Investigations on the accuracy and evaluation of the uncertainty of stitching in optical surface metrology

Abstract

Exemplified by a stitching procedure that is frequently applied in optical surface metrology and that is based on the maximization of the cross-correlation function, the article shows the dependency of the accuracy of a stitching result on many different interdependent influence factors. Furthermore it is shown that the remaining deviations of the regions that are regarded to be the overlapping ones is no generally valid indication for the accuracy of a stitching result. Thus, in the second part of the article, a method to determine the uncertainty of a stitching result based on a Monte Carlo simulation is presented. The input quantities of the stitching procedure, namely the topographic data of the sub-apertures and the position and orientation data of the positioning system are characterized by a probability density function. Afterwards, it is sampled randomly from these probability density functions and the stitching procedure is applied many times. From the obtained distributions, the result of the stitching procedure along with its uncertainty is derived. The obtained results show metrological compatibility to the true values and furthermore enable the recognition of the cases for which the stitching did not improve but impair the accuracy compared to the accuracy of the positioning system.