The influence of wave vector error on surface form reconstruction employing a multiple aperture shear interferometer

Multiple Aperture Shear-Interferometry (MArS) [1] measurements are based on wave vector measurements in the focal plane of the experimental setup. If the positions of the light sources and the focal plane are known, each wave vector can be traced to its source and the surface form on which the wave vectors are reflected can be retrieved. Because the surface form is reconstructed in a mathematical optimization process, two key questions arise: 1. Is there only one single solution to which the optimization process converges? 2. How do errors in the input wave vectors translate into errors in the reconstructed surface form? To address these questions, a theoretical model of surface form reconstruction will be compared to results obtained from actual measurements. The insights gained will then be used to evaluate the capability of the model to make predictions about measurement errors. [1] André F. Müller, Claas Falldorf, Marcel Lotzgeselle, Gerd Ehret, and Ralf B. Bergmann, "Multiple Aperture Shear-Interferometry (MArS): a solution to the aperture problem for the form measurement of aspheric surfaces," Opt. Express 28, 34677-34691 (2020)