Deterministic control of material removal distribution to converge surface figure in full-aperture polishing

Full-aperture polishing is one of the most important processes in fabricating large flat optical elements. Control of the elements’ surface figure to a high precision in a determined manner has been a major challenge in this process. This study focuses on the converging mechanism and deterministic control of the surface figure in the full-aperture polishing process. A novel balance equation for material removal is proposed to correlate the primary aspects of the polishing condition to the surface figure. The removal balance equation reveals that the final surface figure is determined by the spatial distributions of three factors, including the relative velocity, polishing pressure, and removal coefficient. The dependence of these factors’ distribution on the polishing condition is detailed in theory and experiments, and systematic methods to deterministically control these factors’ distribution are proposed. This study is a significant attempt to reveal the converging mechanism of the surface figure and develop a deterministic full-aperture polishing process.