Calculations are performed to relate the stylus profile of a one-dimensionally rough surface to the angular distribution of the light scattered by such a surface. In the direct problem, the angular distribution of the scattered light calculated from the profile is shown to agree with the measured one. In the inverse problem, the rms roughness and the autocorrelation function are found by a least-squares fit to the measured angular distribution. For the smoother surfaces, the rms roughness is mostly determined by the ratio between the power of the specular beam and the total power of the scattered light; the computed values are proportional to those calculated directly from the stylus profiles. The values of the parameters obtained by the least-squares fit are affected by a variety of errors and agree only partially with those obtained from the stylus profile.
Egon Marx and T. V. Vorburger, "Direct and inverse problems for light scattered by rough surfaces," Appl. Opt. 29, 3613-3626 (1990)