1. Introduction . The development of fields such as astronomical observation [ 1 ], laser fusion [ 2 ], and extreme ultraviolet lithography [ 3 – 5 ] has driven the demand for complex curved optical components, thereby setting higher requirements for surface treatment technologies. Numerous sub-aperture polishing technologies, including computer controlled optical surfacing (CCOS), bonnet polishing, and magnetorheological finishing (MRF), demonstrate potential in managing complex su...