title: Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface.
abstract: By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.
authors.affiliation: Shangai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. shj@siom.ac.cn
authors.forename: Jian
authors.initials: J
authors.lastname: Shen
authors.forename: Degang
authors.initials: D
authors.lastname: Deng
authors.forename: Weijin
authors.initials: W
authors.lastname: Kong
authors.forename: Shijie
authors.initials: S
authors.lastname: Liu
authors.forename: Zicai
authors.initials: Z
authors.lastname: Shen
authors.forename: Chaoyang
authors.initials: C
authors.lastname: Wei
authors.forename: Hongbo
authors.initials: H
authors.lastname: He
authors.forename: Jianda
authors.initials: J
authors.lastname: Shao
authors.forename: Zhengxiu
authors.initials: Z
authors.lastname: Fan