Opt Express. 2023 Feb 27;31(5):7707-7724. doi: 10.1364/OE.484309.
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.
分孔径抛光是制造超精密光学器件的关键技术。然而，抛光过程中的误差源复杂性会产生具有混沌特征的大制造误差，这些误差很难通过物理建模进行预测。在本研究中，我们首先证明了混沌误差在统计上是可预测的，并开发了一种统计混沌误差感知（SCP）模型。我们证实了混沌误差的随机性特征（期望和方差）与抛光结果之间的耦合遵循近似线性关系。因此，改进了基于 Preston 方程的卷积制造公式，并定量预测了各种工具在每个抛光周期中的形貌误差演化。在此基础上，提出了一种基于中低空间频率误差准则的自适应决策模型，考虑了混沌误差的影响，实现了工具和加工参数的自动决策。通过适当的工具影响函数（TIF）选择和修改，可以稳定地实现具有等效精度的超精密表面，即使是对于低确定性水平的工具也是如此。实验结果表明，在每个收敛周期内的平均预测误差降低到 6.14%。无需人工参与，仅通过机器人小工具抛光，可将ϕ100mm 平面反射镜的面形均方根（RMS）收敛到 1.788nm，ϕ300mm 高梯度椭圆反射镜的面形均方根（RMS）收敛到 0.008λ。此外，与手动抛光相比，抛光效率提高了 30%。所提出的 SCP 模型提供了有助于实现分孔径抛光工艺进步的见解。
