Polarimetric scattering coefficients of half-space heterogeneous medium

Almost all natural media such as a rain, ice, fog, snow, clouds, leaves, forests, surface soil layer, agricultural plants, etc. can be considered as some kind of heterogeneous random medium embedded with nonspherical discrete particles. In this paper the polarimetric backscattering coefficients of half-space random medium are calculated for the purposes of the environmental remote sensing using polarimetric radars. The stochastic model of the half-space heterogeneous medium consists of a random current propagating in a hypothetical isotropic medium. The parameters of the model used in this paper are derived by the aid of strong permittivity fluctuation theory under a bilocal as well low-frequency approximations. The symmetry of scattering matrix F was proven in backscattering direction of measurement of scattered electromagnetic field in the atmosphere. It was shown that the polarimetric covariance matrix C consists of two polarimetric covariance matrices of unperturbed and random parts of scattered electromagnetic field. It was as well shown that in backscattering direction the scattering coefficients σ_hv, σ_hhhv, σ_hvvv are different from zero in general. The expressions of polarimetric backscattering scattering coefficients given in this paper are valid for arbitrary joint probability density function P(θ,φ) of scatterers spatial orientation. The obtained results can be used for the purposes of polarimetric remote sensing of heterogeneous natural media embedded with discrete scatterers having non spherical geometry