The phase-perturbation method for the computation of fields scattered by rough surfaces is reviewed and then a method for calculating moments of the field scattered from randomly rough surfaces is investigated. In previous work, the authors have shown that the phase-perturbation method can provide an accurate approximation to the fields scattered from deterministic rough surfaces, even in cases when the rms surface-height variation is significant compared to the radiation wavelength. The present work employs cumulants to develop a systematic averaging procedure that retains this advantage, in the case of scalar-wave scattering from surfaces on which Dirichlet boundary conditions hold. The resulting expressions for the moments of the scattered field are shown to reduce to classical small roughness and physical-optics expressions in the appropriate limits. Numerical results for the magnitude of the coherent reflection coefficient in two test cases are also presented.
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