Pseudo-random and dynamic selective trajectories generation for mid-spatial frequency error rapid convergence

Abstract

Due to the limitations of traditional polishing methods in suppressing mid-spatial frequency (MSF) errors, this study proposes an integrated solution combining pseudo-random trajectory with selective dynamic coverage complex trajectory optimization based on MSF error spatial distribution characteristics. A high-degree-of-freedom pseudo-random trajectory generation strategy is developed, utilizing uniformly distributed initial MSF stripe spacing value as input data to generate path retrieval points with optimized spatial distribution. This process ultimately produces high-degree-of-freedom pseudo-random trajectories featuring non-periodic path characteristics, thereby eliminating the inherent repetitiveness of conventional polishing trajectories. The proposed pseudo-random trajectory achieves MSF error rapid convergence while suppressing additional MSF components induced by path periodicity. For addressing inconsistent residual MSF error distribution after pseudo-random trajectory polishing, a dynamic complex trajectory generation method based on error pixel data analysis is established. Based on the spatial distribution characteristics of MSF errors, this method leverages the adaptive capability of trajectories to perform targeted corrections on different error regions. Thereby, it effectively enhances the convergence efficiency and distribution uniformity of residual MSF errors, and ultimately improves the convergence limit of MSF errors. Experimental results demonstrate that the synergistic integration of pseudo-random trajectory and selective dynamic complex trajectory optimization significantly enhances MSF error convergence efficiency without compromising existing surface form accuracy.