Weighted curvature approximation: numerical tests for 2D dielectric surfaces

Abstract

The weighted curvature approximation (WCA) was recently introduced by Elfouhaily et al [7] as a unifying scattering theory that reproduces formally both the tangent-plane and the small-perturbation model in the appropriate limits, and is structurally identical to the former approximation with some different slope-dependent kernel. Due to the simplicity of its formulation, the WCA is interesting from a numerical point of view and the aim of the present paper is to establish its accuracy on some representative test cases. We derive statistical formulae for the coherent field and the cross-section in the case of stationary Gaussian random surfaces. We then specialize to the case of isotropic Gaussian spectra and perform numerical comparisons against rigorous method of moments (MoM)-based results on 2D dielectric surfaces. We show that the WCA remains extremely accurate in a roughness range where other first-order classical approximations (small-slope and Kirchhoff) clearly fail, at the same computational cost.

(Some figures in this article are in colour only in the electronic version)