Backscattering of waves by composite rough surfaces

A general theory of electromagnetic wave scattering is developed using the Stratton-Chu integral as modified by Silver for a gently undulating homogeneous surface on top of which small irregularities are superimposed. It is assumed that the tangent-plane approximation is applicable to the undulating surface so that the local fields can be evaluated by considering a slightly perturbed plane surface. Average powers, both polarized and depolarized, are calculated for the composite surface whose statistical properties are assumed known. Shadowing effects are also included before comparing with experimental results. The comparison between the moon data and the data obtained under laboratory conditions shows very good agreement. The same surface parameters are used for both the polarized and the depolarized returns. Previous theories cannot provide a connection between the parameters used in the polarized return expression and those in the corresponding depolarized expression since only a single-surface model was considered. The results indicate that polarized returns of near vertical incidence are dominated by the large-scale roughnesses, while the depolarized returns are affected by both the large and small roughnesses. As the incident angle increases, the effect of small irregularities becomes increasingly important for both the polarized and the depolarized returns. The cause of depolarization and diffuse scattering, as shown in this theory, is the perturbation of the fields on the surface by the small irregularities.