We present a discrete implementation of generalized Harvey-Shack scalar scattering theory to calculate angular intensity distributions from height profiles of select randomly textured surfaces proposed for use in solar cells and covering a wide range of surface characteristics. We compare these calculations to high-resolution angular intensity distribution measurements. These comparisons suggest that the pupil function does benefit from an additional correction factor for rough surfaces containing lateral feature sizes on the order of the wavelength, which can be attributed to effective medium effects. Moreover, secondary interactions within the surface topography are shown to be a mechanism that partly redistributes scattered power, affecting angular intensity distribution results. These mechanisms emerge as the two main limitations of the Harvey-Shack scalar scattering theory in the far field, which nonetheless produces remarkable quantitative predictions.