Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters

To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnetic hard disk and silicon wafer surfaces. A novel scheme involving a variable transformation was developed to extract fractal parameters. This scheme was validated by accurate recovery of fractal parameters from simulated surfaces. The fractal dimension, the fractal roughness parameter and the fractal domain length were found for magnetic hard disk and silicon wafer surfaces.