Abstract

We used size distributions of volume equivalent spherical particles with complex refractive index to model the inherent optical properties (IOPs) in four different layers of human skin at ten different wavelengths in the visible and near-infrared spectral bands. For each layer, we first computed the size-averaged absorption coefficient, scattering coefficient, and asymmetry factor for the collection of particles in a host medium using Mie theory and compared these IOPs in each layer with those obtained from a bio-optical model (BOM). This procedure was repeated, using an optimization scheme, until satisfactory agreement was obtained between the IOPs obtained from the particle size distribution and those given by the BOM. The size distribution as well as the complex refractive index of the particles, obtained from this modeling exercise, can be used to compute the phase matrix, which is an essential input to model polarized light transport in human skin tissue.

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2011 (1)

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous and mucous tissues: A review,” J. Innov. Opt. Health Sci. Appl. Phys. 4, 9–38 (2011).
[CrossRef]

2010 (3)

J. C. Lai, Y. Y. Zhang, Z. Li, H. Jiang, and A. He, “Complex refractive index measurement of biological tissues by attenuated total ellipsometry,” Appl. Opt. 49, 3235–3237 (2010).
[CrossRef] [PubMed]

S. L. Jacques, “Optical assessment of cutaneous blood volume depends on the vessel size distribution: a computer simulation study,” J. Biophoton. 3, 75–81 (2010). DOI .
[CrossRef]

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg. 36, 1–8 (2010). DOI:
[CrossRef]

2009 (1)

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol. 15, 330–337 (2009). doi:
[CrossRef] [PubMed]

2008 (1)

K. P. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra - A feasibility study,” J. Photochem. Photobiol. B 93, 23–31 (2008).
[CrossRef] [PubMed]

2007 (4)

K. Zhang, W. Li, H. Eide, and K. Stamnes, “A bio-optical model suitable for use in forward and inverse coupled atmosphere-ocean radiative transfer models,” J. Quant. Spectr. Radiat. Transfer 103, 411–4233 (2007).
[CrossRef]

J. R. Fristvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz-Mie theory,” ACM Trans. Graph. 26, 1–10 (2007).

K. Hestenes, K. P. Nielsen, L. Zhao, J. J. Stamnes, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system,” Appl. Opt. 46, 2333–2350 (2007).
[CrossRef] [PubMed]

C. Magnain, M. Elias, and J. Frigerio, “Skin color modelling using the radiative transfer equation solved by the auxiliary function method,” J. Opt. Soc. Am. A 24, 2196–2203 (2007).
[CrossRef]

2006 (4)

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X.-H. Hu, “Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm,” Phys. Med. Biol. 51, 1479–1489, (2006).
[CrossRef] [PubMed]

M. I. Mishchenko, “The electromagnetic optical theorem revisited,” J. Quant. Spectr. Radiat. Transfer 101, 404–410 (2006).
[CrossRef]

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “Importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. 82, 194–198 (2006).
[CrossRef]

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Radiat. Transfer 102, 85–110 (2006).
[CrossRef]

2005 (2)

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]

M. Jermy, “New model for light propagation in highly inhomogeneous polydisperse turbid media with applications in spray diagnostics,” Opt. Express 13, 1981–1995 (2005).

2004 (4)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (A Wiley-VCH, GmbH & Co.Weinheim, 2004), pp. 82–129.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. 93, 1–4 (2004).
[CrossRef]

K. P. Nielsen, L. Zhao, P. Juzenas, J. J. Stamnes, K. Stamnes, and J. Moan, “Reflectance spectra of pigmented and non-pigmented skin in the UV spectral region,” Photochem. Photobiol. 80, 450–455 (2004).
[PubMed]

B. Hamre, J. Winther, S. Gerland, J. J. Stamnes, and K. Stamnes, “Modelled and measured optical transmittance of snow-covered first-year sea ice in Kongfjorden, Svalbard,” J. Geophys. Res. 109, 1–14 (2004).
[CrossRef]

2003 (3)

E. J. Dennis, G. J. Dolmans, R. K. Jain, and D. Fukumura, “Photodynamic therapy for cancer,” Nature Reviews Cancer 3, 380–387 (2003).
[CrossRef]

J. Sandby-Møller, T. Paulsen, and H. C. Wulf, “Epidermal thickness at different body sites: relationship to age, gender, pigmentation, blood content, skin type and smoking,” Acta Derm. Venereol. 83, 410–413 (2003).
[CrossRef] [PubMed]

J. Mobley and T. V. Dinh, “Optical properties of tissue,” in Biomedical Photonics Handbook , T. V. Dinh, ed.(CRC press, 2003), pp. 12–36.

