Copolarized and depolarized backscattering enhancement of random discrete scatterers of large size based on second-order ladder and cyclical theory

Recently, backscattering enhancement has been observed in the depolarized component of scattering from a sparse concentration of large discrete scatterers. In this paper we study the backscattering enhancement of the copolarized return and depolarized return from a random distribution of scatterers of large size by summing the first- and second-order ladder terms and the second-order cyclical term of the Bethe–Salpeter equation. It is shown that the ladder terms give a minimum for the depolarized component in the backscattering direction. Thus the cyclical term must be included since this term contributes directly to a maximum of the depolarized component in the backscattering direction. The Mie scattering amplitude function is used to compute both the copolarized and the cross-polarized enhancements for a sparse distribution of scatterers. These results are compared with calculations based on the second-order transport theory. The copolarized enhancements for both cases agree favorably, however the transport theory does not give a depolarized enhancement. On the other hand, the second-order ladder and cyclical theory is shown to give a depolarized enhancement. It also gives a reasonable comparison with experimental data for the case of a slab medium that consists of a sparse distribution of dielectric spheres with average ka of 298 and optical thickness of 1.98.