A rigorous theory for the study of scattering from non-periodic rough surfaces is presented. Two numerical applications are envisaged. First, some properties of gratings having a finite number of grooves are investigated. Secondly, rigorous computations of speckle patterns generated by random rough surfaces with finite length are made. A phenomenon of 'short coupling range' is demonstrated. It enables the computation of the field scattered by a rough surface of arbitrary length.
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D. Maystre (1984) studied this question.
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