Abstract

We use a layered model of normal human skin based on size distributions of polydisperse spherical particles and their complex refractive indices to compute the Stokes scattering matrix at wavelengths in the visible spectral band. The elements of the Stokes scattering matrix are required in a polarized radiative transfer code for a coupled air–tissue system to compute the polarized reflectance and examine how it is dependent on the vertical structure of the inherent optical properties of skin, including the phase matrix. Thus, the elements of the Stokes scattering matrix can be useful for investigating polarization-dependent light propagation in turbid optical media, such as human skin tissue.

© 2012 Optical Society of America

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  52. S. Bartel and A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt. 39, 1580–1588 (2000).
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    [CrossRef]
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2012

F. Voit, A. Hohmann, J. Schäfer, and A. Kienle, “Multiple scattering of polarized light: comparasion of Maxwell theory and radiative transfer theory,” J. Biomed. Opt. 17, 045003 (2012).
[CrossRef]

2011

K. Muinonen, J. Tyynela, E. Zubko, H. Lindqvist, A. Penttila, and G. Videen, “Polarization of light backscattered by small particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2193–2212 (2011).
[CrossRef]

J. M. Dlugach, M. I. Mishchenko, L. Liu, and D. W. Mackowski, “Numerically-exact computer simulations of light scattering by densely packed, random particulate media,” J. Quant. Spectrosc. Radiat. Transfer 112, 2068–2078 (2011).
[CrossRef]

M. Rubinstein and W. B. Armstrong, “Transoral laser microsurgery for laryngeal cancer: a primer and review of laser dosimetry,” Lasers Med. Sci. 26, 113–124 (2011).
[CrossRef]

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Haus, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Sprectrosc. Radiat. Transfer 112, 714–726 (2011).
[CrossRef]

A. Bhandari, B. Hamre, Ø. Frette, K. Stamnes, and J. J. Stamnes, “Modeling optical properties of human skin using Mie theory for particles with different size distributions and refractive indices,” Appl. Opt. 19, 14549–14567 (2011).
[CrossRef]

2010

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer 111, 616–633 (2010).
[CrossRef]

E. J. Bae, S. H. Seo, Y. C. Kye, and H. H. Ahn, “A quantitative assessment of the human skin surface using polarized light digital photography and its dermatologic significance,” Skin Res. Technol. 16(3), 270–274 (2010).

J. Begic-Rahic and S. Vranic, “The application of bioptron light therapy in dermatology and wound healing,” Eur. Dermatol. 5, 57–60 (2010).

2009

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).
[CrossRef]

M. I. Mishchenko and L. Liu, “Electromagnetic scattering by densely packed particulates ice at radar wavelength: exact theoretical results and remote-sensing implications,” Appl. Opt. 48, 2421–2425 (2009).
[CrossRef]

2008

S. R. Sharma, R. Poddar, P. Sen, and J. T. Andrews, “Effect of vitamin C on collagen biosynthesis and degree of birefringence in polarization sensitive optical coherence tomography (PS-OCT),” Afr. J. Biotech. 7, 2049–2054 (2008).

2007

2006

R. Vilaplana, F. Moreno, and A. Molina, “Study of the sensitivity of size-averaged scattering matrix elements of nonspherical particles to changes in shape, porosity and refractive index,” J. Quant. Spectrosc. Radiat. Transfer 100, 415–428 (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]

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]

2005

D. M. Stam and J. W. Hovenier, “Errors in calculated planetary phase functions and albedos due to neglecting polarization,” Astron. Astrophys. 444, 275–286 (2005).
[CrossRef]

M. Itoh, M. Yamanari, Y. Yasuno, and T. Yatagai, “Polarization characteristics of multiple backscattering in human blood cell suspensions,” Opt. Quantum Electron. 37, 1277–1285 (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]

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

2004

M. Pircher, E. Goetzinger, R. Leitgeb, and C. K. Hitzenberger, “Three dimensional polarization sensitive OCT of human skin in vivo,” Opt. Express 12, 3236–3244 (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).

O. V. Postylyakov, “Linearized vector radiative transfer model MCC++ for a spherical atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 88, 297–317 (2004).
[CrossRef]

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]

V. P. Tishkovets and M. I. Mishchenko, “Coherent backscattering of light by a layer of discrete random medium,” J. Quant. Spectrosc. Radiat. Transfer 86, 161–180 (2004).
[CrossRef]

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Birefringence measurements in human skin using polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 9, 287–291 (2004).
[CrossRef]

2003

E. J. Dennis, G. J. Dolmans, R. K. Jain, and D. Fukumura, “Photodynamic therapy for cancer,” Nat. Rev. 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).

2002

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef]

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

2001

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

2000

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).

