Research on deterministic compliant figuring processes removal functions and algorithms for nickel-phosphorus alloy optics

Deterministic polishing is critical to the fabrication of ultra-precision aspheric optics, where precise dwell time algorithms are used to remove surface material. However, the sub-aperture polish removal function introduces surface ripple characteristics and degrades optical performance due to its narrow full width at half maximum and mismatched spatial wavelengths, reducing volume removal rate and introducing high and medium spatial frequency errors on the surface. Therefore, there is an urgent need to introduce pre-processing and post-processing to improve flexibility control in deterministic small tool polishing, enhance the adaptability of the tool to the workpiece surface with changing curvature, and obtain a stable Gaussian-like tool influence function. This paper explores the surface finishing removal mechanism based on the compliant figuring process and verifies the robustness and machining accuracy of the tool influence function for plane and variable curvature Nickel-phosphorous alloy machined surfaces. Firstly, based on the removal mechanism of the figuring process, the relative velocity and contact pressure models were established. Secondly, the influence of the radius of curvature and the amount of offset on the removal function is discussed. Finally, the high frequency band and middle frequency band of the one-dimensional power spectral density curve are analyzed in detail, and the reliability and modification ability of the compliant figuring process are verified according to the amplitude spectrum image.