Multi-tool optimization for computer controlled optical surfacing

Abstract

With the rapid development of precision technologies, the demand of high-precision optical surfaces has drastically increased. These optical surfaces are mainly fabricated with computer controlled optical surfacing (CCOS). In a CCOS process, a target surface removal profile is achieved by scheduling the dwell time for a set of machine tools. The optimized dwell time should be positive and smooth to ensure convergence to the target while considering CNC dynamics. The total run time of each machine tool is also expected to be balanced to improve the overall processing efficiency. In the past few decades, dwell time optimization for a single machine tool has been extensively developed. While the methods are applicable to multi-tool scenarios, they fail to consider the overall contributions of multiple tools simultaneously. In this paper, we conduct a systematic study on the strategies for multi-tool dwell time optimization and propose an innovative method for simultaneously scheduling dwell time for multiple tools for the first time. First, the influential factors to the positiveness and smoothness of dwell time solutions for a single machine tool are analyzed. The compensation strategies that minimize the residual while considering the CNC dynamics limit are then proposed. Afterwards, these strategies are extended to the proposed multi-tool optimization that further balances the run time of machine tools. Finally, the superiority of each strategy is carefully studied via simulation and experiment. The experiment is performed by bonnet polishing a 60 mm × 60 mm mirror with three tools of different diameters (i.e., 12 mm, 8 mm, and 5 mm). The figure error of the mirror is reduced from 45.42 nm to 11.18 nm root mean square in 13.28 min. Moreover, the measured polishing result well coincides with the estimation, which proves the effectiveness of the proposed method.

A comprehensive review of dwell time optimization methods in computer-controlled optical surfacing

“…5 shows the one-dimensional TIF profiles of an ideal Gaussian TIF versus other common TIFs found in CCOS processes. The bonnet [58], spin [68], and fluid-jet [49] TIFs violate NC1 since they either have a biased peak location or peaks are not unique. The spin and orbital [68,69] TIFs do not satisfy NC2, as their functions end abruptly, and the second derivatives are singular.…”

“…The function-form methods include the function-form iterative method (FIM) [10,37,38,39,40,41], Bayesian method (BAM) [28,42], Fourier transform methods (FTM) [20,38,43], robust iterative Fourier transform-based dwell time optimization algorithm (RIFTA) [44], robust iterative surface extension-based method (RISE) [45], and others [46,47,48]. The matrix-form methods comprise the matrixform iterative method (MIM) [49], Tikhonov-regularized methods [11,16,17,29,30,31,50,51,52,53,54,55,56,57,58], constrained linear least-squares methods (CLLS) [30,59,60], and universal dwell time optimization method (UDO) [32]. Based on these matrix-form methods, modeling the surface error using Zernike polynomials [61] or B-splines [62] before dwell time optimization help obtain smoother dwell time solutions while maintaining a relatively sparser and more computationally efficient dwell time solver.…”

Hybrid height and slope figuring method for grazing-incidence reflective optics

“…It is worth mentioning that, to make the comparison fair, both the height-based and slope-based methods use the same optimizer proposed by Ke et al (2022). Moreover, the heightbased method is performed iteratively on the residual height errors until either all the rms , rms However, as shown in Fig.…”

“…Otherwise, the objectives f 2 (t) and f 3 (t) are alternatively optimized. In this study, we employed an efficient dwell time optimizer proposed in our previous work (Ke et al, 2022) to calculate the intermediate dwell time, which is used to update t slope opt . Finally, it is crucial to update z r…”

Research on High‐Efficiency Curved Surface Polishing with Even Distribution of Slurry Based on Dielectrophoresis

“…The surface roughness dispersion coefficient was reduced from 41.6% to 12.7%. Ke et al [ 18 ] optimized the strategies for multitool dwell time to control the surface removal profile and used three tools of different diameters to polish the mirror. The figure error of the mirror decreased from 45.42 nm to 11.18 nm within 13.28 min.…”