Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer problems in slab geometries, where the discrete ordinates method can be applied to solve the problem. Furthermore, such an implementation is a more convenient discretization of the problem than the traditional direction cosine space that has its strengths in analytical problems and intuitive understanding (mainly due to its translation invariance). A computer implementation of scattering from a Gaussian rough surface with Gaussian autocovariance written in Python is included at the end of the paper. © 2015 Optical Society of America