Cross-scale surface shape error correction in the bonnet polishing of a freeform surface

High-precision freeform surfaces are widely used in ultra-precision optical systems to improve imaging performance and reduce optical system weight. With the development of short wavelength optics represented by extreme ultraviolet lithography, the high-precision requirements for the full frequency errors and geometrical complexity of optical freeform surfaces pose great challenges to optical processing and are difficult to achieve by traditional manufacturing processes. This paper proposes a cross-scale surface shape error correction method to correct surface shape errors in different cycles in bonnet polishing. First, the material removal mechanism based on physical and chemical effects was discussed to obtain the method of cross-scale removal functions. Secondly, the analysis method of the frequency response characteristics of the tool based on power spectral density was discussed to analyze, evaluate, and guide the bonnet polishing process of freeform surfaces. Finally, the proposed method was verified by the experiments in processing a fused silica freeform surface of 120 mm diameter; the final root-mean-square (RMS) of surface shape accuracy was better than λ /100.