Mechanisms influencing and prediction of tool influence function spots during hemispherical sub-aperture tool polishing on fused silica

Sub-aperture tool polishing of precision optics requires a detailed understanding of the local material removal [tool influence function (TIF)] at the contact spot between the workpiece and tool to achieve high removal determinism and hence precision of the optic relative to the desired/design surface figure. In this study, the mechanisms influencing and the quantitative prediction of the removal rate and shape of TIF spots during polishing of fused silica glass with cerium oxide slurry using a rotating hemispherical pad-foam tool for a wide variety of process conditions (including tool properties, kinematics, and applied displacements) are investigated. The TIF volumetric removal rate can be estimated utilizing the average relative velocity and contact area using a simple analytical model. In addition, stability of the volumetric removal rate for fixed process conditions is shown to be greatly dependent on the pad preparation and amount of tool use (affecting both pad topography and slurry buildup), whose general behavior shows an increase in removal rate followed by stabilization with polishing time. The determination of the TIF removal shape is more complex. An extended version of the Preston removal model is developed to explain a comprehensive set of measured TIF removal shapes to within ∼ 22 % . This model incorporates a number of phenomena impacting the TIF removal shape including: (a) temporal and spatial dependent relative velocity between the workpiece and tool; (b) an elastic mechanics based, as well as hydrodynamic, pressure distribution; (c) a spatially dependent friction coefficient possibly caused by both reduced slurry replenishment in low velocity regions and pad slurry islands (100 µm scale) and porosity (millimeter scale); and (d) a shear-based removal mechanism on the periphery of the contact spot.