Investigation of minimum zone assessment methods for aspheric shapes

Abstract

Improvement in metrology of asphere and freeform surfaces is requested in many sectors and industries. ISO standards of Geometrical Product Specifications recommend the usage of the infinite norm L∞ (min-max) to determine the minimum zone (MZ). This is performed by directly minimizing the peak-to-valley (PV) which is the difference between maximum and minimum deviations of the dataset and the reference surface. Performing data fitting according to L∞ remains a major challenge when considering complex geometries such as aspheres and freeform surfaces. In this work, two algorithms for aspheres minimum zone fitting were implemented and compared on generated reference and measured datasets, namely the Exponential Penalty Function and Primal-Dual Interior Point Method The obtained results show that both methods give accurate values of minimum zone. When the number of points increases, a decay in the latter method’ performances was also noticed especially for calculation time and accuracy of returned minimum zone values.