Restraint of tool path ripple based on the optimization of tool step size for sub-aperture deterministic polishing

Tool path ripple error (TPR_error) is one of the main reasons due to the medium-high spatial frequency error on the surface of aspheric optics. The purpose of this paper is to analyze the effect of the tool step size to the TPR_error in sub-aperture deterministic polishing (SDP) and study a method which can optimize the tool step size to restrain this error. Three groups of simulation experiments were conducted using three different tool influence functions to simulate the uniform removal of the material. As the TPR_error is influenced by three factors, which are full width at half maximum (FWHM) of tool influence function (TIF), tool step size, and depth of material removed, each group of the experiments was conducted under the fixed TIF and depth of material removed. It turns out that both peak-to-valley (PV) and root-mean-square (RMS) values of the TPR_error become larger with the increase of the tool step size, and the variation tendency likes a reversed “L” shape curve. And, the method adopted in the simulation was further validated by the experiment. Therefore, the tool step size at the inflection point would be optimal to restrain the TPR_error together with saving the polishing time to a certain extent. This method could be used to determine the best-suited tool step size in SDP whose typical TIF is a Gaussian or Gaussian-like shape.