S. Bartel and A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt. 39, 1580–1588 (2000).
[CrossRef]

1999

R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference, time-domain simulations and goniometric measurements,” Appl. Opt. 38, 3651–3661 (1999).
[CrossRef]

A. R. Jones, “Light scattering for particle characterization,” Progr. Energy Combust. Sci. 25, 1–53 (1999).

F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT: an improved generalized discrete ordinate method for polarized (vector) radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 61, 105–122 (1999).
[CrossRef]

1998

M. I. Mishchenko, and L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatters,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

A. B. David, “Mueller matrices and information derived from linear polarization lidar measurements: theory,” Appl. Opt. 37, 2448–2463 (1998).
[CrossRef]

A. M. K. Nilsson, P. Alshom, A. Karlson, and S. A. Andersson-Engels, “T-matrix computations of light scattering by red blood cells,” Appl. Opt. 37, 2735–2747 (1998).
[CrossRef]

1996

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

1994

1991

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).
[CrossRef]

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991).
[CrossRef]

P. A. Payne, “Measurement of properties and function of skin,” Clin. Phys. Physiol. Meas. 12, 105–129 (1991).
[CrossRef]

1989

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]

1988

J. W. Hovenier and C. V. M. van der Mee, “Scattering of polarized light: properties of the elements of the phase matrix,” Astron. Astrophys. 196, 287–295 (1988).

1985

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light scattering,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

1984

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).

K. J. Voss, “Measurement of Mueller matrix for ocean water,” Appl. Opt. 23, 4427–4439 (1984).
[CrossRef]

1982

C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys. 109, 195–200 (1982).

1981

T. Mar, “Measurement of mitochondrial volume independent of refractive index by light scattering,” J. Biochem. Biophys. Methods 4, 177–184 (1981).
[CrossRef]

1980

1974

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1971

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

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]

Ahn, H. H.

E. J. Bae, S. H. Seo, Y. C. Kye, and H. H. Ahn, “A quantitative assessment of the human skin surface using polarized light digital photography and its dermatologic significance,” Skin Res. Technol. 16(3), 270–274 (2010).

Alshom, P.

Andersson-Engels, S. A.

Andrews, J. T.

S. R. Sharma, R. Poddar, P. Sen, and J. T. Andrews, “Effect of vitamin C on collagen biosynthesis and degree of birefringence in polarization sensitive optical coherence tomography (PS-OCT),” Afr. J. Biotech. 7, 2049–2054 (2008).

Armstrong, W. B.

M. Rubinstein and W. B. Armstrong, “Transoral laser microsurgery for laryngeal cancer: a primer and review of laser dosimetry,” Lasers Med. Sci. 26, 113–124 (2011).
[CrossRef]

Backman, V.

Y. Liu, Y. L. Kim, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for early cancer detection,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, Technical Digest (Optical Society of America, 2003), paper CMG4.

Bae, E. J.

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Figures (4)

Fig. 1.
Fig. 1.

Elements of the normalized Stokes scattering matrix for a log-normal size distribution of spherical particles in the upper epidermis layer. The colored curves in each panel indicate the geometric mean size parameter (xu=2πr¯g,u/λ, where λ=λ0/1.36) at the five different wavelengths λ0 given in (d).

Fig. 2.
Fig. 2.

Same as in Fig. 1, but for the lower epidermis skin layer.

Fig. 3.
Fig. 3.

Same as in Fig. 1, but the skin layer is the dermis.

Fig. 4.
Fig. 4.

Same as in Fig. 1, but the layer is the subcutis.

Tables (2)

Tables Icon

Table 1. Input Variables Used to Calculate the Stokes Scattering Matrix for Four Different Human Skin Layersa

Tables Icon

Table 2. Tabulated Values of the Size-Averaged Optical Mean Free Path ˜, the Optical Depth τ˜, and the Single-Scattering Albedo ω˜a

Equations (16)

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

1211dμp(μ)=1.
[IQUV]=[EE*+EE*EE*EE*EE*+EE*i(EE*EE*)],
(EsEs)=ei(kRkz)ikR(S2S3S4S1)(EE).
P={(Q2+U2+V2)12Ifor elliptical polarization(Q2+U2)12Ifor linear polarizationVIfor circular polarization},
D=(1100110000100001).
Isc=M(μ)I,
Fij(μ)=r1r2Mij(μ,r)n(r)dr,
F(μ)=(a1(μ)b1(μ)00b1(μ)a1(μ)0000a3(μ)b2(μ)00b2(μa3(μ)).
a1(μ)=12(|S2|2+|S1|2),
a3(μ)=12(S1S2*+S2S1*),
b1(μ)=12(|S2|2|S1|2),
b2(μ)=i2(S1S2*S2*S1).
M(τ,u,u,φφ)=L(πσ2)F(τ,u)L(σ1),
cosΘ=cosϑcosϑ+sinϑsinϑcos(φφ).
n(r)=1rlnσg2πexp[(lnrlnr¯g)2/(2ln2σg)],
r1r2n(r)dr=1.

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