Abstract

In problems relating to light propagation in biomedical tissues, the tissue is generally modeled as a turbid medium and Monte Carlo (MC) simulation is employed to compute quantities such as diffuse reflectance, fluence, and transmittance. Two prescriptions are available in the literature for MC simulations. The first prescription considers all input quantities, including phase function, as an average over the particle size distribution, and the second prescription considers the phase function of each scatterer individually. The two prescriptions have been compared and contrasted in this paper for a given soft tissue model. It is demonstrated that, in general, the two recipes do not yield identical results. The source of this disagreement has been traced.

© 2010 Optical Society of America

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2007 (1)

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A: Pure Appl. Opt. 8, 1–7 (2007).
[CrossRef]

2005 (7)

2004 (1)

2003 (3)

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

S. K. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A: Pure Appl. Opt. 5, 294–302(2003).
[CrossRef]

F. Jallion and H. Saint-Jalmes, “Description and time reduction of a Monte Carlo code to simulate propagation of polarized light through scattering media,” Appl. Opt. 42, 3290–3295 (2003).
[CrossRef]

2001 (2)

N. Ghosh, S. K. Mohanty, S. K. Majumder, and P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissue,” Appl. Opt. 40, 176–184(2001).
[CrossRef]

W. Bauer and C. D. Mackenzie, “Cancer detection on a cell by cell basis using fractal dimension analysis,” Heavy Ion Phys. 14, 39–46 (2001).
[CrossRef]

2000 (2)

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

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed. 61, 163–170(2000).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

J. M. Schmitt and G. Kumar G, “Optical scattering properties of soft tissue: a discrete particle model,” Appl. Opt. 37, 2788–2798 (1998).
[CrossRef]

1996 (2)

D. Toublanc, “Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations,” Appl. Opt. 35, 3270–3274 (1996).
[CrossRef] [PubMed]

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

1995 (1)

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

1992 (1)

1941 (1)

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

Avrillier, S.

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Backman, V.

Y. Liu, Y. L. Kim, and V. Backman, “Investigation of depth selectivity of polarization gating for tissue characterization,” Opt. Express 13, 601–611 (2005).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Banerjee, S.

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A: Pure Appl. Opt. 8, 1–7 (2007).
[CrossRef]

S. K. Sharma and S. Banerjee S, “Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model,” Med. Phys. 32, 1767–1174 (2005).
[CrossRef] [PubMed]

S. K. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A: Pure Appl. Opt. 5, 294–302(2003).
[CrossRef]

Bauer, W.

W. Bauer and C. D. Mackenzie, “Cancer detection on a cell by cell basis using fractal dimension analysis,” Heavy Ion Phys. 14, 39–46 (2001).
[CrossRef]

Bayvel, L. P.

L. P. Bayvel and A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, 1981).

Berrocal, E.

Bevilacqua, F.

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

Bigio, I. J.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Bohren, C. F.

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

Bonner, R. F.

Boyer, J.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Charvet, I.

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

Conn, R. L.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Cote, D.

Crawford, J. M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Depeursinge, C.

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

Drezek, R.

Dunn, A.

Feld, M. S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Gandjbakhche, A. H.

Gelebart, B.

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Ghislain, M. S.

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

Ghosh, N.

Greenstein, J. L.

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

Guerra, R.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, “Tissue phantom for optical diagnostics based on suspension of microspheres with a fractal distribution,” J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Gupta, P. K.

Hamano, T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Hebden, J. C.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, “Tissue phantom for optical diagnostics based on suspension of microspheres with a fractal distribution,” J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Henyey, L. G.

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

Huffman, D. R.

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

Itzkan, I.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Jacques, S. L.

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 4420–4438(2005).
[CrossRef] [PubMed]

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques S L, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express 13, 10392–10405(2005).
[CrossRef] [PubMed]

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed. 61, 163–170(2000).
[CrossRef] [PubMed]

S. L. Jacques and L. H. Wang “Monte Carlo modeling of light transport in tissues,” in Optical Thermal Response of Laser Irradiated Tissues, A.J.Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 73–100.

