On the Rayleigh assumption in scattering by a periodic surface. II

Abstract

The Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic planewave excitation, is re-examined. The analysis employs a technique developed to locate singularities of solutions to the Helmholtz equation. When applied to the surface profile v = b cos considered originally by Lord Rayleigh, it is found that the Rayleigh assumption is valid if 0 this is more precise than an earlier result. It is shown how these findings may be reconciled with the work of others who have suggested, or concluded, that the Rayleigh assumption is never valid. © 1971, Cambridge Philosophical Society. All rights reserved.