2002 (3)

A. J. Cox, A. J. Deweerd, and J. Linden, “An experiment to measure Mie and Rayleigh total scattering cross sections,” Am. J. Phys. 70, 620–625 (2002).
[CrossRef]

M. Moncrieff, S. Cotton, E. Claridge, and P. Hall, “Spectrophotometric intracutaneous analysis - a new technique for imaging pigmented skin lesions,” Br. J. Dermatol. 146, 448–457 (2002).
[CrossRef] [PubMed]

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University Press, 2002), pp. 74–79.

2001 (2)

E. Limpert, W. A. Stahel, and M. Abbt, “Log-normal distributions across the science: keys and clues,” BioScience 51, 341–351 (2001).
[CrossRef]

Q. Fu and W. Sung, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

2000 (4)

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–267 (2000).
[CrossRef]

R. M. Lewis, V. Torczon, and M. W. Trosset, “Direct search methods: then and now,” J. Compt. Appl. Math. 124, 191–207, (2000).
[CrossRef]

S. L. Jacques, “Optical assessment of tissue heterogeneity in biomaterial and implants,” Proc. SPIE 3914, 576–580 (2000), doi: .
[CrossRef]

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, and R. Marchesini, “Multispectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (3)

1997 (2)

A. R. Young, “Chromophores in Human Skin,” Phys. Med. Biol. 42, 789–802 (1997).
[CrossRef] [PubMed]

V. V. Tuchin, I. L. Maksinova, D. A. Zimnyakov, I. L. Kon, A. H. Mavlutov, and A. A. Mishin, “Light propagation in tissues with controlled optical properties,” J. Biomed. Opt. 2, 401–417 (1997).
[CrossRef]

1996 (1)

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A Review,” J. Quant. Spectr. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

1995 (3)

1993 (1)

1991 (2)

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]

1987 (1)

M. J. C. van Gemert, A. J. Welch, W. M. Star, M. Motamedi, and W.-F. Cheong, “Tissue Optics for a slab geometry in the diffusion approximation,” Laser Med. Sci. 2, 295–302 (1987). DOI:
[CrossRef]

1984 (1)

W. A. de Rooij and C. C. A. H. Van der Stap, “Expansion of Mie scattering matrices in generalized spherical functions,” Astron. Astrophys. 131, 237–248 (1984).

1983 (1)

B. L. Diffey, “A Mathematical model for ultraviolet optics in skin,” Phys. Med. Biol. 28, 647–657 (1983).
[CrossRef] [PubMed]

1981 (1)

R. R. Anderson and J. A. Parrish, “The optics of human skin,” J. Invest. Dermat. 77, 13–19 (1981).
[CrossRef]

1980 (1)

W. J. Wiscombe, “Improved Mie scattering algorithms,” Apl. Opt. 19, 1505–1509 (1980).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comp. Jour. 7, 308–313 (1965).

1962 (1)

M. Gillison, A History of the Body Tissues (Williams and Wilkins Co., Baltimore, Maryland, 1962).

1960 (1)

S. Chandrasekhar, Radiative Transfer (Dover Publication, Inc.N.Y., 1960).

1957 (1)

H. C. Van de Hulst, Light Scattering by Small Particles (Dover Publications Inc., New York, 1957), pp. 103–130.

Aalders, M. C. G.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. 93, 1–4 (2004).
[CrossRef]

Abbt, M.

E. Limpert, W. A. Stahel, and M. Abbt, “Log-normal distributions across the science: keys and clues,” BioScience 51, 341–351 (2001).
[CrossRef]

Alshom, P.

Anderson, R. R.

R. R. Anderson and J. A. Parrish, “The optics of human skin,” J. Invest. Dermat. 77, 13–19 (1981).
[CrossRef]

Andersson-Engels, S. A.

Bartoli, C.

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, and R. Marchesini, “Multispectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

Bashkatov, A. N.

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous and mucous tissues: A review,” J. Innov. Opt. Health Sci. Appl. Phys. 4, 9–38 (2011).
[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]

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–267 (2000).
[CrossRef]

Biryulina, M.

