A comparison of backscattering models for rough surfaces

The objective of the study is to examine the ease of applicability of three scattering models. This is done by considering the time taken to numerically evaluate these models and comparing their predictions as a function of surface roughness, frequency, incident angle and polarization with the moment method solution in two dimensions. In addition, the complexity of the analytic models in three dimensions and their analytic reduction to high and low frequency regions are also compared. The selected models are an integral equation model (IEM), a full wave model (FWM), and the phase perturbation model (PPM). It is noted that in three dimensions, the full-wave model requires an evaluation of a 10-fold integral, the phase perturbation model requires a 4- and 2-fold integral while the integral equation model is an algebraic equation in like polarization under single scattering conditions. In examining frequency dependence of IEM and PPM in two dimensions numerically, the same model expression is used for all frequency calculations, it is found that both the IEM and PPM agree with the moment method solution from low to high frequencies numerically