Abstract

Analytical expressions for sampling the scattering angle from a phase function in Monte Carlo simulations of light propagation are available only for a limited number of phase functions. Consequently, numerical sampling methods based on tabulated values are often required instead. By using Monte Carlo simulated reflectance, we compare two existing and propose an improved numerical sampling method and show that both the number of the tabulated values and the numerical sampling method significantly influence the accuracy of the simulated reflectance. The provided results and guidelines should serve as a good starting point for conducting computationally efficient Monte Carlo simulations with numerical phase function sampling.

© 2017 Optical Society of America

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2016 (3)

2015 (2)

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

2014 (2)

S. C. Kanick, D. M. McClatchy, V. Krishnaswamy, J. T. Elliott, K. D. Paulsen, and B. W. Pogue, “Sub-diffusive scattering parameter maps recovered using wide-field high-frequency structured light imaging,” Biomed. Opt. Express 5(10), 3376–3390 (2014).
[Crossref] [PubMed]

K. W. Calabro and I. J. Bigio, “Influence of the phase function in generalized diffuse reflectance models: review of current formalisms and novel observations,” J. Biomed. Opt. 19(7), 75005 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

2008 (1)

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[Crossref] [PubMed]

2005 (1)

2003 (2)

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8(1), 121–147 (2003).
[Crossref] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

2000 (1)

R. K. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatterers,” J. Mod. Opt. 47(1), 103–120 (2000).
[Crossref]

1999 (2)

F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source-detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16(12), 2935–2945 (1999).
[Crossref]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
[Crossref] [PubMed]

1998 (1)

1997 (1)

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

1996 (3)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

1994 (1)

1983 (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

1980 (1)

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Aalders, M.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

Adam, G.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

Alerstam, E.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[Crossref] [PubMed]

Amelink, A.

Andersson-Engels, S.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[Crossref] [PubMed]

Avrillier, S.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. J. Eur. Opt. Soc. Part A 5(4), 377–388 (1996).
[Crossref]

Backman, V.

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

Beek, J. F.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

Bevilacqua, F.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source-detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16(12), 2935–2945 (1999).
[Crossref]

Bigio, I. J.

K. W. Calabro and I. J. Bigio, “Influence of the phase function in generalized diffuse reflectance models: review of current formalisms and novel observations,” J. Biomed. Opt. 19(7), 75005 (2014).
[Crossref] [PubMed]

J. R. Mourant, J. Boyer, A. H. Hielscher, and I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source-detector separations,” Opt. Lett. 21(7), 546–548 (1996).
[Crossref] [PubMed]

Blokland, P.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

Bodenschatz, N.

N. Bodenschatz, P. Krauter, A. Liemert, and A. Kienle, “Quantifying phase function influence in subdiffusively backscattered light,” J. Biomed. Opt. 21(3), 35002 (2016).
[Crossref] [PubMed]

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Bosch, J. J.

Boyer, J.

Bravo, J. J.

Calabro, K. W.

K. W. Calabro and I. J. Bigio, “Influence of the phase function in generalized diffuse reflectance models: review of current formalisms and novel observations,” J. Biomed. Opt. 19(7), 75005 (2014).
[Crossref] [PubMed]

Charvet, I.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

Cheney, P. P.

de Bruijn, H. S.

Depeursinge, C.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source-detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16(12), 2935–2945 (1999).
[Crossref]

Ding, H.

Elliott, J. T.

Eshein, A.

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

Foschum, F.

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Gamm, U. A.

Gélébart, B.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. J. Eur. Opt. Soc. Part A 5(4), 377–388 (1996).
[Crossref]

Goldbach, T.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
[Crossref] [PubMed]

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hennessy, R.

R. Hennessy, S. L. Lim, M. K. Markey, and J. W. Tunnell, “Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy,” J. Biomed. Opt. 18(3), 037003 (2013).
[Crossref] [PubMed]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hielscher, A. H.

Hu, X.-H.

Hwang, J. C.

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Kanick, S. C.

Kienle, A.

N. Bodenschatz, P. Krauter, A. Liemert, and A. Kienle, “Quantifying phase function influence in subdiffusively backscattered light,” J. Biomed. Opt. 21(3), 35002 (2016).
[Crossref] [PubMed]

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Krauter, P.

N. Bodenschatz, P. Krauter, A. Liemert, and A. Kienle, “Quantifying phase function influence in subdiffusively backscattered light,” J. Biomed. Opt. 21(3), 35002 (2016).
[Crossref] [PubMed]

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Krishnaswamy, V.

Kumar, G.

