Effect of lateral resolution on topographical images and three-dimensional functional parameters

The influence of the analysis scale on the characterisation of surface roughness is set out in this work. First the effect of lateral resolution on the local morphology of a random engineered surface is shown. The effect of the geometry of a tactile profilometer tip is studied by the variation of the tip radius of curvature. The incidence of the scale observation is analysed from micro- to nano-scale with three microscopes: a tactile, laser and atomic force microscope. The lateral resolution influences not only the roughness amplitude parameters, but also spectral range, slopes, local radius of curvature of the summits, bearing area, developed surface, the void or material volume. In the second half of this work the contribution of fractal geometry is examined. This is because, through its roughness index, called the Holder index, it may be independent of the measurement. By using the Weierstrass-Mandelbrot function as a three-dimensional multi-scale model of the topography, the evolution of the bearing area, the developed surface and the volume as a function of the Holder roughness index can be shown.

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