Rough surfaces: gaussian or exponential statistics?

Abstract

The authors make use of a numerical method for generating random rough surfaces to study the effects of sampling interval on measured surface correlation functions. This numerical investigation avoids some of the complications present in experimental studies of the effects of this parameter, such as instrument resolution and measurement reproducibility. The numerical technique is used to generate surfaces with exponential correlation functions and surfaces with gaussian correlations. The short-wavelength fluctuations on the exponential surfaces are clearly seen, these arising from the high-frequency tail in the surface power spectrum. The authors are able to quantify the sampling interval necessary to record this short-range surface behaviour. They conclude that the sampling interval must be at least as small as one tenth of the surface correlation length, for these high-frequency variations to be recorded and hence for the inherent exponential nature of the surface to be measured.