Kinematic model for material removal distribution and surface figure in full-aperture polishing

Full-aperture polishing is a significant process for fabricating large ultra-precision optic flats. The surface figure is one of the key specifications required of the optic flats, which is determined by the material removal distribution during polishing. To date, the most frequently referred to equation, the Preston equation, only provides a solution for qualitative calculation of material removal of a single point on the optic surface. In this study, we present a kinematic model for deterministic calculation of the removal amount at every local optic position. The model is based on the sliding track of each local optic position on the lap, and it incorporates local pressure and most key kinematic parameters and considers the effect of the lap grooves. With this model, we analyzed the impacts of various kinematic parameters and groove features on the distribution of the removal amount in terms of sliding distance, assuming a uniform pressure distribution at the lap/optic interface. Several polishing experiments have been carried out in which the model is validated.