MUELLER MATRIX REPRESENTATION FOR A SLAB OF RANDOM MEDIUM WITH DISCRETE PARTICLES AND RANDOM ROUGH SURFACES WITH MODERATE SURFACE-ROUGHNESS

Mueller matrices are calculated for a slab of random medium containing both Gaussian-statistical-type random rough surfaces and discrete sph erical particles. The refractive indices of the surrounding media are different from the background refractive index of the random medium. K irchhoff rough-surface scattering theory associated with the geometric -optics approach is used to calculate the waves scattered from the rou gh surfaces. The scattered waves contain both coherent and incoherent waves. This method applies to rough surfaces with moderate surface rou ghness. In addition, the scattered waves can be related to the inciden t waves by means of the transmittivity and reflectivity matrices. Thes e matrices are used to determine a pair of boundary conditions for the vector radiative transfer equation. The multiple scattering due to th e discrete particles is computed by solving the vector radiative trans fer equation numerically. Numerical illustrations are given for the op tical thickness of the slab from 0.4 to 5 and the mean size parameter of the particles with Gaussian distribution, ka!, from 0.3 to 1. The surface root-mean-square slope varies from 0.1 to 0.3. Mueller matrice s which characterize the random medium are constructed from the scatte red Stokes vectors due to four independent polarized incident waves. T he Mueller matrices are found to have eight non-vanishing matrix eleme nts and some symmetrical properties.