Accuracy of several alternative forms of the operator expansion solution for scattering from 1-D randomly rough Dirichlet surfaces

We have examined the operator expansion (OE) method in computing scattering over a wide range of scattering regimes, for l-D Dirichlet surfaces with Gaussian spectra, and with Pierson-Moskowitz spectra (used to model the ocean surface). We give a brief review of a derivation of the standard OE solution, and show how the short series are obtained. Numerical examples are presented illustrating the rapid convergence and wide accuracy of the various forms of the OE solution in several scattering regimes. Our results indicate that the short series provide efficient and accurate alternatives to the standard solution, a finding which is of significant practical value in treating scattering from 2-D surfaces. In general, our results for scattering from l-D surfaces suggest that the OE is a very attractive method for computing scattering from a wide range of realistic 2-D rough surfaces with a Dirichlet boundary condition. We also present the alternative forms of the OE solution and give one example for scattering from surfaces with a Gaussian spectrum.<>