Kernel TIF method for effective material removal control in rotating pitch tool-based optical figuring

While opticians have used pitch tools for superb surface finishing, their poor controllability in material removal and associated lengthy tooling overhead have been well known in optics fabrication communities. We report a new computational technique called kernel tool influence function (KTIF) that can bring higher predictability to pitch tool-based material removal. The term "kernel" is defined as the ratio of experimental to simulated removal depth, therefore transforming the material removal coefficient of Preston's equation to a removal scaling function at each point on the tool surface. This approach offers a unique inherent control feature incorporating "real-life shop floor effects associated with pitch tool polishing variables" into the tool influence functions without the need for theoretical expressions for the effects of individual variables on material removal behavior. Using a modified Draper-type polishing machine and a rotating pitch tool, we first generated kernel TIFs with zero stroke and used them for simulation and trial experiments of extended TIFs with variable tool strokes. The results show that the root mean square (rms) TIF profile differences between the prediction and experiments are in the range of 11 to 29 nm for conventional TIF and 7 to 15 nm for the KTIF. We then generated conventional TIF and KTIF database sets and applied them to surface figuring simulations. The results confirm that the kernel TIF has superior performance to the conventional TIF in controlling the material removal for correction of the chosen surface error.