Master thesis and internship[BR]- Master's thesis : Modelling of the wear function for polishing of freeform optical surfaces[BR]- Integration internship

Abstract

To develop the manufacturability of freeform surfaces, this work investigates the feasibility of polishing freeform optical components and the adaptation of dwell time estimation methods to such geometries. In particular, feasibility criteria are introduced using a pitch lap polishing tool, considering the pressure distribution that varies across the tool. The first criterion ensures sufficient contact pressure between the polishing tool and the surface at all locations. The second defines a limit on the root mean square value of the gap between the tool and the surface. A parametric analysis is conducted to determine the maximum tool radius that satisfies these requirements, with the goal of finding an optimal radius balancing polishing time and feasibility. For the large freeform surface designed for the future Sentinel-2 Next Generation mission, which serves as the reference throughout this study, a maximum radius of 23.2 mm satisfies the imposed criteria. However, this radius is considered small relative to the surface, as it leads to long polishing times and a higher risk of inducing high-frequency surface errors. Therefore, a larger radius of 50 mm, combined with a higher applied load, is studied in the remainder of this work.

Following this, numerical simulations are performed to characterize a tool wear function that varies spatially across the surface. The surface is segmented into zones with similar tool wear function characteristics using the Gaussian mixture models method, which showed improved performance compared to the K-means algorithm. Based on this zonal segmentation, several deconvolution methods are investigated to compute the dwell time: the Richardson–Lucy algorithm, Wiener filtering, and robust iterative Fourier transform-based dwell time optimization algorithm (RIFTA). The results demonstrate that RIFTA yields the smoothest dwell time maps and the lowest RMS errors, with a polishing convergence ratio of 99.76%.

Finally, this study justifies the use of zonal decomposition to account for the tool’s pressure distribution. The results confirm the importance of this approach when using large tool radii and support the development of efficient polishing strategies for freeform optical surfaces.