Diffuse and coherent backscattering by discrete random media—I. Radar reflectivity, polarization ratios, and enhancement factors for a half-space of polydisperse, nonabsorbing and absorbing spherical particles

Abstract

It has been demonstrated recently that diffuse, incoherent multiple scattering of electromagnetic waves by media composed of randomly positioned, discrete scattering particles is always accompanied by coherent backscattering and may explain intriguing opposition phenomena observed for some solar system bodies, in particular peculiar characteristics of radar returns from icy satellite surfaces. In this paper, we study theoretically photometric and polarization characteristics of diffuse and coherent backscattering by discrete random media. The cyclical component of the Stokes reflection matrix at exactly the backscattering direction is expressed in terms of the ladder component, and the ladder component is accurately computed by numerically solving the vector radiative transfer equation. We give formulas expressing the radar reflectivity, radar linear and circular polarization ratios, and backscattering enhancement factors in the elements of the Stokes reflection matrix and describe in detail the computational technique used. Assuming that the scattering medium is homogeneous and semi-infinite and that scattering particles are polydisperse spheres, we report the results of a comprehensive theoretical survey of the dependence of the photometric and polarization characteristics of the radar return on the illumination zenith angle and on the particle effective size parameter and real and imaginary parts of the refractive index.