Jallion, F.

Jermy, M.

Johnson, T.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Jones, A. R.

L. P. Bayvel and A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, 1981).

Khlebtsov, N. G.

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. V. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Medical Diagnostics, V.V.Tuchin, ed. (SPIE, 2002), pp. 31–168.

Kim, Y. L.

Kumar, G.

Lima, C.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Liu, Y.

Mackenzie, C. D.

W. Bauer and C. D. Mackenzie, “Cancer detection on a cell by cell basis using fractal dimension analysis,” Heavy Ion Phys. 14, 39–46 (2001).
[CrossRef]

Majumder, S. K.

Maksimova, I. L.

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. V. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Medical Diagnostics, V.V.Tuchin, ed. (SPIE, 2002), pp. 31–168.

Manoharan, R.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Marquet, P.

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

Meda, P.

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

Meglinski, I.

Mohanty, S. K.

Mourant, J. R.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Nusrat, A.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Ory, G.

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

Passos, D.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, “Tissue phantom for optical diagnostics based on suspension of microspheres with a fractal distribution,” J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Perelman, L. T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Pinto, P. N.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, “Tissue phantom for optical diagnostics based on suspension of microspheres with a fractal distribution,” J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

Prahl, S. A.

Ramella-Roman, J. C.

Richards-Kortum, R.

Saint-Jalmes, H.

Schmitt, J. M.

Seiler, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Sharma, S. K.

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A: Pure Appl. Opt. 8, 1–7 (2007).
[CrossRef]

S. K. Sharma and S. Banerjee S, “Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model,” Med. Phys. 32, 1767–1174 (2005).
[CrossRef] [PubMed]

S. K. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A: Pure Appl. Opt. 5, 294–302(2003).
[CrossRef]

Shields, S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Shimada, T.

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
[CrossRef] [PubMed]

Sokolov, K.

Thueler, P.

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

Tinet, E.

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Toublanc, D.

Tualle, J. M.

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, “Light–tissue interactions,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003), pp. 3-1–3-26.

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. V. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Medical Diagnostics, V.V.Tuchin, ed. (SPIE, 2002), pp. 31–168.

Van Dam, J.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

van Gemert, M. J. C.

S. L. Jacques and L. H. Wang “Monte Carlo modeling of light transport in tissues,” in Optical Thermal Response of Laser Irradiated Tissues, A.J.Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 73–100.

Vermeulen, B.

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

Vitkin, I. A.

Wallace, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Wang, L. H.

S. L. Jacques and L. H. Wang “Monte Carlo modeling of light transport in tissues,” in Optical Thermal Response of Laser Irradiated Tissues, A.J.Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 73–100.

Wang, L. V.

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed. 61, 163–170(2000).
[CrossRef] [PubMed]

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. V. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Medical Diagnostics, V.V.Tuchin, ed. (SPIE, 2002), pp. 31–168.

Wang, R. K.

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

Xu, M.

Yadav, M. K.

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A: Pure Appl. Opt. 8, 1–7 (2007).
[CrossRef]

Zonios, G.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Appl. Opt. (5)

Astrophys. J. (1)

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

Comput. Methods Programs Biomed. (1)

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed. 61, 163–170(2000).
[CrossRef] [PubMed]

Heavy Ion Phys. (1)

W. Bauer and C. D. Mackenzie, “Cancer detection on a cell by cell basis using fractal dimension analysis,” Heavy Ion Phys. 14, 39–46 (2001).
[CrossRef]

J. Biomed. Opt. (2)

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

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, “Tissue phantom for optical diagnostics based on suspension of microspheres with a fractal distribution,” J. Biomed. Opt. 10, 064036 (2005).
[CrossRef]

