Abstract

In this study, we discussed the efficiency and spatial resolution of a granular X-ray scintillator using an analytic solution of the radiative transfer equation (RTE). A conventional X-ray scintillator employs a large high-density charge-coupled device (CCD) in direct contact with thin phosphor layers to remove imaging optics. To analyze the performance of the scintillator using the CCD, we derive the analytic solution of the RTE in order to calculate light propagation in a double-layer structure without imaging optics. The analytic solution calculates multiple light sources and scatterings in the phosphor layer as well as refraction in the dielectric-layer interface between the phosphor layer and the CCD. For the calculations, we introduced the scattering phase function, including the backward scattering due to micron-sized phosphor particles, and included the geometrical relations of the refraction at the interface. We analyzed the performance of the scintillator with respect to various scintillator design parameters, such as the size of phosphor particles, the thickness of the phosphor layer, and the thickness and refractive index of the dielectric interlayer. We confirmed the analytic calculation by comparing the results with those obtained using a Monte Carlo (MC) simulation tool. The results are in good agreement, with small differences of 1% and 3% on average for the total efficiency and spatial resolution of the scintillator, respectively.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (3)

F. Zhang and J. Li, “A note on double Henyey–Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transf. 184, 40–43 (2016).

E. K. Moghadam, R. N. Isfahani, and A. Azimi, “Numerical Investigation of the Transient Radiative Heat Transfer inside a Hexagonal Furnace Filled with Particulate Medium,” Am. J. Mech. Eng. 4(2), 42–49 (2016).

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

2014 (1)

V. Cuplov, I. Buvat, F. Pain, and S. Jan, “Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging,” J. Biomed. Opt. 19(2), 026004 (2014).
[PubMed]

2013 (2)

G. G. Poludniowski and P. M. Evans, “Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation,” Med. Phys. 40(4), 041904 (2013).
[PubMed]

J. Colombi and K. Louedec, “Monte Carlo simulation of light scattering in the atmosphere and effect of atmospheric aerosols on the point spread function,” J. Opt. Soc. Am. A 30(11), 2244–2252 (2013).

2012 (4)

2009 (2)

P. W. Zhai, Y. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17(4), 2057–2079 (2009).
[PubMed]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[PubMed]

2008 (2)

J. Hedley, “A three-dimensional radiative transfer model for shallow water environments,” Opt. Express 16(26), 21887–21902 (2008).
[PubMed]

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Lévy flight for light,” Nature 453(7194), 495–498 (2008).
[PubMed]

2007 (1)

2006 (3)

M. Nikl, “Scintillation detectors for x-rays,” Meas. Sci. Technol. 17(4), R37–R54 (2006).

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

A. Klose and E. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220(1), 441–470 (2006).

2005 (1)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).

2004 (1)

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, “A finite element-spherical harmonics radiation transport model for photon migration in turbid media,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 247–260 (2004).

2001 (1)

I. Kandarakis and D. Cavouras, “Role of the activator in the performance of scintillators used in X-ray imaging,” Appl. Radiat. Isot. 54(5), 821–831 (2001).
[PubMed]

1998 (1)

K. F. Evans, “The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55(3), 429–446 (1998).

1997 (1)

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24(6), 895–902 (1997).
[PubMed]

1995 (1)

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[PubMed]

1989 (1)

M. Ljungberg and S.-E. Strand, “A Monte Carlo program for the simulation of scintillation camera characteristics,” Comput. Methods Programs Biomed. 29(4), 257–272 (1989).
[PubMed]

1975 (1)

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transf. 15(9), 839–849 (1975).

1965 (2)

W. M. Irvine, “Multiple scattering by large particles,” Astrophys. J. 142, 1563 (1965).

B. M. Herman and S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 22(5), 559–566 (1965).

Arridge, S. R.

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24(6), 895–902 (1997).
[PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[PubMed]

Aydin, E. D.

E. D. Aydin, “Three-dimensional photon migration through voidlike regions and channels,” Appl. Opt. 46(34), 8272–8277 (2007).
[PubMed]

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, “A finite element-spherical harmonics radiation transport model for photon migration in turbid media,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 247–260 (2004).

Azimi, A.

E. K. Moghadam, R. N. Isfahani, and A. Azimi, “Numerical Investigation of the Transient Radiative Heat Transfer inside a Hexagonal Furnace Filled with Particulate Medium,” Am. J. Mech. Eng. 4(2), 42–49 (2016).

