of the calibration factor to the derivative data in Fig. 4, yields the desired angular differential dose in nGy (T) min-~ per degree as shown by the right hand y-axis units in Fig. 4. Note that the scan data are actually the integral of the intensity distribution that is described by the first derivative of the scan. Thus, the normalization by means of the 20 laGy dosimeter measurement can be directly applied to the experimental response of the detector. In contrast to this procedure, the application of a collimator plus some type of detector would measure the angular intensity distribution, and, consequently, the integral curve would have to be calculated via integration before the normalization could be accomplished. This process would introduce a large error in the normalization, which does not apply to the D D sensor. As discussed in previous publications (Kronenberg et al., 1996, 1997), the directional sensor produces two types of images, namely, a direct, and what we refer hereto as a mirror, image of each source due to the direction of rotation and the different signals generated by the front and back edges of the sensor. Thus, in this experiment, a total of four images were generated in the 0--360 ° scan. Those publications also showed how both the scan data and the
derivatives of the scan data yield the angular locations of the sources being scanned. Consequently, the plot in Fig. 4 shows that source I was located at 43.7 ° and source 2 at 136.25 ° and similarly, the mirror images yield corresponding values of 223.65 ° - 180 ° = 43.65 ° and 316.25 ° - 1 8 0 ° = 136.25 °, respectively. Equivalent source locations can also be deduced from the four transition regions in the scan data shown in Fig. 3. The excellent agreement between these two sets of angles is a strong verification of the measurements of the angular distribution. Scanning mCs gamma ray back-scatter f r o m a water target
Figure 5 shows the experimental arrangement of ~37Cs source and water target. Figure 6 shows the results of the scan with the D D sensor of the radiation. The detector response in units of ~tGy (T) per minute versus angle of rotation for a 360 ° scan of the 137Cs photon back-scatter from the container of water is shown in the figure. The corresponding derivatives of the scan data are also shown in the figure by the right hand y-axis in units o f n G y (T) per minute per degree. The calibration procedure to convert the arbitrary units to absolute values was the same as in the scan of the two ~37Cs sources.
Angular differential dose of ionizing radiation 33 cm
as calculated from the ruler measurements of distances is 29.9 ° (see Fig. 5). The mirror image is 180° out of phase with the direct image but must also yield the same subtended angle for the tank of water. The scan curve in Fig. 6 indicates that the transition region of the mirror image starts at an angle of 245 ° and ends at an angle of 275 °, that is, the subtended angle is again 30 ° in exact agreement with the direct image value. It can be seen that the direct and mirror image derivatives correspond to the transition regions, and their angular widths are about 30° in agreement with the scan data.
Water Tank
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~/
',
,'
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~
~
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Conclusions It can be concluded from the results of this study that the Directional Dosimeter is a sensor that can be used to measure the angular differential dose or dose rate of incident gamma rays or x-rays on a target; consequently, a new and useful quantity is now available to the radiation effects and medical communities. The simple and direct normalization procedure for this sensor makes it practical, easy to apply, and at the same time, accurate. In addition, the device is capable of locating radiation sources at very low dose rates. Calibration results indicate that the
31.8 cm Pb Shield Fig. 5. Experimental setup for the D D scan of backscattered ~37Csg a m m a rays from a polyethylene container of water.
The transition region of the direct image starts at an angle of 65° and terminates at an angle of 95 °. The angle subtended at the detector is the difference of these two angles, namely, 30° . The value of this angle 4 --
--
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Arbitrary Angle O f Rotation, deg Fig. 6. D D scan data of the ~37Csg a m m a ray back-scatter from a polyethylene container o f water. The derivatives of the scan data are also shown. It can be seen from the width of the transition regions and the derivatives that the radiation scatter pattern representing the angular width of the container is 30 ° .
1256
S. Kronenberg et al.
present design used in this study has a sensitivity of 208 n G y (T) per scale unit for incident ~37Cs g a m m a rays o f 662 keV energy.
