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)
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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Input Variables Used to Calculate the Stokes Scattering Matrix for Four Different Human Skin Layersa
—
U. Epidermis
L. Epidermis
Dermis
Subcutis
—
—
—
—
[nm]
368
403
510
579
632
and the are respectively the geometric mean radius and the standard deviation of a log-normal distribution of homogeneous spherical particles. The parameters and are respectively the largest and smallest radii of the particles, which are embedded in a nonabsorbing host medium of constant refractive index equal to 1.36 [55]. [nm] is the wavelength of light in air.
Table 2.
Tabulated Values of the Size-Averaged Optical Mean Free Path , the Optical Depth , and the Single-Scattering Albedo a
Layer
[nm]
[mm]
(BOM)
(Mie)
(-matr.)
(BOM)
(Mie)
(-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
These values were obtained from a BOM, from Mie calculations (Mie) according to Bhandari et al. [55], and from the -matrix method (-matr.) computed using Mishchenko’s -matrix method [46]. Note that (BOM), (BOM), and the values of (Mie) inside parentheses include contributions from Rayleigh scattering with scattering coefficients that are the same for all four layers. In units of , is 10.9060 for , 7.5829 for , 2.9565 for , 1.7797 for , and 1.2537 for .
Tables (2)
Table 1.
Input Variables Used to Calculate the Stokes Scattering Matrix for Four Different Human Skin Layersa
—
U. Epidermis
L. Epidermis
Dermis
Subcutis
—
—
—
—
[nm]
368
403
510
579
632
and the are respectively the geometric mean radius and the standard deviation of a log-normal distribution of homogeneous spherical particles. The parameters and are respectively the largest and smallest radii of the particles, which are embedded in a nonabsorbing host medium of constant refractive index equal to 1.36 [55]. [nm] is the wavelength of light in air.
Table 2.
Tabulated Values of the Size-Averaged Optical Mean Free Path , the Optical Depth , and the Single-Scattering Albedo a
Layer
[nm]
[mm]
(BOM)
(Mie)
(-matr.)
(BOM)
(Mie)
(-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
These values were obtained from a BOM, from Mie calculations (Mie) according to Bhandari et al. [55], and from the -matrix method (-matr.) computed using Mishchenko’s -matrix method [46]. Note that (BOM), (BOM), and the values of (Mie) inside parentheses include contributions from Rayleigh scattering with scattering coefficients that are the same for all four layers. In units of , is 10.9060 for , 7.5829 for , 2.9565 for , 1.7797 for , and 1.2537 for .