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg. 36, 1–8 (2010). DOI:
[CrossRef]

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol. 15, 330–337 (2009). doi:
[CrossRef] [PubMed]

Biryulina, M. S.

K. P. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra - A feasibility study,” J. Photochem. Photobiol. B 93, 23–31 (2008).
[CrossRef] [PubMed]

Bohren, C. F.

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[PubMed]

B. Hamre, J. Winther, S. Gerland, J. J. Stamnes, and K. Stamnes, “Modelled and measured optical transmittance of snow-covered first-year sea ice in Kongfjorden, Svalbard,” J. Geophys. Res. 109, 1–14 (2004).
[CrossRef]

Stamnes, K.

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg. 36, 1–8 (2010). DOI:
[CrossRef]

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol. 15, 330–337 (2009). doi:
[CrossRef] [PubMed]

K. P. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra - A feasibility study,” J. Photochem. Photobiol. B 93, 23–31 (2008).
[CrossRef] [PubMed]

K. Hestenes, K. P. Nielsen, L. Zhao, J. J. Stamnes, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system,” Appl. Opt. 46, 2333–2350 (2007).
[CrossRef] [PubMed]

K. Zhang, W. Li, H. Eide, and K. Stamnes, “A bio-optical model suitable for use in forward and inverse coupled atmosphere-ocean radiative transfer models,” J. Quant. Spectr. Radiat. Transfer 103, 411–4233 (2007).
[CrossRef]

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “Importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. 82, 194–198 (2006).
[CrossRef]

K. P. Nielsen, L. Zhao, P. Juzenas, J. J. Stamnes, K. Stamnes, and J. Moan, “Reflectance spectra of pigmented and non-pigmented skin in the UV spectral region,” Photochem. Photobiol. 80, 450–455 (2004).
[PubMed]

B. Hamre, J. Winther, S. Gerland, J. J. Stamnes, and K. Stamnes, “Modelled and measured optical transmittance of snow-covered first-year sea ice in Kongfjorden, Svalbard,” J. Geophys. Res. 109, 1–14 (2004).
[CrossRef]

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University Press, 2002), pp. 74–79.

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]

M. J. C. van Gemert, A. J. Welch, W. M. Star, M. Motamedi, and W.-F. Cheong, “Tissue Optics for a slab geometry in the diffusion approximation,” Laser Med. Sci. 2, 295–302 (1987). DOI:
[CrossRef]

Sterenborg, H. J. C. 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]

Sung, W.

Swanson, D. L.

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg. 36, 1–8 (2010). DOI:
[CrossRef]

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol. 15, 330–337 (2009). doi:
[CrossRef] [PubMed]

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D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Radiat. Transfer 102, 85–110 (2006).
[CrossRef]

Tearney, G. J.

Thomas, G. E.

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University Press, 2002), pp. 74–79.

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R. M. Lewis, V. Torczon, and M. W. Trosset, “Direct search methods: then and now,” J. Compt. Appl. Math. 124, 191–207, (2000).
[CrossRef]

Tragni, G.

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, and R. Marchesini, “Multispectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

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M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A Review,” J. Quant. Spectr. Radiat. Transfer 55, 535–575 (1996).
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R. M. Lewis, V. Torczon, and M. W. Trosset, “Direct search methods: then and now,” J. Compt. Appl. Math. 124, 191–207, (2000).
[CrossRef]

Tuchin, V. V.

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous and mucous tissues: A review,” J. Innov. Opt. Health Sci. Appl. Phys. 4, 9–38 (2011).
[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]

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–267 (2000).
[CrossRef]

V. V. Tuchin, I. L. Maksinova, D. A. Zimnyakov, I. L. Kon, A. H. Mavlutov, and A. A. Mishin, “Light propagation in tissues with controlled optical properties,” J. Biomed. Opt. 2, 401–417 (1997).
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H. C. Van de Hulst, Light Scattering by Small Particles (Dover Publications Inc., New York, 1957), pp. 103–130.

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W. A. de Rooij and C. C. A. H. Van der Stap, “Expansion of Mie scattering matrices in generalized spherical functions,” Astron. Astrophys. 131, 237–248 (1984).

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D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. 93, 1–4 (2004).
[CrossRef]

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514, (1991).
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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]

M. J. C. van Gemert, A. J. Welch, W. M. Star, M. Motamedi, and W.-F. Cheong, “Tissue Optics for a slab geometry in the diffusion approximation,” Laser Med. Sci. 2, 295–302 (1987). DOI:
[CrossRef]

van Leeuwen, T. G.

