FRACTAL AND MULTIFRACTAL DESCRIPTION OF SURFACE TOPOGRAPHY

Abstract

Six regular surfaces with same root-mean-square(rms) roughness are constructed by six typical generators. Variation method is used to calculate the fractal dimensions of these surfaces. The results suggest that fractal dimension can describe total topography of a surface quantitatively and can distinguish the surfaces which have same rms roughness. Multifractal method is further used in the analysis of surface. It is found that multifractal spectrum can reflect the overall characteristic of the distribution of probability of a surface. The width of multifractal spectrum can characterize the degree of the undulation of a surface quantitatively. The difference of the fractal dimensions between the maximum probability and the minimum probability subsets can give a statistical result of the ratio between the numbers of lowest and highest sites.