Modified subaperture tool influence functions of a flat-pitch polisher with reverse-calculated material removal rate

Numerical simulation of subaperture tool influence functions (TIF) is widely known as a critical procedure in computer-controlled optical surfacing. However, it may lack practicability in engineering because the emulation TIF (e-TIF) has some discrepancy with the practical TIF (p-TIF), and the removal rate could not be predicted by simulations. Prior to the polishing of a formal workpiece, opticians have to conduct TIF spot experiments on another sample to confirm the p-TIF with a quantitative removal rate, which is difficult and time-consuming for sequential polishing runs with different tools. This work is dedicated to applying these e-TIFs into practical engineering by making improvements from two aspects: (1) modifies the pressure distribution model of a flat-pitch polisher by finite element analysis and least square fitting methods to make the removal shape of e-TIFs closer to p-TIFs (less than 5% relative deviation validated by experiments); (2) predicts the removal rate of e-TIFs by reverse calculating the material removal volume of a pre-polishing run to the formal workpiece (relative deviations of peak and volume removal rate were validated to be less than 5%). This can omit TIF spot experiments for the particular flat-pitch tool employed and promote the direct usage of e-TIFs in the optimization of a dwell time map, which can largely save on cost and increase fabrication efficiency.