D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. van Gemert, and T. G. van Leeuwen, “Oxygen saturation-dependent absorption and scattering of blood,” Phys. Rev. Lett. 93, 1–4 (2004).
[CrossRef]

van Marie, J.

van Staveren, H. J.

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D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Radiat. Transfer 102, 85–110 (2006).
[CrossRef]

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P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
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M. J. C. van Gemert, A. J. Welch, W. M. Star, M. Motamedi, and W.-F. Cheong, “Tissue Optics for a slab geometry in the diffusion approximation,” Laser Med. Sci. 2, 295–302 (1987). DOI:
[CrossRef]

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B. Hamre, J. Winther, S. Gerland, J. J. Stamnes, and K. Stamnes, “Modelled and measured optical transmittance of snow-covered first-year sea ice in Kongfjorden, Svalbard,” J. Geophys. Res. 109, 1–14 (2004).
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W. J. Wiscombe, “Improved Mie scattering algorithms,” Apl. Opt. 19, 1505–1509 (1980).
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H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X.-H. Hu, “Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm,” Phys. Med. Biol. 51, 1479–1489, (2006).
[CrossRef] [PubMed]

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J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J: Optimization 9, 112–147 (1998).
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J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J: Optimization 9, 112–147 (1998).
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J. Sandby-Møller, T. Paulsen, and H. C. Wulf, “Epidermal thickness at different body sites: relationship to age, gender, pigmentation, blood content, skin type and smoking,” Acta Derm. Venereol. 83, 410–413 (2003).
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K. Zhang, W. Li, H. Eide, and K. Stamnes, “A bio-optical model suitable for use in forward and inverse coupled atmosphere-ocean radiative transfer models,” J. Quant. Spectr. Radiat. Transfer 103, 411–4233 (2007).
[CrossRef]

Zhang, Y. Y.

Zhao, L.

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg. 36, 1–8 (2010). DOI:
[CrossRef]

D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol. 15, 330–337 (2009). doi:
[CrossRef] [PubMed]

K. P. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra - A feasibility study,” J. Photochem. Photobiol. B 93, 23–31 (2008).
[CrossRef] [PubMed]

K. Hestenes, K. P. Nielsen, L. Zhao, J. J. Stamnes, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system,” Appl. Opt. 46, 2333–2350 (2007).
[CrossRef] [PubMed]

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “Importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. 82, 194–198 (2006).
[CrossRef]

K. P. Nielsen, L. Zhao, P. Juzenas, J. J. Stamnes, K. Stamnes, and J. Moan, “Reflectance spectra of pigmented and non-pigmented skin in the UV spectral region,” Photochem. Photobiol. 80, 450–455 (2004).
[PubMed]

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V. V. Tuchin, I. L. Maksinova, D. A. Zimnyakov, I. L. Kon, A. H. Mavlutov, and A. A. Mishin, “Light propagation in tissues with controlled optical properties,” J. Biomed. Opt. 2, 401–417 (1997).
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K. P. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra - A feasibility study,” J. Photochem. Photobiol. B 93, 23–31 (2008).
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H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X.-H. Hu, “Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm,” Phys. Med. Biol. 51, 1479–1489, (2006).
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H. C. Van de Hulst, Light Scattering by Small Particles (Dover Publications Inc., New York, 1957), pp. 103–130.

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Figures (4)

Fig. 1
Fig. 1

Optimized IOPs in the upper part of the epidermis. (a) Log-normal particle size distribution n(r) [(mm)−3(nm)−1]. (b) Asymmetry factor g. (c) Real part m′ of the refractive index. (d) Scattering coefficient μs . (e) Imaginary part m″ of the refractive index. (d) Absorption coefficient μa .

Fig. 2
Fig. 2

Optimized IOPs in the lower epidermis. (a) Log-normal particle size distribution n(r) [(mm)−3(nm)−1]. (b) Asymmetry factor g. (c) Real part m′ of the refractive index. (d) Scattering coefficient μs . (e) Imaginary part m″ of the refractive index. (f) Absorption coefficient μa .

