规则表面形貌的分形和多重分形描述

FRACTAL AND MULTIFRACTAL DESCRIPTION OF SURFACE TOPOGRAPHY

以 6种具有典型特征的生成元构造了 6个具有相同rms粗糙度的规则表面 ,用变分法计算了这些表面的分形维数 ,结果表明 ,分形维数可以将具有相同rms粗糙度的表面区分开来 ,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中 ,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度 ,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。

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.