Rayleigh method for scattering from random and deterministic interfaces

Abstract

This paper describes Rayleigh methods for computing plane-wave scattering amplitudes for rough interface scattering. For Dirichlet, fluid–fluid, and fluid–solid interfaces, the Rayleigh–Fourier (RF) method is shown to give good results for interfaces with slopes exceeding the limit of the Rayleigh hypothesis. In the case of sinusoidal Dirichlet surfaces, described by z=h cos(2πx/L), the method breaks down for 2πh/L∼2. For gentler surfaces the RF method gives high-quality results more cheaply than boundary integral equation or least-squares methods. In the case of fluid–solid interfaces, results of the RF method, which are apparently presented here for the first time, compare favorably with published results obtained by extinction theorem methods. It is concluded that the RF method is a suitable candidate for studying rough interface scattering by Monte Carlo simulations, even for fluid–solid interfaces.