Calculating BTDF from window surface roughness

The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength, incident angle and polarization. A similar relationship should be available for the situation of a beam transmitting from a region of index greater than 1.0 into a region of unit index through an optically smooth surface. This paper presents such a relationship and compares the result to measured scatter data at two light wavelengths.