J. Mod. Opt. (1)

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

J. Opt. A: Pure Appl. Opt. (2)

S. K. Sharma and S. Banerjee, “Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues,” J. Opt. A: Pure Appl. Opt. 5, 294–302(2003).
[CrossRef]

S. K. Sharma, S. Banerjee, and M. K. Yadav, “Light propagation in a fractal tissue model: a critical study of the phase function,” J. Opt. A: Pure Appl. Opt. 8, 1–7 (2007).
[CrossRef]

Lasers Surg. Med. (1)

J. R. Mourant, I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada, “Spectroscopic diagnosis of bladder cancer with elastic light scattering,” Lasers Surg. Med. 17, 350–357 (1995).
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Med. Phys. (1)

S. K. Sharma and S. Banerjee S, “Volume concentration and size dependence of diffuse reflectance in a fractal soft tissue model,” Med. Phys. 32, 1767–1174 (2005).
[CrossRef] [PubMed]

Opt. Express (7)

Phys. Rev. Lett. (1)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissues: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Pure Appl. Opt. (1)

B. Gelebart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Other (5)

N. G. Khlebtsov, I. L. Maksimova, V. V. Tuchin, and L. V. Wang, “Introduction to light scattering by biological objects,” in Handbook of Optical Medical Diagnostics, V.V.Tuchin, ed. (SPIE, 2002), pp. 31–168.

V. V. Tuchin, “Light–tissue interactions,” in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC Press, 2003), pp. 3-1–3-26.

S. L. Jacques and L. H. Wang “Monte Carlo modeling of light transport in tissues,” in Optical Thermal Response of Laser Irradiated Tissues, A.J.Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 73–100.

L. P. Bayvel and A. R. Jones, Electromagnetic Scattering and Its Applications (Applied Science, 1981).

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

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Figures (8)

Fig. 1
Fig. 1

(a) Variation of R d ( r ) with r. POLMC predictions (lines) have been compared with those given by MCML (points) for MC1 for two volume fractions (i) T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 ; μ a ( cm 1 ) = 3.995 ] and (ii) T v = 0.02728 [corresponding to μ s ( cm 1 ) = 36.305 ; μ a ( cm 1 ) = 0.545 ]. The average g value, as defined by (7) is 0.74. The α = 5.0 in these comparisons, and incident light is unpolarized. (b) Variation of ϕ ( z ) with z. POLMC predictions (lines) have been compared with those given by MCML (points) for MC1 for two volume fractions (i) T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 ; μ a ( cm 1 ) = 3.995 ] and (ii) T v = 0.02728 [corresponding to μ s ( cm 1 ) = 36.305 ; μ a ( cm 1 ) = 0.545 ]. The average g value, as defined by (7) is 0.74. The α = 5.0 in these comparisons, and incident light is unpolarized.

Fig. 2
Fig. 2

Comparison of R d ( r ) versus r for MC1 and MC2 for T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 , μ a ( cm 1 ) = 3.995 ] and for T v = 0.02728 [corresponding to μ s ( cm 1 ) = 36.305 , μ a ( cm 1 ) = 0.545 ]. The incident light is unpolarized, and the average g value is 0.74.

Fig. 3
Fig. 3

Comparison of ϕ ( z ) versus z for MC1 and MC2. The incident light is unpolarized and T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 , μ a ( cm 1 ) = 3.995 ]. The average g value is 0.74.

Fig. 4
Fig. 4

(a) Comparison R d ( r ) versus r from MC1 and MC2 for incident light polarized linearly [ 1 1 0 0 ] and circularly [ 1 0 0 1 ] . Volume fraction T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 , μ a ( cm 1 ) = 3.995 ] and α = 5.0 : lines, linearly polarized light; points, circularly polarized light. The average g value is 0.74. (b) Comparison of ϕ ( z ) versus z from MC1 and MC2 for incident light polarized linearly [ 1 1 0 0 ] and circularly [ 1 0 0 1 ] . Volume fraction T v = 0.2 [corresponding to μ s ( cm 1 ) = 266.165 , μ a ( cm 1 ) = 3.995 ] and α = 5.0 : lines, linearly polarized light; points, circularly polarized light. The average g value is 0.74.

