Stokes scattering matrix for human skin

Anak Bhandari; Snorre Stamnes; Børge Hamre; Øyvind Frette; Knut Stamnes; Jakob J. Stamnes

doi:10.1364/AO.51.007487

Applied Optics
Vol. 51,
Issue 31,
pp. 7487-7498
(2012)
•https://doi.org/10.1364/AO.51.007487

Stokes scattering matrix for human skin

Anak Bhandari, Snorre Stamnes, Børge Hamre, Øyvind Frette, Knut Stamnes, and Jakob J. Stamnes

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Anak Bhandari, Snorre Stamnes, Børge Hamre, Øyvind Frette, Knut Stamnes, and Jakob J. Stamnes, "Stokes scattering matrix for human skin," Appl. Opt. 51, 7487-7498 (2012)

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- Scattering
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About this Article
History
- Original Manuscript: August 2, 2012
- Revised Manuscript: September 25, 2012
- Manuscript Accepted: October 1, 2012
- Published: October 23, 2012
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 7, Iss. 12

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.

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—	U. Epidermis	L. Epidermis	Dermis	Subcutis
—	$r_{1, u} = 40 nm$	$r_{1, ℓ} = 47 nm$	$r_{1, d} = 87 nm$	$r_{1, s} = 132 nm$
—	$r_{2, u} = 359 nm$	$r_{2, ℓ} = 735 nm$	$r_{2, d} = 1793 nm$	$r_{2, s} = 247 nm$
—	${\bar{r}}_{g, u} = 119.7 nm$	${\bar{r}}_{g, ℓ} = 185.4 nm$	${\bar{r}}_{g, d} = 395.0 nm$	${\bar{r}}_{g, s} = 180.8 nm$
—	$σ_{g, u} = 1.442$	$σ_{g, ℓ} = 1.582$	$σ_{g, d} = 1.656$	$σ_{g, s} = 1.110$
$λ_{0}$ [nm]	$m^{'} + m^{''} \times 10^{- 3}$	$m^{'} + m^{''} \times 10^{- 3}$	$m^{'} + m ″ \times 1 0^{- 3}$	$m^{'} + m^{''} \times 10^{- 3}$
368	$1.559 + i 5.561$	$1.521 + i 4.177$	$1.493 + i 2.021$	$1.580 + i 0.3915$
403	$1.560 + i 4.374$	$1.523 + i 3.253$	$1.502 + i 6.297$	$1.576 + i 0.3483$
510	$1.561 + i 2.303$	$1.527 + i 1.680$	$1.486 + i 0.579$	$1.570 + i 0.2574$
579	$1.563 + i 1.698$	$1.528 + i 1.227$	$1.490 + i 1.427$	$1.568 + i 0.2181$
632	$1.563 + i 1.377$	$1.529 + i 0.990$	$1.493 + i 0.074$	$1.567 + i 0.1945$

Layer	$λ_{0}$ [nm]	$\tilde{l}$ [mm]	$\tilde{τ}$ (BOM)	$\tilde{τ}$ (Mie)	$\tilde{τ}$ ( $T$ -matr.)	$\tilde{ω}$ (BOM)	$\tilde{ω}$ (Mie)	$\tilde{ω}$ ( $T$ -matr.)
Upper	368	0.0035	6.1761	(6.1744)5.8369	5.8261	0.9296	0.9256	0.9253
epidermis	403	0.0042	5.1145	(5.1142)4.8795	4.8929	0.9389	0.9260	0.9360
..	510	0.0068	3.0633	(3.0610)2.9695	2.9785	0.9579	0.9567	0.9567
..	579	0.0089	2.3221	(2.3220)2.2669	2.2785	0.9643	0.9535	0.9635
..	632	0.0109	1.8867	(1.8880)1.8492	1.8571	0.9676	0.9670	0.9671
Lower	368	0.0023	35.2480	(35.8818)34.3268	33.8938	0.9507	0.9493	0.9485
epidermis	403	0.0027	31.1382	(31.1402)30.3268	30.1400	0.9598	0.9584	0.9584
..	510	0.0038	21.4708	(21.4678)21.0462	21.1994	0.9760	0.9755	0.9756
..	579	0.0047	17.2300	(17.2439)16.9902	17.0117	0.9807	0.9805	0.9804
..	632	0.0056	14.6339	(14.6270)14.4482	14.5187	0.9833	0.9831	0.9831
Dermis	368	0.0172	58.2017	(59.4094)36.3647	36.4065	0.9805	0.9689	0.9688
..	403	0.0206	51.5350	(51.5264)35.5035	35.5789	0.9417	0.9155	0.9154
..	510	0.0299	34.0951	(33.6948)27.4477	27.6164	0.9929	0.9913	0.9913
..	579	0.0363	28.3428	(28.0785)24.3180	24.8868	0.9818	0.9789	0.9792
..	632	0.0391	25.5918	(25.5924)22.9433	23.0485	0.9990	0.9989	0.9989
Sub-cutis	368	0.0006	53108	(53091)52955	52726	0.99549	0.9955	0.9954
..	403	0.0007	42703	(42702)42608	42461	0.9955	0.9955	0.9954
..	510	0.0012	24267	(24269)24232	24330	0.9955	0.9955	0.9955
..	579	0.0017	17896	(17901)17879	17935	0.9955	0.9955	0.9955
..	632	0.0021	14503	(14502)14486	14402	0.9955	0.9955	0.9994

