Mueller matrix representation for a slab of random medium with discrete particles and random rough surfaces with moderate surface roughness

Abstract

Mueller matrices are calculated for a slab of random medium containing both Gaussian-statistical-we random rough surfaces and discrete spherical particles. The refractive indices of the surrounding media are different from the background refractive index of the random medium. Kirchhoff rough-surface scattering theory associated with the geometric-optics approach is used to calculate the waves scattered from the rough surfaces. The scattered waves contain both coherent and incoherent waves. This method applies to rough surfaces with moderate surface roughness. In addition, the scattered waves can be related to the incident waves by means of the transmittivity and reflectivity matrices. These matrices are used to determine a pair of boundary conditions for the vector radiative transfer equation. The multiple scattering due to the discrete particles is computed by solving the vector radiative transfer equation numerically. Numerical illustrations are given for the optical thickness of the slab from 0.4 to 5 and the mean size parameter of the particles with Gaussian distribution, ⟨ka⟩ 0.3 to 1. The surface root-mean-square slope varies from 0.1 to 0.3. Mueller matrices which characterize the random medium are constructed from the scattered Stokes vectors due to four independent polarized incident waves. The Mueller matrices are found to have eight non-vanishing matrix elements and some symmetrical properties.