Abstract

We rigorously account for the effects of multiparticle light scattering from a fractal sphere aggregate in order to simulate the optical properties of a soft biological tissue, human skin. Using a computational method that extends Mie theory to the multisphere case, we show that multiparticle scattering significantly affects the computed optical properties, resulting in a reduction in both scattering coefficient and anisotropy for the wavelengths simulated, as well as a significantly enhanced forward peak in the simulated phase function. The model is extended to incorporate the contribution of Rayleigh scatterers, which we show is required to obtain reasonable agreement with experimentally measured optical properties of skin tissue.

© 2007 Optical Society of America

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    [CrossRef]

2007 (1)

2005 (3)

M. Xu and R. R. Alfano, "Fractal mechanisms of light scattering in biological tissue and cells," Opt. Lett. 30,3051-3053 (2005).
[CrossRef] [PubMed]

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (2005).
[CrossRef]

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

2004 (1)

2003 (1)

2001 (3)

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6,167-176 (2001).
[CrossRef] [PubMed]

Y. -L. Xu and B. Å. S. Gustafson, "A generalized multiparticle Mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transfer 70,395-419 (2001).
[CrossRef]

2000 (2)

1998 (5)

G. Videen, R. G. Pinnick, D. Ngo, Q. Fu, and P. Ch’ylek, "Asymmetry parameter and aggregate particles" Appl. Opt. 37,1104-1109 (1998).
[CrossRef]

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

J. M. Schmitt and G. Kumar, "Optical scattering properties of soft tissue: a discrete particle model," Appl. Opt. 37,2788-2797 (1998).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: asymmetry parameter," Phys. Lett. A 249,30-36 (1998).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58,3931-3948 (1998).
[CrossRef]

1997 (3)

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

J. M. Schmitt and A. Knüttel, "Model of optical coherence tomography of heterogeneous tissue," J. Opt. Soc. Am. A 14,1231-1242 (1997).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: far field," Appl. Opt. 36,9496-9508 (1997).
[CrossRef]

1996 (5)

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. 21,546-548 (1996).
[CrossRef] [PubMed]

J. M. Schmitt and G. Kumar, "Turbulent nature of refractive-index variations in biological tissue," Opt. Lett. 21,1310-1312 (1996).
[CrossRef] [PubMed]

B. Gélébart, 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]

A. Dunn and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Topics Quantum Electron. 2,898-905 (1996).
[CrossRef]

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

1995 (4)

L. Wang, S. L. Jacques, and L. Zheng, "MCML - Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47,131-146 (1995).
[CrossRef] [PubMed]

P. A. J. Bascom and R. S. C. Cobbold, "On a fractal packing approach for understanding ultrasonic backscattering from blood," J. Acoust. Soc. Am. 98,3040-3049 (1995).
[CrossRef] [PubMed]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres," Appl. Opt. 34,4573-4588 (1995).
[CrossRef] [PubMed]

I. S. Saidi, S. L. Jacques, and F. K. Tittel, "Mie and Rayleigh modeling of visible-light scattering in neonatal skin," Appl. Opt. 34,7410-7418 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1991 (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

1989 (1)

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

1984 (1)

W. A. G. Bruls and J. C. van der Leun, "Forward scattering properties of human epidermal layers," Photochem. Photobiol. 40,231-242 (1984).
[CrossRef] [PubMed]

1978 (1)

V. Twersky, "Acoustic bulk parameters in distributions of pair-correlated scatterers," J. Acoust. Soc. Am. 64,1710-1719 (1978).
[CrossRef]

1965 (1)

Aalders, M.

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

Aarnoudse, J. G.

Alfano, R. R.

Avrillier, S.

B. Gélébart, 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]

Bascom, P. A. J.

P. A. J. Bascom and R. S. C. Cobbold, "On a fractal packing approach for understanding ultrasonic backscattering from blood," J. Acoust. Soc. Am. 98,3040-3049 (1995).
[CrossRef] [PubMed]

Bashkatov, A. N.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

Beek, J. F.

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

Bigio, I. J.

Blokland, P.

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

Boyer, J.

Bruls, W. A. G.

W. A. G. Bruls and J. C. van der Leun, "Forward scattering properties of human epidermal layers," Photochem. Photobiol. 40,231-242 (1984).
[CrossRef] [PubMed]

Cariveau, M.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Ch’ylek, P.

Chan, E. K.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Chiu, C. -L.

Cobbold, R. S. C.

