The relationship between the height autocorrelation function of a one-dimensionally rough surface and the Fourier transform of the intensity distribution of the light scattered by that surface is tested experimentally. The theory is derived by using the Fraunhofer approximation, without recourse to the inconsistent Kirchhoff boundary conditions. In spite of the limitations imposed by the approximations used, the results obtained from optical data agree well with those obtained from stylus data, even for an autocorrelation length as small as the optical wavelength. However, this method should be limited to surfaces with rms roughness smaller than approximately 0.14 times the wavelength of light.
Egon Marx, Brigitte Leridon, T. R. Lettieri, J.-F. Song, and T. V. Vorburger, "Autocorrelation functions from optical scattering for one-dimensionally rough surfaces," Appl. Opt. 32, 67-76 (1993)