REFLECTION FROM A CORRUGATED SURFACE REVISITED

The problem of scattering of a plane sonic wave from a soft surface wi th periodic (sinusoidal) unevenness along one direction is examined by means of the Rayleigh plane-wave expansion and the Waterman extinctio n methods, numerically implemented by Fourier projection and expansion , respectively. The computations are done with real, double-precision, stochastic arithmetic instead of the usual complex, double-precision floating-point arithmetic in order to precisely evaluate the numerical accuracy of the results conditioned by round-off errors. It is shown that the low-order plane-wave coefficients obtained by the Rayleigh an d Waterman methods are identical when obtained from matrix systems tha t are large enough to give ''convergence'' of these coefficients. For the same matrix size, the higher-order coefficients differ the higher the diffraction order. It is also shown that the Waterman (Fourier-ser ies) computation of the near field is generally meaningful, whereas th at of Rayleigh, involving summation of the plane waves is generally me aningless except near the points of the scattering surface first encou ntered by the incident wave (i.e., those in the valleys when the incid ent wave comes from below). Low-order plane-wave scattering coefficien ts, with at least two-to-three-digit accuracy, and which are identical (to this precision) to the plane-wave coefficients computed by the ri gorous integral equation method. are obtained by both the Rayleigh and Waterman methods for scattering surfaces with slopes as large as 2.26 when the number of nonevanescent waves is 5. The number of significan t digits decreases as the slope increases.