P. A. J. Bascom and R. S. C. Cobbold, "On a fractal packing approach for understanding ultrasonic backscattering from blood," J. Acoust. Soc. Am. 98,3040-3049 (1995).
[CrossRef] [PubMed]

Cope, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

Dassel, A. C. M.

de Mul, F. F. M.

Deng, X.

Dong, G.

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

Drezek, R.

Du, Y.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Dunn, A.

Essenpreis, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Fu, Q.

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Gan, X.

Gélébart, B.

B. Gélébart, 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]

Genina, E. A.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

Graaff, R.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Gu, M.

Guerra, R.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (2005).
[CrossRef]

Gustafson, B. Å. S.

Y. -L. Xu and B. Å. S. Gustafson, "A generalized multiparticle Mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transfer 70,395-419 (2001).
[CrossRef]

Hebden, J. C.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (2005).
[CrossRef]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Hielscher, A. H.

Hu, X. H.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Jacobsen, R.

Jacques, S. L.

I. S. Saidi, S. L. Jacques, and F. K. Tittel, "Mie and Rayleigh modeling of visible-light scattering in neonatal skin," Appl. Opt. 34,7410-7418 (1995).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, "MCML - Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47,131-146 (1995).
[CrossRef] [PubMed]

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

Kalmus, G. W.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Kerker, M.

Knüttel, A.

Kochubey, V. I.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

Koelink, M. H.

Kohl, M.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

Kratohvil, J. P.

Kumar, G.

Lavker, R. M.

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Lock, J. A.

Lu, J. Q.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Ma, X.

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Matijevic, E.

Motamedi, M.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Mourant, J. R.

Murphy, G. F.

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

Ngo, D.

O’Neil, M.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Passos, D.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (2005).
[CrossRef]

Pickering, J. W.

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

Pinnick, R. G.

Pinto, P. N.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (2005).
[CrossRef]

Posthumus, P.

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

Protsenko, D.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Richards-Kortum, R.

Saidi, I. S.

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Simpson, C. R.

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

Smart, C.

Sorg, B.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Star, W. M.

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

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

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Thennadil, S. N.

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6,167-176 (2001).
[CrossRef] [PubMed]

Tinet, E.

B. Gélébart, 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]

Tittel, F. K.

Troy, T. L.

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6,167-176 (2001).
[CrossRef] [PubMed]

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. 5,377-388 (1996).
[CrossRef]

Tuchin, V. V.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

Twersky, V.

V. Twersky, "Acoustic bulk parameters in distributions of pair-correlated scatterers," J. Acoust. Soc. Am. 64,1710-1719 (1978).
[CrossRef]

van der Leun, J. C.

W. A. G. Bruls and J. C. van der Leun, "Forward scattering properties of human epidermal layers," Photochem. Photobiol. 40,231-242 (1984).
[CrossRef] [PubMed]

van Gemert, M. J. C.

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

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

Videen, G.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML - Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47,131-146 (1995).
[CrossRef] [PubMed]

Wang, R. K.

R. K. Wang, "Modelling optical properties of soft tissue by fractal distribution of scatterers," J. Mod. Opt. 47,103-120 (2000).

Welch, A. J.

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

Xu, M.

Xu, Y. -L.

Y. -L. Xu, "Scattering Mueller matrix of an ensemble of variously shaped small particles," J. Opt. Soc. Am. A 20,2093-2105 (2003).
[CrossRef]

Y. -L. Xu and B. Å. S. Gustafson, "A generalized multiparticle Mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transfer 70,395-419 (2001).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: asymmetry parameter," Phys. Lett. A 249,30-36 (1998).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58,3931-3948 (1998).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: far field," Appl. Opt. 36,9496-9508 (1997).
[CrossRef]

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres," Appl. Opt. 34,4573-4588 (1995).
[CrossRef] [PubMed]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML - Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47,131-146 (1995).
[CrossRef] [PubMed]

Zheng, P.

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

Zijlstra, W. G.

Am. J. Pathol. (1)

R. M. Lavker, G. Dong, P. Zheng, and G. F. Murphy, "Hairless micropig skin. A novel model for studies of cutaneous biology," Am. J. Pathol. 138,687-697 (1991).
[PubMed]

Appl. Opt. (8)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML - Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47,131-146 (1995).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, "Effects of compression on soft tissue optical properties," IEEE J. Quantum Electron. 2,943-950 (1996).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

A. Dunn and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Topics Quantum Electron. 2,898-905 (1996).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36,1146-1154 (1989).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (2)

V. Twersky, "Acoustic bulk parameters in distributions of pair-correlated scatterers," J. Acoust. Soc. Am. 64,1710-1719 (1978).
[CrossRef]