References Brucker G., Kronenberg J. S. and Gentner F. (1995) Effects of package geometry, materials, and die design on energy dependence of P-MOS dosimeters. IEEE Transactions on Nuclear Science NS-42, 33-40. Dellin T. A., Huddleston R. E. and MacCallum C. J. (1975) Second generation analytical photo-Compton current methods. IEEE Transaction on Nuclear Science NS-22, 2549-2555. Frederickson A. R. and Burke E. A. (1971) Ionization,
secondary emission, and Compton currents at gammairradiated interfaces. IEEE Transactions on Nuclear Science NS-18, 162-169. Kronenberg S., Brucker G. J., Bechtel E. and Gentner F. (1996) Directional detector for arrays of gamma ray and X-ray sources. Nuclear Instruments and Methods in Physics Research A 378, 531-540. Kronenberg, S., Brucker, G. J., Bechtel, E., Gentner, F. and Lee, A. (1997) Sensors for locating and imaging sources of gamma and x-ray radiation either directly or through thick shields. Nuclear Instruments and Methods, Physics Research, A, 387, 401-409.. Wall J. A. and Burke E. A. (1970) Gamma dose distributions at and near the interface of different materials. IEEE Transactions on Nuclear Science NS-17, 305-309.
Appl. Radiat. lsot. Vol. 48, No. 9, pp. 1251-1256, 1997 Published by ElsevierScienceLtd Printed in Great Britain P l h S0969-8043(97)00110-3 0969-8043/97 $17.00+ 0.00
The Concept of the Angular Differential Dose of Ionizing Radiation and Its Measurement S. KRONENBERG, G. J. BRUCKER and E. BECHTEL* US Army CECOM, NV Laboratory, Fort Monmouth, N J, U.S.A.
(Received 3 February 1997; accepted 28 March 1997) Radiation-induced effects often depend not only on the absorbed dose but also on the distribution of directions from which it is delivered. This distribution can be described by using the angular differential dose, whose integral over all angles equals the integrated dose. A directional sensor was developed to measure this quantity. The design of the sensor is based on a carbon fiber, self-reading, electrometer dosimeter. Its sensitivity to the direction of incident gamma rays or x-rays makes it possible to measure dose or dose rate as a function of the angle of incident radiation. Experiments to demonstrate the properties of this sensor (Directional Dosimeter, DD) were conducted, using point sources of 137Cs. Results show that the sensor can detect and locate multiple ~37Cssources and determine the angular differential dose or angular differential dose rate in physical units of grays (tissue) per degree or grays per degree per minute. The DD was also used to scan and image the back-scatter from a water target of monodirectionally incident 137Cs 662 keV gamma rays. Published by Elsevier Science Ltd
The Concept of Angular Differential Dose
D = ~o'~D,~(~p)dc~
Effects produced by ionizing radiation often depend not only on the absorbed dose but also on the direction or distribution of directions from which the dose is delivered to the target. In biological and medical applications, the effects in a body can depend on the direction of incident radiation. When a target material significantly absorbs the incident radiation, the different regions of the target receive different doses, depending on the direction from where the dose is delivered. In solid state devices that consist of materials with different atomic numbers, the dependence of effects on the direction of incident gamma rays or x-rays can be significant due to the p h o t o - C o m p t o n electrons and their distribution at interfaces of dissimilar materials (Wall and Burke, 1970; Frederickson and Burke, 1971; Brucker et al., 1995). To facilitate the work where radiation effects may' depend on the angular distribution of the delivered dose and to describe the radiation environment in a scientifically defined manner, we introduce here the concept of the angular differential dose. This quantity, D,, is defined for a two dimensional geometry where the sources of radiation and the point of interest are located on a plane as: *To whom all correspondence should be addressed at: US Army NBC Defense Systems, RADIAC Project Office, Attn: AMCPM-NNN-F, Fort Monmouth, NJ 07703-5211, U.S.A.
where grays For a in an
D is the dose in grays (e.g. grays (tissue) or (Si)) and the units of D~ are grays per radian. spherical distribution of sources, D~o is defined analogous manner as:
D~,o
D = •0
•0
where the units of D¢o (~b0) are grays per steradian. F o r a parallel beam of incident radiation D~ is a delta function whose integral is defined as D and in the case of isotropic radiation D~ is a constant. Similar definitions can be formulated for angular differential dose rate:with
(dO/dt)~ = D~(d:) for sources distributed on a plane:
b =
b,(4,)d(4,). 0
To measure the angular differential dose, directional sensors are required. One approach is the use of collimators combined with some type of detector which can scan the radiation field. This approach poses several problems. Collimators with a large angle of acceptance have necessarily a poor angular resolution and those with high angular resolution have a small angle of acceptance.
