Anti-reflective nanostructured surfaces (ARSS) enhance optical transmission through suppression of Fresnel reflection at boundaries between layered media by creating a gradually increasing ratio of material to air volume fraction. Previous studies show random ARSS (rARSS) exhibit broadband enhancement and polarization insensitivity in transmission when applied to flat optical windows. Windows with rARSS treatment are characterized (transmittance, reflectance, and angular scatter) using spectrophotometry and scatterometry to assess transmission enhancement over a spectral band of interest. Using measured spectral data, partial-integrated scatter values can be obtained, allowing the comparison of random anti-reflective boundary performance to optically flat surfaces. By comparing axial transmission and specular reflection with the scattered performance, an accurate determination of the redistribution of incident energy is obtained. The results show differences in scattered intensity over the wavelength bands of interest, correlating with surface random feature populations.Rigorous full-wave solvers of light scatter from aperiodic surfaces can be computationally intensive, therefore alternative methods are desired to predict and analyze bi-directional surface scatter. Using a transfer function approach, an approximation of far-field light scatter can be modeled based on surface statistics. rARSS feature topology was determined using optical profilometry to obtain statistical surface roughness parameters and granulometric analysis of nano-roughened substrates SEM images, to assess the structured-surface feature scales. Random rough surfaces, which are generally globally isotropic and polarization insensitive, are well-modeled by Gaussian statistics, making them ideal candidates for a surface transfer function approach of surface scatter analysis. Generalized Harvey-Shack surface scatter theory was used to calculate surface feature diffractive effects. Scatter distributions predicted using a Gaussian parameter model of a random surface and structured surface metrology data were compared to measured scatter data for assessment of the transfer function model validity within the bandlimit of interest. Results show that prediction of wide angle rARSS optical scatter is viable using the transfer function approach, but the theory fails to predict transmission enhancement due to the inclusion of roughness.