Numerical comparisons of a modified rayleigh approach with other rough surface EM scattering solutions

A modification of the classical Rayleigh technique utilizing the fast Fourier transform (FFT) is developed for electromagnetic scattering and is referred to as the Rayleigh-FFT approach. Numerical scattering results from a sinusoidal surface are compared with calculations obtained by a Rayleigh perturbation approach, physical optics, and a rigorous integral equation method. These comparisons together with self-consistent error criteria are used to define the circumstances under which the Rayleigh-FFT approach is valid. For perfectly conducting sinusoidal surfaces, the method is valid at normal incidence when the maximum surface slope is less than about 0.6 (\lsim 31\deg) but no limit on surface height is apparent. Slope restrictions are explained by the inherent Rayleigh error since maximum errors occur in surface troughs as expected. The Rayleigh-FFT approach is increasingly reliable, for a given geometry, when the rough half-space tends toward dielectric from perfectly conducting. Perturbation solutions to Rayleigh's technique are shown to be extremely limited. Physical optics is valid when the minimum radius of curvature of the surface is greater than a wavelength. The Rayleigh-FFT method has been extended to obtain valid scattering results from arbitrary irregular periodic structures composed of a rough layer over a rough half-space.