1251
1252
S. Kronenberg et al.
Our previously reported research (Kronenberg et al., 1996, 1997) has resulted in the development of
sensors which lend themselves very well to measuring D,. These sensors have a 47t solid angle of acceptance and simultaneously, high angular resolution that is limited only by the accuracy of the measurement of the angle. An angular resolution of approximately one second of arc was demonstrated experimentally. Those gamma ray and x-ray directional sensors can scan and generate one-dimensional images of broad and point sources of radiation. Depending on the sensitivity requirements, different sensor types can be used, such as ionization chambers, Geiger-Mueller tubes, scintillation counters, and solid-state detectors. All of those approaches provide the capability of measuring the angular differential dose.
Principle of Directional Sensor Operation For the convenience of the readers, the principle of operation of those sensors (from Kronenberg et al., 1996) is repeated here. A planar detector (e.g. a layer of scintillator) which is thin compared with the applicable ranges of the photo-Compton electrons is sandwiched between plates of low and high Z (atomic number) materials. For quantum energies of gamma rays greater than 0.6 MeV, the number of electrons emitted from the surfaces of the two layers into the detector is greater when the gamma rays enter through the low Z-layer than when they enter through the high Z-layer (Dellin et al., 1975). For lower quantum energies the emission effect is reversed, but now the incident gamma rays are attenuated more by the high Z-layer than the low Z-layer. Thus the signal is again greater when the gamma rays enter through the low Z-material as compared to the signal when the gamma rays enter through the high Z-layer. Those directional sensors produce response functions that look like step functions when the detectors are rotated in the fields of gamma ray or x-ray photons generated by point sources, and the incident radiation is parallel to the surfaces of the layers. It has been shown (Kronenberg et al., 1997) that the first derivative of the output of such a sensor versus angle is proportional to the incident intensity versus angle, thus, it is proportional to D~. To express the output in correct units, for example, D s in grays per minute per degree, the output function of the sensor must be normalized. To accomplish this, the sensor output that is the integral of the angular differential dose rate taken between its maximum (i.e. q~ = 0 °) and its minimum (i.e. q~ = 180 °) must be made equal to the dose rate obtained from an independent measurement made at the location of the sensor with a dosimeter that is calibrated in the desired units, e.g. grays (tissue) (hereafter Gy (T)). A new version of the directional sensor was used in experiments described here. The sensor was
fabricated from a carbon fiber, self-reading electrometer type of dosimeter. Figure 1 shows a drawing of the Directional Dosimeter (DD) and its dimensions. It performs on the same basic principle as the other previously described sensors, but is operable from intensities of 100 nGy (T) h -~ to 104 Gy (T) h -~. This performance range can be accomplished by the addition of capacitors to reduce the instrument's basic sensitivity. The capacitors can be connected in parallel between the electrometer chamber and ground.
