A modification of the method for determination of surface fractal dimension and multifractal analysis

Purpose: In this work modification of the PCM method for determination of the surface fractal dimension is proposed. Complete reasoning, leading to correct formula for determination Ai(δ) is presented. In order to test modified method, data sets characterised by fractional fractal dimension were generated. Design/methodology/approach: Three different algorithms to receive data sets describing surfaces with fractional fractal dimension were exploited (two algorithms of midpoint displacement and Falconer algorithm). Findings: In this work detailed methodology for surface multifractal description, which may be directly applied for data obtained from the AFM microscope, was presented. Research limitations/implications: The geometrical features description of surfaces of the coatings obtained in the PVD and CVD processes. Practical implications: In presented work modified PCM method for determination of the surface fractal dimension was proposed. Performed calculations proved that new method make possible to determine this parameter more correctly. Differences are especially significant for rough surfaces, as what tested using series of data sets generated by algorithms for modelling surfaces with fractional fractal dimension. Proposed modified method for determination of the fractal dimension can be used for description of the geometrical features of coatings obtained in the PVD and CVD processes. Originality/value: Fractal and multifractal analysis gives possibility to characterise the extent of irregularities of the analysed surface in the quantitative way.