Barrett, H. H.

Barthelemy, P.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Lévy flight for light,” Nature 453(7194), 495–498 (2008).
[PubMed]

Bertolotti, J.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Lévy flight for light,” Nature 453(7194), 495–498 (2008).
[PubMed]

Bortoli, D.

Browning, S. R.

B. M. Herman and S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 22(5), 559–566 (1965).

Buvat, I.

V. Cuplov, I. Buvat, F. Pain, and S. Jan, “Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging,” J. Biomed. Opt. 19(2), 026004 (2014).
[PubMed]

Carlson, B. E.

Cavouras, D.

I. Kandarakis and D. Cavouras, “Role of the activator in the performance of scintillators used in X-ray imaging,” Appl. Radiat. Isot. 54(5), 821–831 (2001).
[PubMed]

Cavouras, D. A.

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

Chu, M.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[PubMed]

Clarkson, E.

Colombi, J.

Cramer, M.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Cuplov, V.

V. Cuplov, I. Buvat, F. Pain, and S. Jan, “Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging,” J. Biomed. Opt. 19(2), 026004 (2014).
[PubMed]

de Oliveira, C. R. E.

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, “A finite element-spherical harmonics radiation transport model for photon migration in turbid media,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 247–260 (2004).

Dehghani, H.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[PubMed]

Delis, H. B.

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[PubMed]

Evans, K. F.

K. F. Evans, “The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55(3), 429–446 (1998).

Evans, P. M.

G. G. Poludniowski and P. M. Evans, “Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation,” Med. Phys. 40(4), 041904 (2013).
[PubMed]

Gerke, M.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Geßner, M.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Giovanelli, G.

Goddard, A. J. H.

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, “A finite element-spherical harmonics radiation transport model for photon migration in turbid media,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 247–260 (2004).

Hartman, J. H.

Hedley, J.

Herman, B. M.

B. M. Herman and S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 22(5), 559–566 (1965).

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2 Pt 1), 299–309 (1993).
[PubMed]

Hu, Y.

Irvine, W. M.

W. M. Irvine, “Multiple scattering by large particles,” Astrophys. J. 142, 1563 (1965).

Isfahani, R. N.

E. K. Moghadam, R. N. Isfahani, and A. Azimi, “Numerical Investigation of the Transient Radiative Heat Transfer inside a Hexagonal Furnace Filled with Particulate Medium,” Am. J. Mech. Eng. 4(2), 42–49 (2016).

Jan, S.

V. Cuplov, I. Buvat, F. Pain, and S. Jan, “Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging,” J. Biomed. Opt. 19(2), 026004 (2014).
[PubMed]

Jha, A. K.

Kahn, J. M.

Kandarakis, I.

I. Kandarakis and D. Cavouras, “Role of the activator in the performance of scintillators used in X-ray imaging,” Appl. Radiat. Isot. 54(5), 821–831 (2001).
[PubMed]

Kandarakis, I. S.

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

Kattawar, G. W.

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transf. 15(9), 839–849 (1975).

Klose, A.

A. Klose and E. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220(1), 441–470 (2006).

Klose, A. D.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).

Kraft, Th.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Kupinski, M. A.

Larsen, E.

A. Klose and E. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220(1), 441–470 (2006).

Li, J.

F. Zhang and J. Li, “A note on double Henyey–Greenstein phase function,” J. Quant. Spectrosc. Radiat. Transf. 184, 40–43 (2016).

Liaparinos, P. F.

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

Ljungberg, M.

M. Ljungberg and S.-E. Strand, “A Monte Carlo program for the simulation of scintillation camera characteristics,” Comput. Methods Programs Biomed. 29(4), 257–272 (1989).
[PubMed]

Louedec, K.

Lucker, P. L.

Macke, A.

Mahalati, R. N.

Masieri, S.

Maslov, A. V.

Masumura, T.

Meißner, H.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Mishchenko, M. I.

Moghadam, E. K.

E. K. Moghadam, R. N. Isfahani, and A. Azimi, “Numerical Investigation of the Transient Radiative Heat Transfer inside a Hexagonal Furnace Filled with Particulate Medium,” Am. J. Mech. Eng. 4(2), 42–49 (2016).

Muinonen, K.

Narasimhan, S. G.

S. G. Narasimhan and S. K. Nayar, “Shedding Light on the Weather,” in Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, pp. 665–672 (2003).