Examples of Measurements of D, Scanning two point sources
Two sources of 137Cswere arranged to irradiate the DD sensor from different locations and planes relative to the detector. The geometry of the setup is described by the drawing in Fig. 2. The exposure times were 1.0 min. Sensor scans were made for an angular range of 0-360 ° with the detector rotating on the horizontal plane. The dose at the detector per one minute exposure was measured by a special 20 laGy (T) full-scale, self-reading dosimeter constructed in a similar manner to the DD sensor, except that there was no layer of lead in the ionization chamber, and it was cylindrically shaped with a chamber diameter and height of 5.1 cm. This device was calibrated by Shonka-Wyckoff (Far West Technology, Inc., Santa Barbara, CA) air ionization chambers __+5%, traceable to NIST (National Institute of Standards and Technology). The absorbed dose rates produced by the two sources at the detector location were: source 1, 7.10 laGy (T) min - ~; source 2, 12.65 laGy (T) min-
~ ) Axis of ~'-~/rotation Occular Lens c"~ tl/ ["--1 I Top part of a 200 mr l ~ I Range All Plastic Readout ctra) Dosimeter ~ i r o s c o p e ~
~ '
Carbon F i b e r / Electrometer
/ Charging
~
Objective
Pb Plate 1.7 mm
I,..LJr'~Insulator (Cerex 250 i-'~ Pr~eferredFormula) Switch
Bottom Part of the 200 mr Dosimeter
Plastic Body Made of 5 mm Thick Plates on Top and Bottom and 3 mm Thick Plates on the Sides Conductive Carbon Paint on the Inside Air Tight, Filled With Dry Air at Standard Pressure Fig. 1. Drawing of the Directional Dosimeter (DD)
sensor.
Angular differential dose of ionizing radiation Plane of Sensor's Rotation
1253
0o
..s"
45 °
Source I
136.9 cm
40.1
/
/
Source 2 Fig. 2. Experimental setup for scanning the radiation from two mCs sources with the DD sensor.
Figure 3 shows the mean values of two independent scans generated by the D D sensor. The data represent the responses of the detector as it rotated from 0 to 360 ° in the gamma ray fields from the two ~3~Cs sources. To convert the arbitrary scale readings per minute of the DD sensor to units of Gy (T) rain- ~, the difference in the maximum and minimum scale
L°-°.o.o.o,q
260
readings of the sensor response (range of angles from 0 to 180°) in Fig. 3, namely, 95 scale units rain - ~were set equal to the 20 I~Gy full-scale, tissue-equivalent, dosimeter measurement of 19.75 ttGy (T) minThis yielded a calibration factor of 0.2079 ~tGy (T) per scale reading per minute. The left hand y-axis in Fig. 3 is in arbitrary scale units rain - ~ (as measured)
One Scale Unit min-I = 0.2079 ~Gys (T) rain-t
50
Direct Image ! S;ur..ce #I
240
!d
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Source #2
220 ~0.
o "~ 200
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180 200
I
I
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220
240
260
I
I
280 300
L
L
320 340 360
Arbitrary A n g l e O f Rotation, deg
Fig. 3. DD scan results showing the sensor's responses as a function of ~37Csgamma ray incident angles for the range 0-360 ° . The four direct and mirror images representing each of the two source locations are indicated in the plot.
S. Kronenberg et al.
1254 12 - -
One Scale Unit min-1 = 207.9 nGys (T) min-1 deg-! 11
2400
--
--
Mirror Image Source #2 10
2200
-2000
7
7
9 --
1800
Direct Image Source #2
7
Direct Image Source #1
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r-r280
300
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Arbitrary Angle Of Rotation, deg Fig. 4. Derivatives of the DD scan data as a function of radiation incident angles. These derivatives represent the angular differential dose rate measured by the sensor. Normalization of the DD's arbitrary scale units to physical units of nGy (tissue) min - ~ deg - ' is indicated by the right hand y-axis of the plot.
