A Simple Path to the Small Perturbation Method for Scattering from Slightly Rough Dielectric Surfaces

Abstract

We propose a perturbative method to compute electromagnetic scattering from slightly rough dielectric surfaces, which leads to the same result as the usual Small Perturbation Method (SPM) in a surprisingly simple way. The proposed method is based on three pillars: the volumetric perturbative approach, the reciprocity theorem, and a proper approximation of the electric field within the perturbation volume, that we name Internal Field Approximation (IFA). The proposed new mathematical derivation of the SPM turns out to be much simpler and more concise than the classical one. In addition, being based on a volumetric perturbation approach, it has the potential of dealing in future with surface and volume scattering within a unitary framework, which is useful in modelling scattering from, e.g., vegetated soil, snow-covered terrain, and inhomogeneous soils. Therefore, although the presented result is mainly theoretical, it can have important applications in remote sensing.