Studies on Super-Smooth Polishing (2nd Report)

-Deconvolution Algorithm for Corrective Polishing-

Abstract

For the purpose of fabricating free-form optical elements to an accuracy of 80 nmPV, the CSSP (Canon Super-Smooth Polisher) has been developed. This device fmishes workpieces by alternately repeating contour measuring and corrective polishing. The tactics of corrective polishing are based on the tool's dwell-time control. In such a system, total processing time closely depends on the performance of a dwell-time calculation called deconvolution. A new deconvolution algorithm has been proposed, by which less residual error and shorter calculation time than the conventional algorithm, based on a simulation of polishing, is possible. This method is based on an analysis of spatial frequency domain. Therefore, by using an FFT (Fast Fourier Transformation) it can greatly reduce the calculation time. In this case, however, it tends to give unstable dwell-times because the unit removal function has limited frequency response. To address this difficulty, two methods have been devised. The first one is based on a low-pass filter technique, and the second is based on optimizing a functional. By comparing these methods to the simulation method, their performances are checked in the fields of residual error, predicted processing time and calculation time. An areal calculation shows that the new method can achieve a 1/4.3 smaller residual error, a 4 % longer but much smoother dwell-time distribution, and 1/45 shorter calculation time.