Statistical Tool Size Study for Computer-Controlled Optical Surfacing

Abstract

Over the past few decades, computer-controlled optical surfacing (CCOS) systems have become more deterministic. A target surface profile can be predictably achieved with a combination of tools of different sizes. However, deciding the optimal set of tool sizes that will achieve the target residual error in the shortest run time is difficult, and no general guidance has been proposed in the literature. In this paper, we present a computer-assisted study on choosing the proper tool size for a given surface error map. First, we propose that the characteristic frequency ratio (CFR) can be used as a general measure of the correction capability of a tool over a surface map. Second, the performance of different CFRs is quantitatively studied with a computer simulation by applying them to guide the tool size selection for polishing a large number of randomly generated surface maps with similar initial spatial frequencies and root mean square errors. Finally, we find that CFR = 0.75 achieves the most stable trade-off between the total run time and the number of iterations and thus can be used as a general criterion in tool size selection for CCOS processes. To the best of our knowledge, the CFR is the first criterion that ties tool size selection to overall efficiency.

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 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 orbital TIF is also a piecewise function with discontinuous even derivatives at the transition points.…”

Analysis of low-spatial frequency response in magnetorheological finishing process

“…[4] Generally, specific TIFs can effectively control features larger than TIF size, but smaller features remain challenging to control effectively. [5] However, concrete research findings regarding the efficiency of correctional polishing based on TIF dimensions with respect to feature size are currently insufficient. To achieve efficient process improvements, it is crucial to understand the efficiency of correctional polishing concerning feature size based on TIF dimensions and develop appropriate polishing strategies based on the initial surface conditions.…”

Benefits of Intelligent Fuzzy Controllers in Comparison to Classical Methods for Adaptive Optics

“…Telescopes are instruments designed to observe distant celestial bodies. Normally, a few photons from these bodies reach the instrument, which requires the development of an infrastructure for capturing and correcting noise and distortions [1][2][3][4][5].…”