The generalized Harvey-Shack (GHS) surface scatter theory has been shown to accurately predict the BRDF produced by moderately rough mirror surfaces from surface metrology data. The predicted BRDF also holds for both large incident and scattering angles. Furthermore, it provides good agreement with the classical Rayleigh-Rice theory for those surfaces that satisfy the smooth-surface criterion. The two-dimensional band-limited portion of the surface PSD contributing to scattered radiation is discussed and illustrated for arbitrary incident angles, and the corresponding relevant roughness necessary to calculate the total integrated scatter (TIS) is determined. It is shown that BRDF data measured with a large incident angle can be used to expand the range of surface roughness for which the inverse scattering problem can be solved; i.e., for which the surface PSD can be calculated from measured BRDF data. This PSD and the GHS surface scatter theory can then be used to calculate the BRDF of that surface for arbitrary incident angles and wavelengths that do not satisfy the smooth-surface criterion. Finally, the surface transfer function characterizing both the BTDF and the BRDF of a moderately rough interface separating two media of arbitrary refractive index is derived in preparation for modeling the scattering of structured thin film solar cells.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.