An improved formalism for wave scattering from rough surfaces

Abstract

The scattered field and its normal gradient obey a mutual linear relation at the scattering surface that is distinct from the physical boundary condition connecting either quantity to the incident radiation. On a moderately rough surface this relation can be represented by an operator whose series expansion in surface slope converges nicely even for large values of the Rayleigh parameter. This allows the Helmholtz integral for scattering amplitude to be written as a series of readily computable terms, one or two of which provide good approximations for surfaces too irregular for the usual Bragg expansion. This formulation reproduces the Bragg series for small surface elevations, and in the limit of low roughness wavenumber gives the Kirchhoff approximation with an explicit correction term in surface curvature. The usual results for a composite surface also emerge naturally. On several test profiles the method produces better overall accuracy than other multiscale approximations, at comparable efficiency.