Stochastic analysis of different rough surfaces

Abstract

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more detail. In particular we show evidence of the Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of the conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in detail the advantages and disadvantages of these methods.