Modified dwell time optimization model and its applications in subaperture polishing

Abstract

The optimization of dwell time is an important procedure in deterministic subaperture polishing. We present a modified optimization model of dwell time by iterative and numerical method, assisted by extended surface forms and tool paths for suppressing the edge effect. Compared with discrete convolution and linear equation models, the proposed model has essential compatibility with arbitrary tool paths, multiple tool influence functions (TIFs) in one optimization, and asymmetric TIFs. The emulational fabrication of a $\mathrm{\Phi }200\mathrm{mm}$ workpiece by the proposed model yields a smooth, continuous, and non-negative dwell time map with a root-mean-square (RMS) convergence rate of 99.6%, and the optimization costs much less time. By the proposed model, influences of TIF size and path interval to convergence rate and polishing time are optimized, respectively, for typical low and middle spatial-frequency errors. Results show that (1) the TIF size is nonlinear inversely proportional to convergence rate and polishing time. A TIF size of $\sim 1/7$ workpiece size is preferred; (2) the polishing time is less sensitive to path interval, but increasing the interval markedly reduces the convergence rate. A path interval of $\sim 1/8–1/10$ of the TIF size is deemed to be appropriate. The proposed model is deployed on a JR-1800 and MRF-180 machine. Figuring results of $\mathrm{\Phi }920\mathrm{mm}$ Zerodur paraboloid and $\mathrm{\Phi }100\mathrm{mm}$ Zerodur plane by them yield RMS of $0.016\lambda$ and $0.013\lambda$ ($\lambda =632.8\mathrm{nm}$), respectively, and thereby validate the feasibility of proposed dwell time model used for subaperture polishing.