Universal dwell time optimization for deterministic optics fabrication

Abstract

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

Statistical Tool Size Study for Computer-Controlled Optical Surfacing

“…When utilizing the calibration of the f c TIF (see Equation ( 8)) by means of the reference TIF illustrated in Section 3.1, we can determine the size of any kind of TIF by simply applying a scale factor, depending on the given TIF shape. In the following subsections, we provide examples that employ Equation ( 8) to determine the appropriate size of three kinds of typical TIFs in CCOS to correct the reference surface in Figure 3, namely Gaussian TIFs [10], Spin TIFs [22], and Orbital TIFs [22], with the objective that the CF of these TIFs matches the only error frequency present in the reference surface in Section 3.1.…”

“…where R O is the radius of the orbital stroke and all the other variables are the same as those presented in Equation (10). Unlike the previous two TIFs, the Orbital TIF is defined by two parameters: R T and R O , where R TIF = R O + R T .…”

“…Computer-controlled optical surfacing (CCOS) [1,2] systems have been successfully used to fabricate high-precision optics in various cutting-edge applications, such as telescopes for space exploration [3][4][5], X-ray mirrors for synchrotron radiation and free-electron laser facilities [6][7][8][9][10], and optics in EUV lithography [11,12]. Different CCOS systems use different tools, which can be adopted based on the requirements for the precision and shape of the desired optical surface.…”

High-Precision Ion Beam Figuring of X-Ray Plane Mirrors for the Bendable KB Focusing System

“…They first proposed an effective 1D-IBF method with improved calibration of coordinate correspondence and dwell time calculation [13]. Several new dwell time calculations and optimization algorithms were further developed to reduce the estimated figure error residuals and enhance the computation efficiency [14,15]. These methods were demonstrated in their own-built IBF system.…”

“…Two elliptical mirrors of 80 mm in length were fabricated from cylinders which showed 0.62 and 0.71 nm RMS figure error, respectively [14]. The figure error of a flat mirror over an aperture of 92.3 mm × 15.7 mm was reduced from 6.32 to 0.2 nm RMS [15].…”