Surface shape development of the pitch lap under the loading of the conditioner in continuous polishing process

Continuous polishing using the pitch lap is a key process in finishing large flat optical elements. The optical elements' surface figure is primarily dependent on the surface shape of the pitch lap, which is controlled by a large-size conditioner. However, underlying fundamentals of the process control is not yet clear, and it remains empirical and nondeterministic to date. In this study, a novel analysis model is proposed for exploring the surface shape development of the pitch lap under the conditioner loading. The analysis model divides the polishing time into a series of segments, in which the shape variation of the pitch lap due to viscoelastic creep is derived from the pressure distribution at the conditioner-lap contact interface. Further, a contact model of the lap and conditioner is built to obtain the pressure distribution at the interface, and a novel creep model is proposed for the viscoelastic behavior of the pitch lap under the pressure. The analysis model combined with the contact and viscoelastic models can be used to explore the pitch lap shape development under various conditions and hence reveal the underlying fundamentals of controlling the lap shape by the conditioner.