Tilt angle correction based forming algorithm for high steepness aspheric surfaces polishing

Abstract

According to the varying characteristics of removal function in steep aspheric surface polishing, the calculation algorithm of removal function at arbitrary polishing position was given in the best fitting plane of steep aspheric based on the experiment of removal function with several inclined angles and the feature of polishing surface. The forming model was then discretized into the form of large sparse matrix product, and the dwell time was solved efficiently by SBB algorithm. The discrete matrix model describing nonlinear polishing process of steep aspheric surface was established, and finally the process flow was verified by experiment. The experiment was conducted on a 200 mm aperture off-axis aspheric surface, finally the root mean square error of the surface was 0.022 λ and the processing convergence rate was 3.23 after two polishing runs. The research results show that the forming model with plane projection and tilt-angle-correction removal function is reasonable, and the dwell time solving algorithm based on SBB principle is a fast and efficient surface shape control technology, which could fulfill deterministic and accurate shaping for steep aspheric surface.