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Colored tracks of heavy ion particles recorded on photographic color film
Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Colored tracks of heavy ion particles recorded on photographic color film K. Kugea, N. Yasudab,*, H. Kumagaic, N. Aokia, A. Hasegawaa a
Department of Information and Image Sciences, Faculty of Engineering, Chiba University, Inage, Chiba, 263-8522, Japan b National Institute of Radiological Sciences, Anagawa 4-9-1, Inage, Chiba 263–8555, Japan c Radioisotope Research Center, Chiba University, Inage, Chiba 263-8522, Japan Received 2 January 2001; received in revised form 7 March 2001; accepted 7 July 2001
Abstract A new method to obtain the three-dimensional information on nuclear tracks was developed using color photography. Commercial color films were irradiated with ion beam and color-developed. The ion tracks were represented with color images in which different depths were indicated by different colors, and the three-dimensional information was obtained from color changes. Details of this method are reported, and advantages and limitations are discussed in comparison with a conventional method using a nuclear emulsion. r 2002 Elsevier Science B.V. All rights reserved. PACS: 07.68; 29.40.G; 42.66.N Keywords: Nuclear track; Color photography; Nuclear emulsion
1. Introduction Nuclear emulsions can record the charged particle tracks with an accuracy of less than 1 mm while keeping their three-dimensional structure. Since no other detector with a spatial resolution like that of emulsions exists, nuclear emulsions are widely used today for particle physics [1], nuclear physics [2], cosmic-ray physics [3], and space radiation dosimetry [4]. The standard emulsion contains silver halide grains as an active compo*Corresponding author. Fax: +81-43-251-4531. E-mail addresses: [email protected] (K. Kuge), [email protected] (N. Yasuda).
nent dispersed in a gelatin layer, and it is normally used in the form of an emulsion plate on a transparent base (some kind of plastic or glass). Since the focus depth of a microscope is much less (B10 mm) than the emulsion plate thickness, the focal plane of the objective lens is moved up and down in order to obtain the three-dimensional information. Thus, considerable time is needed for the track recognition in the emulsion. Recently, applications to experiments which required high statistical reliability have been carried out [1,5] using a fully automated high-speed analyzing system with high-speed processing. As for the emulsion itself, though the fine grain (small particle size) emulsion is available, a method for
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 5 1 6 - 9
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
coating the emulsion at a thickness with good homogeneity in a large area was developed, resolution for the depth direction has not been improved regarding the microscope used. Thus, the full potential of emulsions for providing three-dimensional information cannot be utilized. We propose here a new method for displaying colored tracks; color photography is used to obtain depth information in the emulsion by different colors. Normal color photographic films are made from stacking of three emulsion layers, which are individually sensitive to red, green or blue light [6]. When the film is exposed to light, silver halide grains dispersed in the emulsion undergo chemical changes to form a latent image speck on the grains [7]. Color negatives represented as cyan, magenta or yellow dyes are produced from color couplers within the layers through color development. During development, the developer reduces the grains having latent image specks to metallic silver, and at the same time oxidized developing agent combines with the couplers to form dye molecules [8]. The dyes form in the emulsion at the exact location of the exposed silver halide grains. Later, all silver and silver salt are removed and the dyes are left behind to form the image of the object. Fig. 1 shows a schematic drawing of the principle proposed here. Since silver halide grains are also sensitive to charged particles, the particles form latent image specks on the grains along the track. Dyes are formed along the track after the color development. Since each layer includes different couplers, different color dyes are formed in each layer. The difference in track depth leads to the difference in color, so that we can obtain threedimensional information on the track by observation of color. We examined the method to display the track as a color image and discussed its advantages and limitations, using commercial color films, in comparison with nuclear emulsions.
2. Experimental Commercial color films (Superia: Fuji Photo Film) with different sensitivity (ISO 100 and ISO
559
800) were used for this study. These films are composed of three main layers which display yellow, magenta and cyan colors from the top after the color development. The rolled film in a cartridge was irradiated by 290 MeV/n carbon or 290 MeV/n xenon ion beams at a density of 104 –105 ions/cm2 accelerated by HIMAC (Heavy Ion Medical Accelerator in Chiba) in the National Institute of Radiological Sciences. The exposed films were developed with a standard color development treatment in a commercial lab. The developed films were observed with an optical microscope. In order to measure the thickness of each layer a section of the film was made with a microtome and observed with the optical microscope.
