In this paper, the Rayleigh hypothesis in the theory of reflection by a grating is investigated analytically. Conditions are derived under which the Rayleigh hypothesis is rigorously valid. A procedure is presented that enables the validity of the Rayleigh hypothesis to be checked for a grating whose profile can be described by an analytic function. As examples, we consider some grating profiles described by a finite Fourier series. Numerical results are then presented.
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Berg et al. (1979) studied this question.
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