Holistic approximation of combined surface data

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.