Polarization characteristics of scattered light from macroscopically rough surfaces

Lianhua Jin; Koji Yamaguchi; Mitsuhiro Watanabe; Shinichiro Hira; Eiichi Kondoh; Bernard Gelloz

doi:10.1007/s10043-015-0117-2

Optical Review

August 2015, Volume 22, Issue 4, pp 511–520 | Cite as

Polarization characteristics of scattered light from macroscopically rough surfaces

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Authors and affiliations

Lianhua JinEmail author
Koji Yamaguchi
Mitsuhiro Watanabe
Shinichiro Hira
Eiichi Kondoh
Bernard Gelloz

Regular Paper

First Online: 04 July 2015

Received: 02 March 2015

Accepted: 21 June 2015

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3 Citations

Abstract

The polarization status of in- and out-of-plane scattered light from macroscopically rough surfaces was measured and expressed in a scattering coordinate system. In this coordinate system, the direction of the scattered light was decided by the transverse and longitudinal scattering angles, both of which are defined by using the incident ray and its section plane as the fundamental axis and plane. The polarization characteristics of scattering, which consist of patterns of polarization degrees and the Stokes of the scattered light in terms of transverse and longitudinal scattering angles, was presented and investigated. The Stokes patterns of scattered light exhibited independence from the transverse scattering angle. Furthermore, the ellipsometric parameters of samples, which were deduced from the polarization status of full scattering, showed the validity as well as limitations of the facet model for macroscopically rough surface.

Keywords

Polarization Scattering measurements Rough surfaces Stokes parameter Facet model

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Appendix

The Stokes of the reflected lights are related to the polarization state of the incident light (right circularly polarized in this work), and given by [19],

$$S_{0} = r_{p}^{2} + r_{s}^{2} ,$$

(A-1)

$$S_{1} = r_{p}^{2} - r_{s}^{2} = - \cos 2\varPsi ,$$

(A-2)

$$S_{2} = 2r_{p} r_{s} \cos (\Delta + 90^\circ ) = - \sin 2\varPsi \sin \Delta ,$$

(A-3)

$$S_{3} = 2r_{p} r_{s} \sin (\Delta + 90^\circ ) = \sin 2\varPsi \cos \Delta ,$$

(A-4)

where Δ is the phase difference of p and s polarized light by reflection, and Ψ is the ratio of p and s polarized light. The phase 90° in Eqs. (A-3) and (A-4) is invoked due to the right circularly polarized incident light.

Fresnel reflection coefficients r _p and r _s are reflection layer related factors. For the reflection at a single interface between medium 1 (refractive index N ₁) and medium 3 (refractive index N ₃), the coefficients become,

$$r_{p}^{13} = \frac{{N_{1} \sin \frac{{\theta_{\text{ls}} }}{2} - N_{3} \left[ {1 - (N_{1} /N_{3} )^{2} \cos^{2} \frac{{\theta_{\text{ls}} }}{2}} \right]^{1/2} }}{{N_{1} \sin \frac{{\theta_{\text{ls}} }}{2} + N_{3} \left[ {1 - (N_{1} /N_{3} )^{2} \cos^{2} \frac{{\theta_{\text{ls}} }}{2}} \right]^{1/2} }} ,$$

(A-5)

$$r_{s}^{13} = \frac{{N_{3} \sin \frac{{\theta_{\text{ls}} }}{2} - N_{1} \left[ {1 - (N_{1} /N_{3} )^{2} \cos^{2} \frac{{\theta_{\text{ls}} }}{2}} \right]^{1/2} }}{{N_{3} \sin \frac{{\theta_{\text{ls}} }}{2} + N_{1} \left[ {1 - (N_{1} /N_{3} )^{2} \cos^{2} \frac{{\theta_{\text{ls}} }}{2}} \right]^{1/2} }} .$$

(A-6)

For the successive reflection from two interfaces between medium 1, medium 2 (refractive index N ₂), and medium 3, the total reflection coefficients will be [20],

$$r_{p}^{123} = \frac{{r_{p}^{12} + r_{p}^{23} \exp ( - j2\beta )}}{{1 + r_{p}^{12} r_{p}^{23} \exp ( - j2\beta )}} ,$$

(A-7)

$$r_{s}^{123} = \frac{{r_{s}^{12} + r_{s}^{23} \exp ( - j2\beta )}}{{1 + r_{s}^{12} r_{s}^{23} \exp ( - j2\beta )}} ,$$

(A-8)

where the subscript “12” and “23” denote that the coefficients are for interfaces between medium 1 and medium 2, and medium 2 and medium 3, respectively. β is the phase thickness of the medium 2 and is given by [20]

$$\beta = \frac{2\pi d}{\lambda }N_{2} \left[ {1 - (N_{1} /N_{2} )^{2} \cos^{2} \frac{{\theta_{\text{ls}} }}{2}} \right]^{1/2} ,$$

(A-9)

where d is the thickness of medium 2.

