A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces

Predictions of the fourth-order small perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fields and incoherent ensemble-averaged normalized radar cross sections (NRCSs) up to the third and the fourth order in surface rms heights, respectively, are reviewed. It is shown that the fourth-order NRCS includes distinct contributions from upper and lower interface roughnesses, as well as an “interaction” term that couples the upper and lower interface roughnesses. A comparison with NRCS values computed using the “numerically exact” method of moments in the full bistatic scattering pattern is shown for verification, and NRCS values at the second and the fourth order are compared in order to assess the convergence of the SPM series. Although the number of parameters inherent in the two-layer rough surface scattering problem makes an exhaustive study of scattering effects difficult, several illustrative examples are presented to capture a range of scattering behaviors. The results emphasize the importance of interactions between the rough surfaces in producing cross-polarized backscattering and also indicate an increased significance of fourth-order contributions in the two-layer geometry as compared to the single-layer case.