Liemert, A.

N. Bodenschatz, P. Krauter, A. Liemert, and A. Kienle, “Quantifying phase function influence in subdiffusively backscattered light,” J. Biomed. Opt. 21(3), 35002 (2016).
[Crossref] [PubMed]

Lim, S. L.

R. Hennessy, S. L. Lim, M. K. Markey, and J. W. Tunnell, “Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy,” J. Biomed. Opt. 18(3), 037003 (2013).
[Crossref] [PubMed]

Löwik, C. W. G. M.

Lu, J. Q.

Ma, X.

Markey, M. K.

R. Hennessy, S. L. Lim, M. K. Markey, and J. W. Tunnell, “Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy,” J. Biomed. Opt. 18(3), 037003 (2013).
[Crossref] [PubMed]

Marquet, P.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

McClatchy, D. M.

McCormick, N. J.

Meda, P.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

Mol, I. M.

Mourant, J. R.

Nguyen, T.-Q.

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

Nothelfer, S.

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Ory, G.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

Paulsen, K. D.

Pickering, J. W.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

Pogue, B. W.

Posthumus, P.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

R Zijp, J.

Radosevich, A. J.

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

Reynolds, L. O.

Richards-Kortum, R. R.

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8(1), 121–147 (2003).
[Crossref] [PubMed]

Rizzo, E. J.

Roberts, D. W.

Robinson, D. J.

Schmitt, J. M.

Schwarzmaier, H.-J.

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
[Crossref] [PubMed]

Simon, E.

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

Snoeks, T. J. A.

St Ghislain, M.

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

Sterenborg, H. J.

S. C. Kanick, V. Krishnaswamy, U. A. Gamm, H. J. Sterenborg, D. J. Robinson, A. Amelink, and B. W. Pogue, “Scattering phase function spectrum makes reflectance spectrum measured from Intralipid phantoms and tissue sensitive to the device detection geometry,” Biomed. Opt. Express 3(5), 1086–1100 (2012).
[Crossref] [PubMed]

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E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
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B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. J. Eur. Opt. Soc. Part A 5(4), 377–388 (1996).
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Toublanc, D.

Tualle, J. M.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. J. Eur. Opt. Soc. Part A 5(4), 377–388 (1996).
[Crossref]

Tunnell, J. W.

R. Hennessy, S. L. Lim, M. K. Markey, and J. W. Tunnell, “Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy,” J. Biomed. Opt. 18(3), 037003 (2013).
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U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8(1), 121–147 (2003).
[Crossref] [PubMed]

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J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
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A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
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A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
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L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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Appl. Opt. (3)

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Biomed. Opt. Express (3)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

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K. W. Calabro and I. J. Bigio, “Influence of the phase function in generalized diffuse reflectance models: review of current formalisms and novel observations,” J. Biomed. Opt. 19(7), 75005 (2014).
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N. Bodenschatz, P. Krauter, A. Liemert, and A. Kienle, “Quantifying phase function influence in subdiffusively backscattered light,” J. Biomed. Opt. 21(3), 35002 (2016).
[Crossref] [PubMed]

A. N. Yaroslavsky, I. V. Yaroslavsky, T. Goldbach, and H.-J. Schwarzmaier, “Influence of the scattering phase function approximation on the optical properties of blood determined from the integrating sphere measurements,” J. Biomed. Opt. 4(1), 47–53 (1999).
[Crossref] [PubMed]

P. Krauter, S. Nothelfer, N. Bodenschatz, E. Simon, S. Stocker, F. Foschum, and A. Kienle, “Optical phantoms with adjustable subdiffusive scattering parameters,” J. Biomed. Opt. 20(10), 105008 (2015).
[Crossref] [PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[Crossref] [PubMed]

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8(1), 121–147 (2003).
[Crossref] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. St Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8(3), 495–503 (2003).
[Crossref] [PubMed]

A. J. Radosevich, A. Eshein, T.-Q. Nguyen, and V. Backman, “Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm,” J. Biomed. Opt. 20(9), 097002 (2015).
[Crossref] [PubMed]

R. Hennessy, S. L. Lim, M. K. Markey, and J. W. Tunnell, “Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy,” J. Biomed. Opt. 18(3), 037003 (2013).
[Crossref] [PubMed]

J. Mod. Opt. (1)

R. K. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatterers,” J. Mod. Opt. 47(1), 103–120 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Med. Phys. (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

Opt. Lett. (3)

Optica (1)

Phys. Med. Biol. (1)

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42(11), 2255–2261 (1997).
[Crossref] [PubMed]

