ON ANGULAR-SPECTRUM REPRESENTATIONS FOR SCATTERING BY INFINITE ROUGH SURFACES

A plane acoustic wave insonifies an infinite rough surface. The reflec ted field is written as an angular-spectrum representation (plane-wave expansion), with an unknown amplitude function A. It is pointed out t hat A must be considered as a generalized function, and not as a conti nuous function. Various decompositions of A are suggested and analysed . Energy considerations lead to relations between the coefficients in these decompositions, generalizing some known results for scattering b y periodic surfaces (gratings). It is shown that the reflected field m ust include at least one propagating plane wave.