Fast numerical solution for scattering from rough surfaces with small slopes

The rigorous solution of the scattering by two-dimensional rough surfaces can be numerically performed thanks to the sparse matrix flat surface iterative approach (SMFSIA). However, this kind of computation still requires both large CPU time and memory. Consequently, a lot of work has been dedicated at extending the domain of validity of approximate methods beyond that of standard high and low frequency approximations. In this paper it is shown that SMSFIA can be simplified in order to get a fast approximate method, with low memory requirements. This approximation is valid for surfaces with small slopes, and covers the domain of validity of both the Kirchhoff -tangent plane approximation and the first-order small slope approximation.