Mueller matrix calculation for a slab of random medium with both random rough surfaces and discrete particles

A model for a slab of random medium containing both random rough surfaces and discrete scatterers is presented in this paper. The refractive indices of the surrounding media are different from the background refractive index of the random medium. Kirchhoff rough surface theory is used to derive the transmittivity and reflectivity matrices for the scattering of electromagnetic waves from the rough surfaces. These matrices are used to determine a pair of boundary conditions for the vector radiative transfer equation. The multiple scattering due to the discrete scatterers is computed by solving the radiative transfer equation numerically, including the rough surface scattering effect. Mueller matrices characterizing the random medium are constructed from the scattered Stokes vectors due to four independent polarized incident waves. The Mueller matrices are found to have symmetrical properties, and there are eight nonvanishing matrix elements