Modeling and in-depth analysis of the mid-spatial-frequency error influenced by actual contact pressure distribution in sub-aperture polishing

In ultra-precision optical processing, the sub-aperture polishing is prone to produce a mid-spatial-frequency (MSF) error. However, the generation mechanism of the MSF error is still not fully clarified, which seriously affects the further improvement of optical component performance. In this paper, it is proved that the actual contact pressure distribution between the workpiece and tool is a crucial source which affects the MSF error characteristics. A rotational periodic convolution (RPC) model is proposed to reveal the quantitative relationship among the contact pressure distribution, speed ratio (spin velocity/feed speed) and MSF error distribution. In-depth analyses show that the MSF error is linearly related to the symmetry level of contact pressure distribution and inversely proportional to the speed ratio, where the symmetry level is effectively evaluated by the proposed method based on Zernike polynomials. In the experiments, according to the actual contact pressure distribution obtained from the pressure-sensitive paper, the error rate of modeling results under different processing conditions is around 15%, which proves the validity of the proposed model. The influence of contact pressure distribution on the MSF error is further clarified through the establishment of RPC model, which can further promote the development of sub-aperture polishing.