—	U. Epidermis	L. Epidermis	Dermis	Subcutis
—	$r_{1, u} = 40 nm$	$r_{1, ℓ} = 47 nm$	$r_{1, d} = 87 nm$	$r_{1, s} = 132 nm$
—	$r_{2, u} = 359 nm$	$r_{2, ℓ} = 735 nm$	$r_{2, d} = 1793 nm$	$r_{2, s} = 247 nm$
—	${\bar{r}}_{g, u} = 119.7 nm$	${\bar{r}}_{g, ℓ} = 185.4 nm$	${\bar{r}}_{g, d} = 395.0 nm$	${\bar{r}}_{g, s} = 180.8 nm$
—	$σ_{g, u} = 1.442$	$σ_{g, ℓ} = 1.582$	$σ_{g, d} = 1.656$	$σ_{g, s} = 1.110$
$λ_{0}$ [nm]	$m^{'} + m^{''} \times 10^{- 3}$	$m^{'} + m^{''} \times 10^{- 3}$	$m^{'} + m ″ \times 1 0^{- 3}$	$m^{'} + m^{''} \times 10^{- 3}$
368	$1.559 + i 5.561$	$1.521 + i 4.177$	$1.493 + i 2.021$	$1.580 + i 0.3915$
403	$1.560 + i 4.374$	$1.523 + i 3.253$	$1.502 + i 6.297$	$1.576 + i 0.3483$
510	$1.561 + i 2.303$	$1.527 + i 1.680$	$1.486 + i 0.579$	$1.570 + i 0.2574$
579	$1.563 + i 1.698$	$1.528 + i 1.227$	$1.490 + i 1.427$	$1.568 + i 0.2181$
632	$1.563 + i 1.377$	$1.529 + i 0.990$	$1.493 + i 0.074$	$1.567 + i 0.1945$

Layer	$λ_{0}$ [nm]	$\tilde{l}$ [mm]	$\tilde{τ}$ (BOM)	$\tilde{τ}$ (Mie)	$\tilde{τ}$ ( $T$ -matr.)	$\tilde{ω}$ (BOM)	$\tilde{ω}$ (Mie)	$\tilde{ω}$ ( $T$ -matr.)
Upper	368	0.0035	6.1761	(6.1744)5.8369	5.8261	0.9296	0.9256	0.9253
epidermis	403	0.0042	5.1145	(5.1142)4.8795	4.8929	0.9389	0.9260	0.9360
..	510	0.0068	3.0633	(3.0610)2.9695	2.9785	0.9579	0.9567	0.9567
..	579	0.0089	2.3221	(2.3220)2.2669	2.2785	0.9643	0.9535	0.9635
..	632	0.0109	1.8867	(1.8880)1.8492	1.8571	0.9676	0.9670	0.9671
Lower	368	0.0023	35.2480	(35.8818)34.3268	33.8938	0.9507	0.9493	0.9485
epidermis	403	0.0027	31.1382	(31.1402)30.3268	30.1400	0.9598	0.9584	0.9584
..	510	0.0038	21.4708	(21.4678)21.0462	21.1994	0.9760	0.9755	0.9756
..	579	0.0047	17.2300	(17.2439)16.9902	17.0117	0.9807	0.9805	0.9804
..	632	0.0056	14.6339	(14.6270)14.4482	14.5187	0.9833	0.9831	0.9831
Dermis	368	0.0172	58.2017	(59.4094)36.3647	36.4065	0.9805	0.9689	0.9688
..	403	0.0206	51.5350	(51.5264)35.5035	35.5789	0.9417	0.9155	0.9154
..	510	0.0299	34.0951	(33.6948)27.4477	27.6164	0.9929	0.9913	0.9913
..	579	0.0363	28.3428	(28.0785)24.3180	24.8868	0.9818	0.9789	0.9792
..	632	0.0391	25.5918	(25.5924)22.9433	23.0485	0.9990	0.9989	0.9989
Sub-cutis	368	0.0006	53108	(53091)52955	52726	0.99549	0.9955	0.9954
..	403	0.0007	42703	(42702)42608	42461	0.9955	0.9955	0.9954
..	510	0.0012	24267	(24269)24232	24330	0.9955	0.9955	0.9955
..	579	0.0017	17896	(17901)17879	17935	0.9955	0.9955	0.9955
..	632	0.0021	14503	(14502)14486	14402	0.9955	0.9955	0.9994

Abstract

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Tables (2)

Equations (16)

Applied Optics