Tool path generation for ultra-precision polishing of freeform optical surfaces in an off-axis three-mirror imaging system

The optical performance of the off-axis three-mirror imaging system can be greatly improved using freeform surfaces. This article focuses on the polishing of the primary mirror and tertiary mirror in an off-axis three-mirror imaging system. The primary mirror and tertiary mirror are fabricated on one monolithic substrate and described by non-uniform rational B-spline-based freeform surfaces. The separated and integrated polishing strategies are presented for polishing the two mirrors on the four-axis computer numerical control polishing platform. A tool path generation approach is proposed for polishing of the non-uniform rational B-spline-based freeform surface. Three kinds of the tool paths are given for ultra-precision polishing of the primary mirror and tertiary mirror with the freeform surfaces. The concentric circle path and the approximately concentric circle path are generated for polishing two mirrors separately, while the spiral path is calculated for integrated polishing of two mirrors simultaneously. The polishing tool posture along the planned tool paths is also analyzed. The ultra-precision polishing experiments of the primary mirror and tertiary mirror on the four-axis computer numerical control polishing platform are performed to verify the proposed approach for tool path generation.