A Study of Fresnel Scattered Fields for Ellipsoidal and Elliptic-Disk-Shaped Scatterers

The study of scattered fields from nonspherical scatterers is becoming an important subject particularly in the area of theoretical modeling of microwave backscatter from vegetation. The generalized Rayleigh-Gans approximation has been widely used in the calculation of scattered fields from scatterers where at least one of its dimensions is comparably smaller than the wavelength. In such calculations, far-field approximations are used, which are not accurate when the observation points are in the Fresnel and near-field regions of the scatterer. Hence, the effects of Fresnel phase and amplitude corrections for the scattered field of circular disks, needles, and cylinders have been examined and shown to be significant in the calculation of closely spaced scatterers. However, the effects of Fresnel corrections in the scattered fields from general ellipsoids and elliptic disks have not yet been studied. In this paper, the scattered fields from general ellipsoids and elliptic disks are formulated based on the generalized Rayleigh-Gans approximation for cases with and without Fresnel corrections. Theoretical analysis shows that the Fresnel effects are important particularly at larger frequencies and at the null locations in the plots of the backscattering cross section. These effects become more important as the ellipticity of the scatterer increases. Comparisons with measurement data demonstrate that the calculated results with Fresnel corrections provide a better match compared with those without.