3. Results and discussion Fig. 2 shows a photomicrograph of xenon tracks represented by three primary colors. The xenon ions entered the film at a shallow angle from the top right in the figure. The tracks are represented with the three colors, yellow, magenta and cyan, and their mixture. The three colors, which are arranged in the order of yellow, magenta and cyan from the top, indicate the depths of tracks in the film layer. The tracks B, C and E in Fig. 2 are of three colors and this suggests that the ion particles passed through all three layers. Tracks C and E represent the sharp and clear end in the cyan region. These tracks seem to have stopped in the cyan region of the film. On the other hand, there is no cyan region for tracks A and D. They stopped in the magenta layer and did not reach the cyan layer. In other words, the range (energy) difference of each track can be detected by color difference. Fig. 3 shows a photomicrograph of a section of the color film used. A stack of layers is recognized clearly. The layers are arranged in the order of a protecting layer, the blue-sensitive emulsion layer which reveals the yellow color, a yellow filter layer, the green-sensitive layer which reveals the magenta color, an intermediate layer and the red-sensitive layer which reveals the cyan color. Total thickness of the emulsion layers including other intermediate layers is 15 mm. The blue- and
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K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 1. Schematic diagram displaying tracks of different depths with different colors to obtain three-dimensional information on the tracks.
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
561
Fig. 2. Optical photomicrograph of tracks of a xenon ion beam irradiated on the commercial color film at a shallow angle. The bar indicates 100 mm.
green-sensitive layers are each 4 mm thick and the red-sensitive layer is 5 mm thick. Therefore, we can expect the depth resolution corresponding to those values. Fig. 4 also shows a photomicrograph of xenon tracks. In this case, the entrance angles of the ions were also shallow, but they were each different. Although the order of coloring is cyan, magenta and yellow from the right for most of the tracks, that for track A is in the reverse order which is yellow, magenta and cyan from the right. This suggests that the ion forming track A entered from the opposite side of the film with a similar shallow angle. Ions entering the plane symmetrically can be discriminated from the order of the coloring. This is an advantage of this method which cannot be found in normal black and white photographic plates. Figs. 5a and b show microphotographs of carbon tracks exposed on the high (ISO 800) and
the low (ISO 100) sensitivity films, respectively. Carbon ions entered at a right angle to the film. As tracks pass through the three layers perpendicularly, the spots have three overlapped colors and they are observed as black spots. The track sizes are about 3 mm for ISO 100 film and about 7 mm for ISO 800 film. There is also some noise due to g-rays or d-rays. However, the noise consists of a dye cloud of a single color and we observe it as a monochromatic spot. Therefore, it is easy to distinguish the ion tracks from the noise by the color, even though the sizes of noise and tracks are similar. Since sensitivity of the photographic film increases with the size of the silver halide grains and grain size is related to the size of dye cloud, the dye clouds in the ISO 800 film are larger than those in the ISO 100 film. However, the observed dye clouds have a wide size distribution, as the grain size in commercial color film has a wide
562
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 3. Optical photomicrograph of a section of the commercial color film. The film surface is the upper part. The bar indicates 10 mm.