whereas the right hand y-axis is in laGy ( T ) m i n - ~ . Application of the calibration factor to the derivative data in Fig. 4, yields the desired angular differential dose in nGy (T) min-~ per degree as shown by the right hand y-axis units in Fig. 4. Note that the scan data are actually the integral of the intensity distribution that is described by the first derivative of the scan. Thus, the normalization by means of the 20 laGy dosimeter measurement can be directly applied to the experimental response of the detector. In contrast to this procedure, the application of a collimator plus some type of detector would measure the angular intensity distribution, and, consequently, the integral curve would have to be calculated via integration before the normalization could be accomplished. This process would introduce a large error in the normalization, which does not apply to the D D sensor. As discussed in previous publications (Kronenberg et al., 1996, 1997), the directional sensor produces two types of images, namely, a direct, and what we refer hereto as a mirror, image of each source due to the direction of rotation and the different signals generated by the front and back edges of the sensor. Thus, in this experiment, a total of four images were generated in the 0--360 ° scan. Those publications also showed how both the scan data and the
derivatives of the scan data yield the angular locations of the sources being scanned. Consequently, the plot in Fig. 4 shows that source I was located at 43.7 ° and source 2 at 136.25 ° and similarly, the mirror images yield corresponding values of 223.65 ° - 180 ° = 43.65 ° and 316.25 ° - 1 8 0 ° = 136.25 °, respectively. Equivalent source locations can also be deduced from the four transition regions in the scan data shown in Fig. 3. The excellent agreement between these two sets of angles is a strong verification of the measurements of the angular distribution. Scanning mCs gamma ray back-scatter f r o m a water target
Figure 5 shows the experimental arrangement of ~37Cs source and water target. Figure 6 shows the results of the scan with the D D sensor of the radiation. The detector response in units of ~tGy (T) per minute versus angle of rotation for a 360 ° scan of the 137Cs photon back-scatter from the container of water is shown in the figure. The corresponding derivatives of the scan data are also shown in the figure by the right hand y-axis in units o f n G y (T) per minute per degree. The calibration procedure to convert the arbitrary units to absolute values was the same as in the scan of the two ~37Cs sources.
Angular differential dose of ionizing radiation 33 cm
as calculated from the ruler measurements of distances is 29.9 ° (see Fig. 5). The mirror image is 180° out of phase with the direct image but must also yield the same subtended angle for the tank of water. The scan curve in Fig. 6 indicates that the transition region of the mirror image starts at an angle of 245 ° and ends at an angle of 275 °, that is, the subtended angle is again 30 ° in exact agreement with the direct image value. It can be seen that the direct and mirror image derivatives correspond to the transition regions, and their angular widths are about 30° in agreement with the scan data.
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Conclusions It can be concluded from the results of this study that the Directional Dosimeter is a sensor that can be used to measure the angular differential dose or dose rate of incident gamma rays or x-rays on a target; consequently, a new and useful quantity is now available to the radiation effects and medical communities. The simple and direct normalization procedure for this sensor makes it practical, easy to apply, and at the same time, accurate. In addition, the device is capable of locating radiation sources at very low dose rates. Calibration results indicate that the
31.8 cm Pb Shield Fig. 5. Experimental setup for the D D scan of backscattered ~37Csg a m m a rays from a polyethylene container of water.
The transition region of the direct image starts at an angle of 65° and terminates at an angle of 95 °. The angle subtended at the detector is the difference of these two angles, namely, 30° . The value of this angle 4 --
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present design used in this study has a sensitivity of 208 n G y (T) per scale unit for incident ~37Cs g a m m a rays o f 662 keV energy.
References Brucker G., Kronenberg J. S. and Gentner F. (1995) Effects of package geometry, materials, and die design on energy dependence of P-MOS dosimeters. IEEE Transactions on Nuclear Science NS-42, 33-40. Dellin T. A., Huddleston R. E. and MacCallum C. J. (1975) Second generation analytical photo-Compton current methods. IEEE Transaction on Nuclear Science NS-22, 2549-2555. Frederickson A. R. and Burke E. A. (1971) Ionization,
secondary emission, and Compton currents at gammairradiated interfaces. IEEE Transactions on Nuclear Science NS-18, 162-169. Kronenberg S., Brucker G. J., Bechtel E. and Gentner F. (1996) Directional detector for arrays of gamma ray and X-ray sources. Nuclear Instruments and Methods in Physics Research A 378, 531-540. Kronenberg, S., Brucker, G. J., Bechtel, E., Gentner, F. and Lee, A. (1997) Sensors for locating and imaging sources of gamma and x-ray radiation either directly or through thick shields. Nuclear Instruments and Methods, Physics Research, A, 387, 401-409.. Wall J. A. and Burke E. A. (1970) Gamma dose distributions at and near the interface of different materials. IEEE Transactions on Nuclear Science NS-17, 305-309.