Study of Validity Region of Small Perturbation Method for Two-Layer Rough Surfaces

We previously derived the bistatic scattering coefficients of a 3-D two-layer dielectric structure with slightly rough boundaries using the small perturbation method (SPM). The use of SPM raises the question about its region of validity, which pertains to the conditions on each layer roughness, slope, and permittivity for which the first-order SPM is accurate within a specified error bound. To this end, the SPM solution needs to be compared with an accurate solution that does not impose roughness restrictions. We use the method of moments to solve an integral equation to analyze electromagnetic scattering from a large ensemble of two-layer structures. Simulations are performed for 1-D rough surfaces represented by zero-mean stationary random processes, separating homogeneous dielectric layers. Observations are reported on the accuracy of the first-order SPM for TM incidence at a fixed incidence angle of 45°.