distribution. The maximum sizes of the dye clouds are 10 mm for yellow, 7 mm for magenta and 6 mm for cyan in the ISO 800 film, and 4 mm for yellow, 3 mm for magenta and 3 mm for cyan in the ISO 100 film. The size of silver halide grains in commercial film is larger than that of a usual nuclear emulsion which is about 3:5 mm and we can observe the former as a black grain (0:7– 1:0 mm) after development. The resolving power of tracks in color films is not as high as the nuclear emulsion. Monochromatic blurs and tails associated with the black spot may be formed by d-rays. However, we cannot observe clearly d-rays near the track when using these commercial films. A production of ‘commercial type’ films using high-quality gel such as nuclear emulsion would offer the ultimate spatial resolution, and may be used for detection and measurement of minimum ionization tracks. In this technique, the resolution for the depth direction does not depend on the focus depth of
the microscope, but rather it is determined by the thickness of each layer at the irradiation. Information for the depth direction is recorded at each layer as the color changes just at irradiation and is kept after the film is developed. Therefore, we do not need to compensate for the change of thickness through the development process. Since multilayer techniques for uniform and thin emulsion coating have been established, it is possible to coat the emulsion as a thin layer, such as 0:5 mm as shown in Fig. 3. The method proposed here can be applied to experiments which search for shortlived particles [9]. Conventionally, for these experiments, the technique for swelling emulsion has been applied in order to compensate for the depth resolution. In recent years, the emulsion has been used as a tracking device in connection with improvement in measurement speed [10]. For this application, the track position and angle may be more quickly analyzed by performing a background elimination and track extraction using the
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
563
Fig. 4. Optical photomicrograph of tracks of a xenon ion beam irradiated on the commercial color film at a shallow but a little different angle. The bar indicates 100 mm.
color information. Simple and precise measurements of the track range will be possible using the color information. In addition, this method can be applied to the radiography, the autoradiography and the neutron radiography. The difference in energy and angle of charged particle are represented by colors [11].
4. Conclusions We described here the advantages of our method, to obtain three-dimensional information of tracks by heavy ion beams using commercial color film. The tracks on the film due to the ion beam were observed as the difference in color relating to the track depth in the layers. An ion entering the plane symmetry can be discriminated by the order of the coloring. This method provided better resolution for the depth direction using a stack of thin layer coatings, and the resolving
power was close to what emulsion plates have originally, about 1 mm. However, commercial film is too thin to obtain the sufficient three-dimensional information. Moreover, as it is not made to be electron sensitive and it has a yellowish color originally, there are some problems in the observation of particle tracks. These problems could be overcome by mixing couplers in the nuclear emulsion and coating the emulsion in a stack of thin layers with different couplers. We have also performed a test using the nuclear emulsion with couplers, and report the results in a separate paper [12].
Acknowledgements We would like to express our thanks to the staff of NIRS-HIMAC for their support during the experiments. This work was carried out as a part of the Research Project with Heavy Ions at
564
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 5. Optical photomicrographs of tracks of carbon ion beam irradiated on the commercial colorfilm at a right angle. The bar indicates 20 mm. (a) High sensitivity ISO 800 film and (b) low sensitivity ISO 100 film.
NIRS-HIMAC. We would like to acknowledge the valuable comments and information provided by K. Nakazawa and H. Shibuya.
References [1] E. Eskut, CHORUS Collaboration, Phys. Lett. B 424 (1998) 202; N. Ushida, E531 Collaboration, Phys. Rev. Lett. 57 (1986) 2897. [2] G. Baroni, et al., Nucl. Tracks Radiat. Meas. 19 (1991) 569. [3] K. Asakimori, JACEE Collaboration, Astrophys. J. 502 (1998) 278. [4] G.D. Badhwar, V.V. Kushin, Yu A. Akatov, V.A. Myltseva, Radiat. Meas. 30 (1999) 415.
[5] S. Aoki, K. Hoshino, M. Nakamura, K. Niu, K. Niwa, N. Torii, Nucl. Inst. and Meth. B 51 (1990) 466. [6] J.R. Thirtle, in: T.H. James (Ed.), The Theory of the Photographic Process, MacMillan, New York, 1975, (Chapter 12.1). [7] T. Tani, Photographic Sensitivity, Oxford University Press, New York, 1995, (Chapter 4). [8] L.K.J. Tong, in: T.H. James (Ed.), The Theory of the Photographic Process, MacMillan, New York, 1975, (Chapter 12.2). [9] S. Aoki, et al., Prog. Theor. Phys. 85 (1991) 951. [10] H. Shibuya, The CHORUS collaboration, Nucl. Phys. B 59 (Proc. Suppl.) (1997) 277. [11] K. Kuge, et al., Annual Meeting of Society of Photographic Science and Technology, Japan 2001, p. 103. [12] K. Kuge, et al., Radiat. Meas. 34 (2001) 203.
