A new exact expression for scattering amplitudes for rough interface scattering is presented. This expression is shown to hold for a variety of boundary conditions; Dirichlet, Neumann, impedance, fluid–fluid, and fluid–solid. The expression is shown to be a convenient starting point for deriving approximations that also respect reciprocity. Examples include a small-slope approximation, a reciprocal phase-perturbation approximation, and a reciprocal smoothing approximation.
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Berman et al. (1990) studied this question.