Loaded Surface Shape Stability Analysis of Short-Focus Off-Axis Aspheres for Stressed Mirror Polishing

The Stressed Mirror Polishing method (SMP) enables the high-quality and efficient fabrication of short-focus off-axis aspheres (SFOA) for overcoming difficulties arising from large asphericity, which makes the polishing tool unfitted for the mirror surface shape and produces mid- and high-frequency errors. However, there remains a lack of precise iterative loading methods and detailed analyses of loaded surface shape stability for processing SFOA through SMP. Therefore, a foundational analysis model for SMP was established, integrating mathematical theoretical modeling with a finite element analysis (FEA). Based on this model, an iterative loading strategy, based on the proportional relationship between the Zernike coefficients and the SMP-type surface shape error, was proposed to achieve a high dynamic range of >100, which is 10 times larger than the reported ones. Moreover, to guide the loading structure design and quantify the surface shape’s sensitivity to design parameters, both design of experiments (DOE) and radial basis function (RBF) methods had been used to ascertain the precision requirement of each force and the corresponding arm length at separated loading points, under the shape precision requirement of PV < 1 μm which coordinates with the ability of the Ion Beam Figuring (IBF) technique.