Holistic approximation of combined surface data

Modern micro-production processes demand fast and robust inspection techniques up to 100% inspection rates. For instance, a fast acquisition of the objects surface in the needed precision and density can be realized by optical measurement systems. In order to extract the relevant geometric quantities from the surface data of prismatic workpieces, the measured data points need to be assigned to the nominal geometric primitives, e. g. cylinder, plane or sphere. For this purpose, an automatable algorithm is desired, which assigns all measured points to the corresponding geometric elements and minimizes the measurement uncertainty. Such an optimal segmentation routine of combined geometric data can either be performed by rating neighboring measurement points based on their curvature or by a holistic approximation. Whereas the first approach is sensitive to noisy data and not able to distinguish between spheres and cylinders with certain radii, the holistic approximation in combination with further statistical methods promises an automatic detection of outliers.

In order to analyze the achievable measurement uncertainty with the holistic approximation approach for an object geometry composed by three-dimensional base elements (cylinder, torus, plane), the method is applied to determine the geometric features of micro deep-drawing dies. For verification, the measured geometry of the object is simulated including uniformly distributed noise within a range of ±2.5 μm. As a result, the determined radius of the cylinder (defined to 412 μm) has a standard uncertainty due to random errors below 11 nm and an uncertainty due to systematic errors less than 1.1 nm. Furthermore, real tactile measurement data are evaluated to validate the holistic approximation. In comparison to certified analysis software, which requires a manual segmentation, the results show differences below 0.25 μm for the cylinder diameter. The increased measurement deviations are caused by assumptions of the model-based evaluation, which is essential for the automated data processing. However, the achievable uncertainty qualifies the holistic approximation for a robust and automated evaluation of geometric tolerances in the field of micro-production.