Pseudo-random path planning for rotationally symmetric aspheric polishing based on the removal of regional overlap rate

Uniform polishing of rotationally symmetric aspheric optical elements has long been a challenge, especially in cases of uneven curvature. Traditional fixed-spacing random paths often result in insufficient coverage and uneven surface quality. To address this issue, the article proposes a pseudo-random path planning method based on removal of regional overlap rates. According to the surface shape and curvature changes of the rotationally symmetric non-spherical surface, a path point set is obtained for achieving an equal overlap rate distribution. Moreover, the path search algorithm is optimized by adjusting the weights of the path points, allowing the paths to precisely converge at the predetermined positions. A two-layer acceleration architecture is established, including the inputting algorithm and the blocking strategy to improve the efficiency of path generation; The integrated angular velocity control module compensates for curvature differences, ensuring consistent removal depth at all locations. The experimental results show that the surface roughness variance obtained by the proposed method is only 2.49 × 10⁻⁷ μm², which is significantly lower than the 3.25 × 10⁻⁴ μm² obtained by the traditional fixed-spacing random path method, thereby validating the uniform coverage and efficient path generation of this method in polishing rotationally symmetric aspherical surfaces. This research provides new theoretical insights and practical approaches for improving the surface quality of ultra-precision optical processing.