Microwave specific attenuation by oblate spheroidal raindrops: an exact analysis of TCS's in terms of spheroidal wave functions

Abstract

The electromagnetic plane wave scattering by oblate spheroidal raindrops is investigated in this paper using the full-wave eigen-expansion in terms of the spheroidal vector wave functions so as to obtain an exact solution of the total (or extinction) cross section of the spheroidal raindrops. In this analysis, both TE- and TM-mode incident plane waves (or parallel and perpendicular polarizations) are considered. As the permittivity of the raindrop water is a function of both the operating frequency and the outdoor temperature, the Ray's program is utilized to compute the lossy raindrop permittivity. A Mathematica program is developed based on the computation of the radial and angular spheroidal wave functions with complex arguments. Comparison between the spheroidal wave function values computed using this algorithm and the available data in the literature shows that the algorithm developed here has a better accuracy. Also, the total cross sections of the raindrops obtained using the full-wave oblate spheroidal eigenfunctions are compared with those using the T-Matrix approach; and a very good agreement between them is found.