A three-dimensional measure of surface roughness based on mathematical morphology

In industrial surface characterization tasks, tactile profile measurement instruments are still the dominating tool for measuring surface roughness. Among the parameters for quantifying surface roughness based on tactile profile sections, RzRz and RaRa are the most popular ones. Nevertheless, it is widely recognized that profile parameters in general should be replaced by parameters which use the whole surface information made available by state-of-the-art 3D-measuring devices like white-light interferometry. In this contribution, a natural and easily interpretable extension of the roughness characteristic RzRz for 3D data, called Szmorph, is proposed and its intimate relation to the volume scale function, a fractal characteristic recently proposed for standardization, is shown. The derivation shows that while the slope of the volume scale function gives an indication of local fractal dimension, its absolute value is closely related to traditional definitions of surface roughness. The proposed characteristic ignores surface directionality and as such is applicable to directional and non-directional surfaces. Experimental results for three different technical surfaces demonstrate the very good correlation of Szmorph with the original parameter RzRz.