Fig. 5
Fig. 5

(a) Comparison of R d ( r ) versus r for MC1 and MC2 in the eight-particle model of Gelebart et al. [13]. Here μ s ( cm 1 ) = 233.720 and μ a ( cm 1 ) = 4.066 . The average g value for this distribution is 0.52, and the other tissue parameters of the model are the same as those used in this paper. (b) Comparison of ϕ ( z ) versus z for MC1 and MC2 in the eight-particle model of Gelebart et al. [13]. Here μ s ( cm 1 ) = 233.720 and μ a ( cm 1 ) = 4.066 . The average g value for this distribution is 0.52, and the other tissue parameters of the model are the same as those used in this paper.

Fig. 6
Fig. 6

(a) Comparison of R d ( r ) versus r and from MC1 (points) and MC2 (line) for a truncated size distribution 1.0 μm d 25.6 μm . The incident light is linearly polarized. Volume fraction T v = 0.2 [corresponding to μ s ( cm 1 ) = 3115.729 , μ a ( cm 1 ) = 0.740 ] and α = 5.0 . The average g value for this distribution is 0.959. (b) Comparison of ϕ ( z ) versus z from MC1 (points) and MC2 (line) for a truncated size distribution. 1.0 μm d 25.6 μm . The incident light is linearly polarized. Volume fraction T v = 0.2 [corresponding to μ s ( cm 1 ) = 3115.729 , μ a ( cm 1 ) = 0.740 ] and α = 5.0 . The average g value for this distribution is 0.959.

Fig. 7
Fig. 7

(a) Same as Fig. 6a but for a distribution with size range of 2.0 μm d 4.0 . Here μ s ( cm 1 ) = 3623.019 and μ a ( cm 1 ) = 0.969 . The average g value for this distribution is 0.969. (b) Same as Fig. 6b but for a distribution with size range of 2.0 μm d 4.0 . Here μ s ( cm 1 ) = 3623.019 and μ a ( cm 1 ) = 0.969 . The average g value for this distribution is 0.969.

Fig. 8
Fig. 8

Variation of anisotropy with particle size.

Tables (2)

Tables Icon

Table 1 Comparison of Total Reflectance in MC1 and MC2 for Three Polarizations a

Tables Icon

Table 2 Comparison of Total Reflectance in MC1 and MC2 for Three Polarizations for Truncated Size Distributions a

Equations (14)

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N ( d i ) = ( d 0 / d i ) α ,
η ( d i ) = ( π d i 3 / 6 ) N ( d i ) π d 0 3 / 6 = η 0 d i 3 α ,
T v = η 0 i = 1 m d i 3 α ,
μ s = ( 6 η 0 / π ) i = 1 m d i α σ s ( d i ) ,
μ a = ( 6 η 0 / π ) i = 1 m d i α σ a ( d i ) ,
p ( θ ) = i = 1 m d i α σ s ( d i ) p ( θ , d i ) / i = 1 m d i α σ s ( d i ) ,
g = i = 1 m d i α σ s ( d i ) g ( d i ) / i = 1 m d i α σ s ( d i ) ,
p ( θ ) h g p f = ( 1 g 2 ) 2 ( 1 + g 2 2 g cos θ ) 3 / 2 ,
1 1 p ( μ ) d μ = 1 ,
ξ ( μ ) = 1 μ p ( μ ) d μ ,
cos θ = 1 2 g [ 1 + g 2 ( 1 g 2 1 g + 2 g ξ ) 2 ] ,
j = 1 v 1 p j < ξ j = 1 v p j ,
P ( d i ) = d i α σ ext ( d i ) / d = d min d max d α σ ext ( d ) ,
i = 1 v 1 P ( d i ) < ξ i = 1 v P ( d i ) ,

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