Nayar, S. K.

S. G. Narasimhan and S. K. Nayar, “Shedding Light on the Weather,” in Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, pp. 665–672 (2003).

Nikl, M.

M. Nikl, “Scintillation detectors for x-rays,” Meas. Sci. Technol. 17(4), R37–R54 (2006).

Ntziachristos, V.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).

Pain, F.

V. Cuplov, I. Buvat, F. Pain, and S. Jan, “Extension of the GATE Monte-Carlo simulation package to model bioluminescence and fluorescence imaging,” J. Biomed. Opt. 19(2), 026004 (2014).
[PubMed]

Palazzi, E.

Panayiotakis, G. S.

P. F. Liaparinos, I. S. Kandarakis, D. A. Cavouras, H. B. Delis, and G. S. Panayiotakis, “Modeling granular phosphor screens by Monte Carlo methods,” Med. Phys. 33(12), 4502–4514 (2006).
[PubMed]

Poludniowski, G. G.

G. G. Poludniowski and P. M. Evans, “Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation,” Med. Phys. 40(4), 041904 (2013).
[PubMed]

Premuda, M.

Przybilla, H. J.

Th. Kraft, M. Geßner, H. Meißner, M. Cramer, M. Gerke, and H. J. Przybilla, “Evaluation of a Metric Camera System Tailored for High Precision UAV Applications,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci 41, 901–907 (2016).

Ravegnani, F.

Schweiger, M.

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24(6), 895–902 (1997).
[PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic of light-propagation mechanisms in granular X-ray scintillator, which includes X-ray absorption and the emission and multiple scattering of visible light.
Fig. 2
Fig. 2 Schematic of varying the distance between the source and the multiple scattering boundary and the entire set of geometrical parameters of the scintillator for the calculation of the RTE solution.
Fig. 3
Fig. 3 Variation in optical resolution with different phosphor layer thicknesses for a 5-μm phosphor particle (a), and different phosphor particle sizes for a 100-μm phosphor layer (b). The dielectric interlayer thickness is 30 μm, and the dielectric refractive index is 1.5 in both cases.
Fig. 4
Fig. 4 (a) Variation in optical resolution with different dielectric interlayer thicknesses for a dielectric refractive index of 1.5. (b) Different dielectric refractive indices for a dielectric interlayer thickness of 30 μm (b). The phosphor layer thickness is 100 μm and the phosphor particle size is 5 μm in both cases.
Fig. 5
Fig. 5 Comparison of the linear profile of the intensity distributions of our analytic model (black solid line) and the Monte Carlo simulation (red dashed line) with respect to different design parameters. (a) The cases with phosphor layer thickness values of 50 μm and 300 μm, (b) phosphor particle size of 2.5 μm and 10 μm, (c) non-dielectric layer and dielectric layer thickness of 40 μm, and (d) dielectric refractive index of 1.353 and 2.0. Each case corresponds to the case of Fig. 3 and Fig. 4.
Fig. 6
Fig. 6 Variation in total efficiency with different phosphor layer thicknesses for a 5-μm phosphor particle (a) and different phosphor particle sizes for a 100-μm-thick phosphor layer (b). The thickness of the dielectric interlayer is 30 μm and the dielectric refractive index is 1.5 in both cases.
Fig. 7
Fig. 7 Variation in total efficiency for different dielectric interlayer thicknesses with a dielectric refractive index of 1.5 (a) and for different dielectric refractive indices with a dielectric interlayer thickness of 30 μm (b). The phosphor-layer thickness is 100 μm and the phosphor particle size is 5 μm in both cases.

Equations (6)

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I(T,α)= I 0 n=0 ( g n ( T )+ g n+1 ( T ) ) L n ( α ) ,
I 0 = I 0 d Ω 0 [ 0 2π 1 1 n=0 ( g n ( T )+ g n+1 ( T ) ) L n ( α )dαdφ ] 1 = I 0 T 2 d Ω 0 /4π,
α=cosθ= R v 1 | R || v 1 | .
R Ω = d Ω 1 d Ω 2 = cos ϕ 1 cos ϕ 1 + cos ϕ 2 cos ϕ 2 + .
W= η Q ( d )( 1 η Q ( L t 0 ) ) η C .
E pixel = R Ω W τ tot ( t 0 ) n=0 ( g n ( T )+ g n+1 ( T ) ) L n ( α ) .

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