In this paper we present an analysis and calculation of scattering patterns from sinusoidal surfaces. An exact space harmonic representation is used for the field on the surface, and as a result, the calculation includes the effects of shadowing, diffraction, and multiple scattering. An asymptotic evaluation has been employed to obtain an exact expression for the scattering pattern as a product of the space harmonic scattering coefficients times the corresponding pattern functions. The formula obtained has been simplified for illuminated areas that are many wavelengths long and plotted for a variety of surface parameters. The present method for scattering pattern calculations can be considered to be complementary to methods using physical optics and point-matching techniques. In addition to the scattering pattern calculations the exact Bragg backscattering amplitudes have been computed and compared with their Rayleigh approximations.
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