The small slope approximation reflection coefficient for scattering from a “Pierson-Moskowitz” sea surface

First- and second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the second-order reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized electromagnetic scattering from one-dimensional, “Pierson-Moskowitz” sea surfaces at low grazing angles. Comparison with exact integral equation results shows that the second-order small slope approximation is extremely accurate and better than both the perturbation and Kirchhoff methods