Model-based approach for planning and evaluation of confocal measurements of rough surfaces

Confocal sensors, along with white light interferometers, have been considered promising candidates for replacing traditional tactile sensors in the inspection of rough surfaces for several years now. However, despite their obvious advantages concerning measurement speed and a non-contact working principle, their acceptance for routine measurement tasks in industry is still unsatisfactory. This is presumably because the mechanisms that limit the resolution of such sensors are more complex than those of tactile sensors. The planning for the measurements, e.g. choosing the proper objective lens, is still a very challenging task. Therefore, many confocal measurements produce erroneous results because of improperly chosen sensor parameters. At the same time, the behavior of improperly configured sensors is not well understood, rendering the recognition of erroneous measurements a hard task as well. Current national as well as international technical standards suggest an approach based on the spatial frequencies of the surface profile and a cut-off frequency that is characteristic for the sensor. While this is in perfect analogy to optical two-dimensional imaging devices, we present theoretical as well as experimental reasoning against this approach. Instead, we propose an approach based on local surface curvatures and the radii of curvature of the illuminating wavefronts. (paper)