Colored tracks of heavy ion particles recorded on photographic color film K. Kugea, N. Yasudab,*, H. Kumagaic, N. Aokia, A. Hasegawaa a
Department of Information and Image Sciences, Faculty of Engineering, Chiba University, Inage, Chiba, 263-8522, Japan b National Institute of Radiological Sciences, Anagawa 4-9-1, Inage, Chiba 263–8555, Japan c Radioisotope Research Center, Chiba University, Inage, Chiba 263-8522, Japan Received 2 January 2001; received in revised form 7 March 2001; accepted 7 July 2001
Abstract A new method to obtain the three-dimensional information on nuclear tracks was developed using color photography. Commercial color films were irradiated with ion beam and color-developed. The ion tracks were represented with color images in which different depths were indicated by different colors, and the three-dimensional information was obtained from color changes. Details of this method are reported, and advantages and limitations are discussed in comparison with a conventional method using a nuclear emulsion. r 2002 Elsevier Science B.V. All rights reserved. PACS: 07.68; 29.40.G; 42.66.N Keywords: Nuclear track; Color photography; Nuclear emulsion
1. Introduction Nuclear emulsions can record the charged particle tracks with an accuracy of less than 1 mm while keeping their three-dimensional structure. Since no other detector with a spatial resolution like that of emulsions exists, nuclear emulsions are widely used today for particle physics [1], nuclear physics [2], cosmic-ray physics [3], and space radiation dosimetry [4]. The standard emulsion contains silver halide grains as an active compo*Corresponding author. Fax: +81-43-251-4531. E-mail addresses: [email protected] (K. Kuge), [email protected] (N. Yasuda).
nent dispersed in a gelatin layer, and it is normally used in the form of an emulsion plate on a transparent base (some kind of plastic or glass). Since the focus depth of a microscope is much less (B10 mm) than the emulsion plate thickness, the focal plane of the objective lens is moved up and down in order to obtain the three-dimensional information. Thus, considerable time is needed for the track recognition in the emulsion. Recently, applications to experiments which required high statistical reliability have been carried out [1,5] using a fully automated high-speed analyzing system with high-speed processing. As for the emulsion itself, though the fine grain (small particle size) emulsion is available, a method for
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 5 1 6 - 9
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
coating the emulsion at a thickness with good homogeneity in a large area was developed, resolution for the depth direction has not been improved regarding the microscope used. Thus, the full potential of emulsions for providing three-dimensional information cannot be utilized. We propose here a new method for displaying colored tracks; color photography is used to obtain depth information in the emulsion by different colors. Normal color photographic films are made from stacking of three emulsion layers, which are individually sensitive to red, green or blue light [6]. When the film is exposed to light, silver halide grains dispersed in the emulsion undergo chemical changes to form a latent image speck on the grains [7]. Color negatives represented as cyan, magenta or yellow dyes are produced from color couplers within the layers through color development. During development, the developer reduces the grains having latent image specks to metallic silver, and at the same time oxidized developing agent combines with the couplers to form dye molecules [8]. The dyes form in the emulsion at the exact location of the exposed silver halide grains. Later, all silver and silver salt are removed and the dyes are left behind to form the image of the object. Fig. 1 shows a schematic drawing of the principle proposed here. Since silver halide grains are also sensitive to charged particles, the particles form latent image specks on the grains along the track. Dyes are formed along the track after the color development. Since each layer includes different couplers, different color dyes are formed in each layer. The difference in track depth leads to the difference in color, so that we can obtain threedimensional information on the track by observation of color. We examined the method to display the track as a color image and discussed its advantages and limitations, using commercial color films, in comparison with nuclear emulsions.
2. Experimental Commercial color films (Superia: Fuji Photo Film) with different sensitivity (ISO 100 and ISO
559
800) were used for this study. These films are composed of three main layers which display yellow, magenta and cyan colors from the top after the color development. The rolled film in a cartridge was irradiated by 290 MeV/n carbon or 290 MeV/n xenon ion beams at a density of 104 –105 ions/cm2 accelerated by HIMAC (Heavy Ion Medical Accelerator in Chiba) in the National Institute of Radiological Sciences. The exposed films were developed with a standard color development treatment in a commercial lab. The developed films were observed with an optical microscope. In order to measure the thickness of each layer a section of the film was made with a microtome and observed with the optical microscope.
