Reflection of a vertically polarized electromagnetic plane wave from a periodic rough surface is considered. The surface is characterized locally by a boundary impedance. By using a perturbation analysis, a general expression is obtained for the amplitudes of the scattered waves which is valid for all spectral and all perturbation orders. It is shown that the results obtained here are consistent with earlier analyses of Rice, Wait, and Barrick. In addition, the general expression permits one to discern some important properties of the amplitudes for a purely sinusoidal surface. Among other things, we show that all odd perturbation orders are zero for the specular mode.
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