Prediction model and experimental investigation of mid-spatial-frequency error in bonnet polishing of off-axis aspheric X-ray mirror

As a sub-aperture technique in ultra-precision optical fabrication, bonnet polishing enables the production of optical components with high figure accuracy and superior surface quality. However, it can introduce periodic or aperiodic surface irregularities, known as mid-spatial-frequency (MSF) errors, which may compromise optical performance. This study examines the geometry, contact pressure, and motion velocity within the contact zone during bonnet polishing of off-axis aspheric X-ray mirrors and establishes the corresponding tool influence function. Based on the tool path parameters, a predictive model for MSF errors is developed to link the post-polishing surface profile characteristics with process parameters. The model is experimentally validated by evaluating the effects of varying velocity ratios and step intervals on MSF error generation. The results show that MSF errors decrease with increasing velocity ratio and decreasing step interval in raster polishing. The proposed model predicts MSF errors on the mirror surface with a maximum deviation of 12.37% relative to experimental measurements, providing a practical basis for suppressing MSF error formation in bonnet polishing processes.