References

1.
Stover, J.C.: Optical scattering: measurement and analysis. SPIE Optical Engineering Press, Bellingham, Washington, USA (1995)Google Scholar
2.
Torrance, K.E., Sparrow, E.M.: Theory for off-specular reflection from roughened surfaces. J. Opt. Soc. Am. 57, 1105–1112 (1967)ADSCrossRefGoogle Scholar
3.
Maxwell, J.R., Beard, J., Weiner, S., Ladd, D.: “Bidirectional reflectance model validation and utilization,” Technical Report AF AL–TR–73–303, Environmental Research Institute of Michigan (ERIM), October (1973)Google Scholar
4.
He, X.D., Torrance, K.E., Sillion, F.X., Greenberg, D.P.: A comprehensive physical model for light reflection. Comput. Graph. 25, 175–186 (1991)CrossRefGoogle Scholar
5.
Li, H., Torrance, K.E.: An experimental study of the correlation between surface roughness and light scattering for rough metallic surfaces. In: Proceedings of SPIE, vol. 5878, p. 58780V (2005)Google Scholar
6.
Jafolla, J.C., Thomas, D.J., Hilgers, J.W., Reynolds, W.R., Blasband, C.: Theory and measurement of bidirectional reflectance for signature analysis. In: Proceedings of SPIE, vol. 3699, pp. 2–15 (1999)Google Scholar
7.
Priest, R., Germer, T.: Polarimetric BRDF in the microfacet model; theory and measurements. In: Proceedings of the 2000 meeting of the Military Sensing Symposia Specialty Group on passive sensors, Infrared Information Analysis Center, Ann Arbor, MI, pp. 169–181 (2000)Google Scholar
8.
Renhorn, I.G., Boreman, G.D.: Analytical fitting model for rough-surface BRDF. Opt. Express 16, 12892–12898 (2008)ADSCrossRefGoogle Scholar
9.
Hyde IV, M.W., Schmidt, J.D., Havrilla, M.J.: A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces. Opt. Express 17, 22138–22153 (2009)ADSCrossRefGoogle Scholar
10.
Rhenhorn, I.G., Hallberg, T., Bergstrom, D., Boreman, G.D.: Four-parameter model for polarization-resolved rough-surface BRDF. Opt. Express 19, 1027–1036 (2011)ADSCrossRefGoogle Scholar
11.
Videen, G., Hsu, J., Bickel, W.S., Wolfe, W.L.: Polarized light scattered from rough surfaces. J. Opt. Soc. Am. A 9, 1111–1118 (1992)ADSCrossRefGoogle Scholar
12.
Jin, L., Kasahara, M., Gelloz, B., Takizawa, K.: Polarization properties of scattered light from macrorough surfaces. Opt. Lett. 35, 595–597 (2010)ADSCrossRefGoogle Scholar
13.
Jin, L., Takizawa, K.: Stokes parameters of reflected and scattered light by a rough surface. Proc. SPIE 7432, 74320B (2009)ADSCrossRefGoogle Scholar
14.
Jin, L., Tsutaki, T., Gelloz, B.: Polarization analysis of scattering light using a facet model. In: Proceedings SPIE 8160, (2011)Google Scholar
15.
Barrick, D.E.: Rough surface scattering based on the specular point theory. IEEE Trans. Ant. Prop. AP-16, pp. 449–454 (1968)Google Scholar
16.
Mendez, E.R., O’Donnell, K.A.: Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces. Opt. Commun. 61, 91–95 (1987)ADSCrossRefGoogle Scholar
17.
O’Donnell, K.A., Mendez, E.R.: Experimental study of scattering from characterized random surfaces. J. Opt. Soc. Am. A 4, 1194–1205 (1987)ADSCrossRefMATHGoogle Scholar
18.
Sant, A.J., Dainty, J.C., Kim, M.J.: Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers. Opt. Lett. 14, 1183–1185 (1989)ADSCrossRefGoogle Scholar
19.
Tompkins, H.G., Irene, E.A.: Handbook of ellipsometry. William Andrew, Newyork (2005)Google Scholar
20.
Tompkins, H.G.: A user’s guide to ellipsometry. Dover Publications, Newyork (2006)Google Scholar
21.
Stankevicha, D., Istominaa, L., Shkuratova, Y., Videen, G.: The scattering matrix of random media consisting of large opaque spheres calculated using ray tracing and accounting for coherent backscattering enhancement. J. Quant. Spectrosc. Radiative Transfer 106, 509–519 (2007)ADSCrossRefGoogle Scholar

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Lianhua Jin
- 1
Email authorView author's OrcID profile
Koji Yamaguchi
- 1
Mitsuhiro Watanabe
- 1
Shinichiro Hira
- 1
Eiichi Kondoh
- 1
Bernard Gelloz
- 2

1.Graduate School of Medicine and EngineeringUniversity of YamanashiYamanashiJapan
2.Graduate School of EngineeringNagoya UniversityNagoyaJapan

Polarization characteristics of scattered light from macroscopically rough surfaces

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