3. Results and discussion Fig. 2 shows a photomicrograph of xenon tracks represented by three primary colors. The xenon ions entered the film at a shallow angle from the top right in the figure. The tracks are represented with the three colors, yellow, magenta and cyan, and their mixture. The three colors, which are arranged in the order of yellow, magenta and cyan from the top, indicate the depths of tracks in the film layer. The tracks B, C and E in Fig. 2 are of three colors and this suggests that the ion particles passed through all three layers. Tracks C and E represent the sharp and clear end in the cyan region. These tracks seem to have stopped in the cyan region of the film. On the other hand, there is no cyan region for tracks A and D. They stopped in the magenta layer and did not reach the cyan layer. In other words, the range (energy) difference of each track can be detected by color difference. Fig. 3 shows a photomicrograph of a section of the color film used. A stack of layers is recognized clearly. The layers are arranged in the order of a protecting layer, the blue-sensitive emulsion layer which reveals the yellow color, a yellow filter layer, the green-sensitive layer which reveals the magenta color, an intermediate layer and the red-sensitive layer which reveals the cyan color. Total thickness of the emulsion layers including other intermediate layers is 15 mm. The blue- and
560
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 1. Schematic diagram displaying tracks of different depths with different colors to obtain three-dimensional information on the tracks.
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
561
Fig. 2. Optical photomicrograph of tracks of a xenon ion beam irradiated on the commercial color film at a shallow angle. The bar indicates 100 mm.
green-sensitive layers are each 4 mm thick and the red-sensitive layer is 5 mm thick. Therefore, we can expect the depth resolution corresponding to those values. Fig. 4 also shows a photomicrograph of xenon tracks. In this case, the entrance angles of the ions were also shallow, but they were each different. Although the order of coloring is cyan, magenta and yellow from the right for most of the tracks, that for track A is in the reverse order which is yellow, magenta and cyan from the right. This suggests that the ion forming track A entered from the opposite side of the film with a similar shallow angle. Ions entering the plane symmetrically can be discriminated from the order of the coloring. This is an advantage of this method which cannot be found in normal black and white photographic plates. Figs. 5a and b show microphotographs of carbon tracks exposed on the high (ISO 800) and
the low (ISO 100) sensitivity films, respectively. Carbon ions entered at a right angle to the film. As tracks pass through the three layers perpendicularly, the spots have three overlapped colors and they are observed as black spots. The track sizes are about 3 mm for ISO 100 film and about 7 mm for ISO 800 film. There is also some noise due to g-rays or d-rays. However, the noise consists of a dye cloud of a single color and we observe it as a monochromatic spot. Therefore, it is easy to distinguish the ion tracks from the noise by the color, even though the sizes of noise and tracks are similar. Since sensitivity of the photographic film increases with the size of the silver halide grains and grain size is related to the size of dye cloud, the dye clouds in the ISO 800 film are larger than those in the ISO 100 film. However, the observed dye clouds have a wide size distribution, as the grain size in commercial color film has a wide
562
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 3. Optical photomicrograph of a section of the commercial color film. The film surface is the upper part. The bar indicates 10 mm.
