Abstract
Exact and approximate solutions to the rough-surface scattering problem are compared to examine the predictive capability of renormalized surface scattering theory. Numerical results are presented for scattering from one-dimensional rough periodic surfaces on which the Dirichlet (acoustic pressure-release) and Neumann (acoustically rigid) boundary conditions are imposed. For scattering from Dirichlet surfaces, the predictions of renormalized scattering theory are found to provide better agreement with exact solutions than perturbation theory. For this boundary condition, many convergent approximations exist, and the small-slope approximation is found to yield an improvement to renormalization. For the Neumann boundary condition, renormalization provides good agreement with exact solutions for scattering from slightly rough surfaces. The Kirchhoff approximation, the only other convergent approximation applicable to the Neumann problem, provides agreement with exact solutions for scattering from moderately rough surfaces for angles of scatter and incidence far from grazing.
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