Fractal Analysis of Surface Topography by the Directional Blanket Covering Method

A new method, called directional blanket covering (DBC) method, was developed in this study to quantify the roughness of surfaces in a multi-scale manner. Unlike the ASME and ISO standards on surface texture that provide a single fractal dimension (FD, roughness measure) for the entire surface, the new method calculates FDs at individual scales and directions. Also, it is invariant to affine transformations of grey-scale levels of surface image. The method calculates FDs using slopes of lines fitted to data point subsets of log–log plots of relative surface areas (differences between surface volumes) against scales of calculation. The scales are ranking from an instrument spatial resolution to 1/10 of the image shortest size. Each FD calculated has its individual scale corresponding to the centre of the subset. A flat surface criterion based on the relative areas was proposed. Using the criterion, a flat surface was identified in computer images of circle, sine wave and fractal surface. The DBC method was applied to computer-generated fractal surfaces with increasing roughness and microscope images of isotropic (sandblasted) and anisotropic (ground) surfaces of steel plates. Results showed that the method is accurate in the measurement of surface roughness and the detection of minute changes in roughness of the steel surfaces over a wide range of scales.