The coherence function and its information content for optical metrology

Abstract

The coherence function offers new possibilities for optical metrology that are not available with conventional wave field sensing. Its measurement involves a spatio-temporal sampling of the wave fields modulated by the object under investigation. Temporal sampling is well known e. g. by means of White Light Interferometry (WLI) and spatial sampling can e. g. performed by Computational Shear Interferometry (CoSI). The present paper describes an approach that combines both temporal and spatial sampling using a robust common-path setup. While the evaluation of the coherence function is more elaborate than approaches that either sample the temporal or the spatial domain, an information theoretical treatment shows that it also delivers more information about the object under investigation. Our approach is based on the mutual information that represents the reduction of uncertainty about the object as a consequence of the measurements performed. Using a simplified measurement case, we calculate the mutual information for different measurement situations and demonstrate that spatio-temporal sampling of the coherence function results in a higher mutual information as compared to classical approaches. Based on the proposed approach, we identify further open research tasks for an efficient information extraction from the coherence function to surpass current limitations of optical metrology.