Fig. 3
Fig. 3

Optimized IOPs in the dermis. (a) Log-normal particle size distribution n(r) [(mm)−3(nm)−1]. (b) Asymmetry factor g. (c) Real part m′ of the refractive index. (d) Scattering coefficient μs . (e) Imaginary part m″ of the refractive index. (f) Absorption coefficient μa .

Fig. 4
Fig. 4

Optimized optical properties in Sub-cutis: (a) log-normal distribution n(r) [(mm) 3 (nm)−1] of particles size, (b) Asymmetry factor g, (c) real part of refractive index m′, (d) the scattering coefficient μs , (e) imaginary part of refractive index m″, and (f) absorption coefficient μa .

Tables (2)

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Table 1 Input parameters to Balter BOM.

Tables Icon

Table 2 Retrieved IOPs in human skin layers. The symbols and v denote the log-normal mean radius and the variance, respectively, of the retrieved particle size distribution.

Equations (27)

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μ a ( λ ) f a μ a , p ( λ ) + ( 1 f a ) μ a , h ( λ )
μ s ( λ ) f s λ b + ( 1 f s ) λ 4
( E | | s E s ) = e i k ( r z ) i k r ( S 2 S 3 S 4 S 1 ) ( E | | i E i ) .
S ( Θ ) = ( S 2 ( Θ ) 0 0 S 1 ( Θ ) ) .
S 1 ( Θ ) = n = 1 2 n + 1 n ( n + 1 ) [ a n π n ( μ ) + b n τ n ( μ ) ]
S 2 ( Θ ) = n = 1 2 n + 1 n ( n + 1 ) [ b n τ n ( μ ) + a n π n ( μ ) ]
Q e x t = 4 x 2 { S ( Θ = 0 ) }
Q e x t ( m , x ) = 2 x 2 n = 1 ( 2 n + 1 ) ( a n + b n )
Q s c a ( m , x ) = 2 x 2 n = 1 ( 2 n + 1 ) ( | a n | 2 + | b n | 2 )
Q a b s ( m , x ) = Q e x t ( m , x ) Q s c a ( m , x ) .
1 4 π 4 π d ω p ( μ ) = 1 2 1 1 d μ p ( μ ) = 1
p ( τ , μ ) = 0 2 N 1 ( 2 + 1 ) χ ( τ ) P ( μ )
χ ( τ ) = 1 2 1 1 d μ P ( μ ) p ( τ , μ ) ,
g = χ 1 ( τ ) = 1 2 1 1 d μ μ p ( τ , μ )
g = 4 x 2 Q s c a n = 1 2 n + 1 n ( n + 1 ) ( a n b n * ) + 4 x 2 Q s c a n = 1 n ( n + 2 ) n + 1 ( a n a n + 1 * + b n b n + 1 * )
n ( r ) = N r σ ( 2 π ) 1 2 exp [ ( ln r r ¯ ) 2 2 σ 2 ] , r > 0
r 1 r 2 n ( r ) d r = N .
μ ˜ e ( λ ) = π r 1 r 2 r 2 Q e x t ( m , x ) n ( r ) d r
μ ˜ s ( λ ) = π r 1 r 2 r 2 Q s c a ( m , x ) n ( r ) d r
g ˜ ( λ ) = 1 μ ˜ s ( λ ) r 1 r 2 C s c a ( m , r , λ ) g ( r , λ ) n ( r ) d r
g ˜ ( λ ) = g ˜ R μ ˜ s R + g ˜ M μ ˜ s M μ ˜ s R + μ ˜ s M = g ˜ M μ ˜ s M μ ˜ s R + μ ˜ s M
μ e , B ( λ ) = d τ B ( λ ) d z = μ ˜ a ( λ ) + μ ˜ s ( λ ) = μ ˜ e ( λ )
μ s , B ( λ ) = ω B ( λ ) d τ B ( λ ) d z = μ ˜ s ( λ )
μ a , B ( λ ) = [ 1 ω B ( λ ) ] d τ B ( λ ) d z = μ ˜ a ( λ )
g B = g ˜ M μ ˜ s M μ ˜ s M + μ ˜ s M .
f ( m , x ) = 1 10 { j = 1 10 [ ( 1 μ ˜ a ( λ j ) μ a , B ( λ j ) ) 2 + ( 1 μ ˜ s ( λ j ) μ s , B ( λ j ) ) 2 + ( 1 g ˜ ( λ j ) g B ( λ j ) ) 2 ] 1 2 }
g e p g d e 0.62 + 0.29 × 10 3 λ

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