P. A. J. Bascom and R. S. C. Cobbold, "On a fractal packing approach for understanding ultrasonic backscattering from blood," J. Acoust. Soc. Am. 98,3040-3049 (1995).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6,167-176 (2001).
[CrossRef] [PubMed]

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10,064036-1-11 (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).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Phys. D: Appl. Phys. (1)

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, "Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000 nm," J. Phys. D: Appl. Phys. 38,2543-2555 (2005).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

Y. -L. Xu and B. Å. S. Gustafson, "A generalized multiparticle Mie-solution: further experimental verification," J. Quant. Spectrosc. Radiat. Transfer 70,395-419 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Photochem. Photobiol. (1)

W. A. G. Bruls and J. C. van der Leun, "Forward scattering properties of human epidermal layers," Photochem. Photobiol. 40,231-242 (1984).
[CrossRef] [PubMed]

Phys. Lett. A (1)

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: asymmetry parameter," Phys. Lett. A 249,30-36 (1998).
[CrossRef]

Phys. Med. Biol. (3)

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

C. R. Simpson, M. Kohl, M. Essenpreis, and M. Cope, "Near-infrared optical properties of ex vivo human skin and subcutaneous tissues measured using the Monte Carlo inversion technique," Phys. Med. Biol. 43,2465-2478 (1998).
[CrossRef] [PubMed]

Y. Du, X. H. Hu, M. Cariveau, X. Ma, G. W. Kalmus, and J. Q. Lu, "Optical properties of porcine skin dermis between 900 nm and 1500 nm," Phys. Med. Biol. 46,167-181 (2001).
[CrossRef] [PubMed]

Phys. Rev. E (1)

Y. -L. Xu, "Electromagnetic scattering by an aggregate of spheres: theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58,3931-3948 (1998).
[CrossRef]

Pure Appl. Opt. (1)

B. Gélébart, 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]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Other (6)

T. Wilson and C. J. R. Sheppard, Theory and practice of scanning optical microscopy (Academic Press, London, 1984).

H. C. van de Hulst, Light scattering by small particles (Dover Publications, New York, 1981).

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley-Interscience, New York, 1983).

G. Kumar and J. M. Schmitt, "Micro-optical properties of tissue," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. R. Alfano, ed., Proc. SPIE 2679, 106-116 (1996).
[CrossRef]

S. A. Prahl, "Light transport in tissue," Ph.D. Dissertation, University of Texas at Austin (1988).

Y. -L. Xu, gmm01s.f, http://atol.ucsd.edu/scatlib (2007).

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Figures (3)

Fig. 1.
Fig. 1.

Visual representation of example aggregates (excluding the smallest sphere size of 50 nm) for a fractal dimension of 3.5 and 3.7 shown in (a) and (b), respectively (scale in micrometers).

Fig. 2.
Fig. 2.

Anisotropy (a) and scattering coefficient (b) for multiparticle (solid lines) and non-multiparticle (dashed lines) scattering effects. The correspondence between fractal dimension and line color is indicated in the legend. The dotted lines in (a) shows the effect of the Rayleigh contribution upon the anisotropy. The reduced scattering coefficient is shown in (c) for multiparticle (solid lines) and an added contribution of Rayleigh (dotted lines) scattering. (No Rayleigh contribution is included for the aggregate of fractal dimension 3.7.) Empirical data points (shown as markers) are from [27] and the references therein [32-36].

Fig. 3.
Fig. 3.

Phase functions of the aggregate for a wavelength of 633 nm and 1300 nm shown in (a) and (b), respectively, with a fractal dimension of 3.6. The dashed lines (blue) and solid lines (red) represent non-multiparticle and multiparticle scattering, respectively. The dotted line (green) represents multiparticle scattering including a contribution of Rayleigh scattering. The inset shows the phase function in the range from 0 to 15 degrees.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

η ( d ) = { K 1 d 3 D f , d min < d< d max 0 , otherwise ,
μ s , agg = σ sca V .
η ( d ) = [ 1 η ( d ) ] 4 [ 1 + 2 η ( d ) ] 2 η ( d ) .
μ s , Rayleigh = K 2 λ 4 ,
g tot = g agg K 2 λ 4 μ s , agg + 1 .
μ s = ( 1 g tot ) ( μ s , agg + K 2 λ 4 )
P ( θ ) = Σ i = 1 M μ s ( d i ) P i ( θ ) Σ i = 1 M μ s ( d i ) ,
P tot ( θ ) = K 2 λ 4 [ 3 16 π ( 1 + cos 2 θ ) ] + μ s , agg P agg K 2 λ 4 + μ s , agg .

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