distribution. The maximum sizes of the dye clouds are 10 mm for yellow, 7 mm for magenta and 6 mm for cyan in the ISO 800 film, and 4 mm for yellow, 3 mm for magenta and 3 mm for cyan in the ISO 100 film. The size of silver halide grains in commercial film is larger than that of a usual nuclear emulsion which is about 3:5 mm and we can observe the former as a black grain (0:7– 1:0 mm) after development. The resolving power of tracks in color films is not as high as the nuclear emulsion. Monochromatic blurs and tails associated with the black spot may be formed by d-rays. However, we cannot observe clearly d-rays near the track when using these commercial films. A production of ‘commercial type’ films using high-quality gel such as nuclear emulsion would offer the ultimate spatial resolution, and may be used for detection and measurement of minimum ionization tracks. In this technique, the resolution for the depth direction does not depend on the focus depth of
the microscope, but rather it is determined by the thickness of each layer at the irradiation. Information for the depth direction is recorded at each layer as the color changes just at irradiation and is kept after the film is developed. Therefore, we do not need to compensate for the change of thickness through the development process. Since multilayer techniques for uniform and thin emulsion coating have been established, it is possible to coat the emulsion as a thin layer, such as 0:5 mm as shown in Fig. 3. The method proposed here can be applied to experiments which search for shortlived particles [9]. Conventionally, for these experiments, the technique for swelling emulsion has been applied in order to compensate for the depth resolution. In recent years, the emulsion has been used as a tracking device in connection with improvement in measurement speed [10]. For this application, the track position and angle may be more quickly analyzed by performing a background elimination and track extraction using the
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
563
Fig. 4. Optical photomicrograph of tracks of a xenon ion beam irradiated on the commercial color film at a shallow but a little different angle. The bar indicates 100 mm.
color information. Simple and precise measurements of the track range will be possible using the color information. In addition, this method can be applied to the radiography, the autoradiography and the neutron radiography. The difference in energy and angle of charged particle are represented by colors [11].
4. Conclusions We described here the advantages of our method, to obtain three-dimensional information of tracks by heavy ion beams using commercial color film. The tracks on the film due to the ion beam were observed as the difference in color relating to the track depth in the layers. An ion entering the plane symmetry can be discriminated by the order of the coloring. This method provided better resolution for the depth direction using a stack of thin layer coatings, and the resolving
power was close to what emulsion plates have originally, about 1 mm. However, commercial film is too thin to obtain the sufficient three-dimensional information. Moreover, as it is not made to be electron sensitive and it has a yellowish color originally, there are some problems in the observation of particle tracks. These problems could be overcome by mixing couplers in the nuclear emulsion and coating the emulsion in a stack of thin layers with different couplers. We have also performed a test using the nuclear emulsion with couplers, and report the results in a separate paper [12].
Acknowledgements We would like to express our thanks to the staff of NIRS-HIMAC for their support during the experiments. This work was carried out as a part of the Research Project with Heavy Ions at
564
K. Kuge et al. / Nuclear Instruments and Methods in Physics Research A 482 (2002) 558–564
Fig. 5. Optical photomicrographs of tracks of carbon ion beam irradiated on the commercial colorfilm at a right angle. The bar indicates 20 mm. (a) High sensitivity ISO 800 film and (b) low sensitivity ISO 100 film.
NIRS-HIMAC. We would like to acknowledge the valuable comments and information provided by K. Nakazawa and H. Shibuya.
References [1] E. Eskut, CHORUS Collaboration, Phys. Lett. B 424 (1998) 202; N. Ushida, E531 Collaboration, Phys. Rev. Lett. 57 (1986) 2897. [2] G. Baroni, et al., Nucl. Tracks Radiat. Meas. 19 (1991) 569. [3] K. Asakimori, JACEE Collaboration, Astrophys. J. 502 (1998) 278. [4] G.D. Badhwar, V.V. Kushin, Yu A. Akatov, V.A. Myltseva, Radiat. Meas. 30 (1999) 415.
[5] S. Aoki, K. Hoshino, M. Nakamura, K. Niu, K. Niwa, N. Torii, Nucl. Inst. and Meth. B 51 (1990) 466. [6] J.R. Thirtle, in: T.H. James (Ed.), The Theory of the Photographic Process, MacMillan, New York, 1975, (Chapter 12.1). [7] T. Tani, Photographic Sensitivity, Oxford University Press, New York, 1995, (Chapter 4). [8] L.K.J. Tong, in: T.H. James (Ed.), The Theory of the Photographic Process, MacMillan, New York, 1975, (Chapter 12.2). [9] S. Aoki, et al., Prog. Theor. Phys. 85 (1991) 951. [10] H. Shibuya, The CHORUS collaboration, Nucl. Phys. B 59 (Proc. Suppl.) (1997) 277. [11] K. Kuge, et al., Annual Meeting of Society of Photographic Science and Technology, Japan 2001, p. 103. [12] K. Kuge, et al., Radiat. Meas. 34 (2001) 203.