Data-based systematic error extraction and compensation methods based on wavelet transform in ultra-precision optical polishing

Sub-aperture polishing is a key technique for fabricating ultra-precision optics. However, the existence of the polishing errors that are difficult to be compensated by physical modeling seriously affects the manufacturing accuracy and efficiency of optical components. To address this problem, a data-based systematic error extraction and compensation (DSEC) method was proposed to enhance the polishing accuracy on optics. To maximize the extraction quality in a small dataset condition, the wavelet transform is introduced into the extraction process, and the uncertainty of the piston term in the interferometer measurement is improved by L1-norm optimization. Furthermore, two typical error sources (loss of polishing fluid in the edge and the robot trajectory error) are used to verify the effectiveness of the proposed method; in experimental verification, the root mean square (RMS) of the surface figure of a ϕ85-mm mirror was decreased from 0.069λ to 0.017λ, and the RMS of the 610 × 440 mm mirrors was achieved at 0.019λ after the edge compensation, where the polishing accuracy can be improved by more than 4 times; additionally, the RMS of the surface figure with an effective aperture of 480 × 360 mm mirror was reached at 0.011λ after the trajectory error compensation, where the polishing accuracy can be improved by more than 2 times. The proposed DSEC model offers insights that will help achieve advancement in the sub-aperture polishing process.