Fractal-based description for the three-dimensional surface of materials

An algorithm called variation-correlation analysis, used to estimate fracta l dimension with good accuracy, has been developed. Applying this model to images of the atomic force microscope, magnetic force microscope, and scann ing electron microscope, it has been demonstrated that there exists a fract al characteristic length epsilon(max). When the scale epsilon is within eps ilon(max), the variation-correlation V-cor(epsilon) of the dimensionless fi eld-like variable H(x,y), which may denote the height of a surface or the m agnetic domain or the angle distribution, obey a power law, while when epsi lon is over epsilon(max), V-cor (epsilon) becomes constant for a given imag e. The concept of "fractal measure" M-F is given, M-F=(1-delta)/(1+delta), where delta is defined as the dispersed degree of points on a log-log plot. M-F is a sort of linear measure of point distribution, which can be used t o determine the fractal characteristic length. Investigation shows that the fractal dimension in the range epsilon <epsilon(max) is associated with th e irregularity of the different processed surfaces. The fractal characteris tic length epsilon(max) can represent the statistical maximum size of the s urface texture. (C) 1999 American Institute of Physics. [S0021-8979(99)0471 7-9].