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 ( ) 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.