Statistical perception of the chaotic fabrication error and the self-adaptive processing decision in ultra-precision optical polishing

Abstract

Subaperture polishing is a key technique for fabricating ultra-precision optics. However, the error source complexity in the polishing process creates large fabrication errors with chaotic characteristics that are difficult to predict using physical modelling. In this study, we first proved that the chaotic error is statistically predictable and developed a statistical chaotic-error perception (SCP) model. We confirmed that the coupling between the randomness characteristics of chaotic error (expectation and variance) and the polishing results follows an approximately linear relationship. Accordingly, the convolution fabrication formula based on the Preston equation was improved, and the form error evolution in each polishing cycle for various tools was quantitatively predicted. On this basis, a self-adaptive decision model that considers the chaotic-error influence was developed using the proposed mid- and low-spatial-frequency error criteria, which realises the automatic decision of the tool and processing parameters. An ultra-precision surface with equivalent accuracy can be stably realised via proper tool influence function (TIF) selection and modification, even for low-deterministic level tools. Experimental results indicated that the average prediction error in each convergence cycle was reduced to 6.14%. Without manual participation, the root mean square(RMS) of the surface figure of a ϕ100-mm flat mirror was converged to 1.788 nm with only robotic small-tool polishing, and that of a ϕ300-mm high-gradient ellipsoid mirror was converged to 0.008 λ. Additionally, the polishing efficiency was increased by 30% compared with that of manual polishing. The proposed SCP model offers insights that will help achieve advancement in the subaperture polishing process.