Backscattering enhancement from a random distribution of large discrete spherical scatterers with a size distribution

We study backscattering enhancement from a sparse random distribution of large scatterers with a size distribution. Second-order multiple-scattering theory based on the Bethe–Salpeter equation is used to compute the scattered field. The second-order cyclical term is used to account for the enhancement. The effects of polarization are included by using the Mie theory to account for scattering by individual particles, and the result is then averaged over the size distribution. Comparisons are made with experimental data for the case of a slab medium of sparsely distributed dielectric spheres with average ka of 298 and moderate optical thickness. Agreement between theory and experiment is good for both the copolarized and the cross-polarized returns. The Mueller matrix is also derived, and the degree of polarization is computed for the same case. Results show that including the cyclical term reduces the degree of polarization of the computed backscattered return.