Statistical characterization of technical surface microstructure

In the development and production of industrial parts, both the macroscopic shape and the microstructure of the parts surface on a µm-scale strongly influence the parts properties. For instance, a surface in frictional contact should be structured in a way to reduce the expected wear by optimizing its lubrication properties. A gasket surface must not be too rough to prevent leakage, etc. The measurement of surface roughness started a few decades ago with the advent of tactile profilometers. These drag a stylus along a line over the surface and record the vertical deflection of the stylus as it moves over the surface, thus recording the height of the surface at the sampling points. Modern measurement techniques make it possible to acquire a complete three-dimensional height map of the surfaces. Obviously, the techniques for analysing two-dimensional profiles are not adequate for the analysis of three-dimensional height maps. Although many propositions for 3D-analysis have been made, these often lack a sound theoretical background. Hence, their understanding is limited and only a few are used regularly, resulting in an inadequate surface descrip- tion. A simple but powerful approach is to use the Minkowski functionals of the excursion sets of the data to charactarize the surface structure. These func- tionals can be interpreted in different ways depending on the model for the surface. Two models seem especially suited for technical surfaces: Random fields for surfaces with no obvious structure, e.g. shot-blasted surfaces and Boolean grain models for surfaces consisting of smaller structuring elements, e.g. sintered materials. In this thesis, a complete framework for the analysis of three-dimensional surface data using the Minkowski functionals is developed. This novel ap- proach allows for a stepwise data reduction: A complex data set is first reduced to three characterizing functions, from which further parameters can be derived. Due to a novel fast and accurate estimator for the characterizing functions, this technique is also suitable for time-critical tasks like the application in production automation