Impact of surface roughness on scatter losses and the scattering distribution of surfaces and thin film coatings

The estimation of the impact of surface roughness on the light scattering losses and the scattering distribution is of crucial importance for deriving roughness specifications for optical surfaces. A detailed roughness analysis should always be based on surface Power Spectral Density functions and the band-limited roughness relevant for the application at hand. The scattering from single surfaces can easily be estimated using rather simple formulas. The most commonly used expression to estimate the total scattering, however, is only valid if the roughness is small and the correlation width is large compared to the wavelength of light. A special expression has been used in the thin film community for surface structures with short correlation lengths. It will be demonstrated that distinguishing between these limiting cases is unnecessary simply by using the concept of band-limited roughness. Different models are compared to results of scatter measurements and discussed with respect to their ranges of validity.