Pure Appl. Opt. J. Eur. Opt. Soc. Part A (1)

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. J. Eur. Opt. Soc. Part A 5(4), 377–388 (1996).
[Crossref]

Other (2)

A. J. Welch and M. J. Van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Springer, 2010).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

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Figures (9)

Fig. 1
Fig. 1 An example of the CDF for the HG phase function. Drawn random number ξ and the sampled cos θξ are given in red. (a) The forward lookup table (cos θj values and their corresponding CDFj values) is presented with blue circles. The values of cos θj in the forward lookup table are evenly spaced. (b) The inverted lookup table (cos θj values and their corresponding CDFj values) is presented with red circles. The CDFj values in the inverted lookup table are evenly spaced.
Fig. 2
Fig. 2 (a) An example of CDF for the HG phase function. The non-linear lookup table (cos θj* values and their corresponding CDFj = f (cos θj) values) is presented with red circles. The evenly spaced points of cos θj are presented with blue circles. Drawn random number ξ and the sampled cos θξ are given in green. (b) Construction of a non-linear lookup table from evenly spaced cos θj. The non-linear lookup table is presented in red. Green diagram highlights the sampling of cos θξ from a random number ξ.
Fig. 3
Fig. 3 RRE maps as a function of the absorption and reduced scattering coefficient at three SDS arising from an undersized lookup table employed by the numerical sampling methods (FLT, ILT and NLT).
Fig. 4
Fig. 4 MC simulated reflectance spectrum of a turbid phantom comprising 5 μm polystyrene spheres computed by varying the lookup table (LUT) size. The phase function was sampled using the ILT sampling method.
Fig. 5
Fig. 5 (top row) Maximum absolute RRE as a function of the lookup table size used by the numerical sampling methods (FLT, ILT and NLT). (middle row) Comparison between the reconstructed and the corresponding true GK phase function obtained by different numerical sampling methods using the lookup table sizes from Table 2. (bottom row) The relative errors of the reconstructed GK phase functions.
Fig. 6
Fig. 6 The average simulation time required to compute a 5 x 5 reflectance map as a function of the lookup table size for each numerical sampling method (FLT, ILT and NLT).
Fig. 7
Fig. 7 Relative reflectance error (RRE) maps as a function of the anisotropy factor and reduced scattering coefficient at three SDS arising from an undersized lookup table employed by the numerical sampling methods (FLT, ILT and NLT).
Fig. 8
Fig. 8 Minimum lookup table size required to keep the maximum absolute RRE computed by different numerical sampling methods (FLT, ILT and NLT) under 2% as a function of the anisotropy factor for three source-detector separations (SDS).
Fig. 9
Fig. 9 The average relative error within 50 bins of the reconstructed phase function histograms from Fig. 5 that represent the contribution of small scattering angles (cos θ between 0.9 and 1) as a function of the lookup table size for each numerical sampling method (FLT, ILT and NLT).

Tables (2)

Tables Icon

Table 1 Phase functions, the corresponding parameters and the resulting observables g and γ used in this study.

Tables Icon

Table 2 Minimum lookup table sizes of the numerical sampling methods (FLT, ILT and NLT) that guarantee maximum absolute RRE under 2% for all the utilized phase functions at all SDS.

Equations (13)

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p HG ( cosθ )= 1 2 1 g 2 ( 1+ g 2 2gcosθ ) 3/2 ,
p MHG (cosθ)=β p HG (cosθ)+(1β) 3 2 cos 2 θ,
p GK (cosθ)= 2 α GK g GK (1 g GK 2 ) 2 α GK [ (1+ g GK ) 2 α GK (1 g GK ) 2 α GK ] (1+ g GK 2 2 g GK cosθ) (1+ α GK ) .
n( d i )=A d i α ,
p Mie ( cosθ )= π C sca | S 1 ( cosθ ) | 2 + | S 2 ( cosθ ) | 2 k 2 ,
p fractal ( cosθ )= i d i α C sca,i p Mie,i ( cosθ ) i d i α C sca,i ,
CD F φ ( φ )= 1 2π 0 φ dφ , CD F cosθ ( cos θ )= 1 cos θ p( cosθ ) dcosθ,
φ=2π ξ 1 , cosθ=CD F cosθ 1 ( ξ 2 ).
CDF j = 1 cosθj p( cosθ ) dcosθ,
CDF J <ξ CDF J+1 .
cos θ ξ =( cos θ J+1 cos θ J CDF J+1 CDF J )( ξ CDF J )+cos θ J .
f(cosθ)= b cosθc +a.
f(1)=0andf(1)=1,

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