Novel suppression strategy of mid-spatial-frequency errors in sub-aperture polishing: adaptive spacing-swing controllable spiral magnetorheological finishing (CSMRF) method

Ultra-high-precision, computer-controlled sub-aperture polishing technology is crucial for achieving full-band, high-precision optical components.However, this convolution material-removal method introduces a significant number of mid-spatial frequency (MSF) errors, which adversely impact the performance of optical systems.To address this problem, we propose a novel controllable spiral magnetorheological finishing (CSMRF) method that disrupts the mechanism of conventional constant tool influence function (TIF) convolution material removal.In this paper, we leverage the advantages of a time-varying spacing strategy and theoretically analyze how time-varying spacing, combined with the spiral swing process of the TIF, mitigates MSF ripple errors.The time-varying spacing method highlights the importance of controlling the characteristic frequency, whereas the CSMRF method has a smoothing effect on the errors within the MSF band.Our findings confirm that time-varying spacing and spiral swinging have complementary effects in managing MSF errors.Furthermore, by constraining the MSF and specific frequency errors, we identify the optimal combination of adaptive spacing and spiral angle using a genetic algorithm.We apply a non-negative gradient constraint dwell-time solution algorithm based on the Lagrange regularization method to deterministically evaluate the specific MSF error.Using the application of an inertial confinement fusion optical element as an example, we observe a 99.938% decrease in the amplitude of the PSD curve of the mid-frequency ripple error with a spatial period of 1 mm, whereas the mid-frequency PSD curve remains within the standard line.Therefore, the proposed method can effectively control the specific MSF error distribution.This variable convolution kernel (TIF) sub-aperture polishing method provides a new concept for full-band cooperative error control.