E-PVT: enhanced position-velocity-time scheduler for computer-controlled optical finishing with comprehensive considerations of dynamics constraints, continuity and efficiency.

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O(n3) to O(n) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

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

Grazing-incidence reflective optics are commonly used in synchrotron radiation and free-electron laser facilities to transport and focus the emitted X-ray beams. To preserve the imaging capability at the diffraction limit, the fabrication of these optics requires precise control of both the residual height and slope errors. However, all the surface figuring methods are height based, lacking the explicit control of surface slopes. Although our preliminary work demonstrated a one-dimensional (1D) slope-based figuring model, its 2D extension is not straightforward. In this study, a novel 2D slope-based figuring method is proposed, which employs an alternating objective optimization on the slopes in the x- and y-directions directly. An analytical simulation revealed that the slope-based method achieved smaller residual slope errors than the height-based method, while the height-based method achieved smaller residual height errors than the slope-based method. Therefore, a hybrid height and slope figuring method was proposed to further enable explicit control of both the height and slopes according to the final mirror specifications. An experiment to finish an elliptical-cylindrical mirror using the hybrid method with ion beam figuring was then performed. Both the residual height and slope errors converged below the specified threshold values, which verified the feasibility and effectiveness of the proposed ideas.

Multi-tool optimization for computer controlled optical surfacing.

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.

Random adaptive tool path for zonal optics fabrication.

Deterministic optics fabrication using sub-aperture tools has been vital for manufacturing precision optical surfaces. The fabrication process requires the tool influence function and the tool path to calculate the dwell time that guides the tool to bring surface quality within tight design tolerances. Widely used spiral and raster paths may leave excess waviness from the tool path, and the unavoidable constant removal layer is added to obtain positive dwell time. This waviness can be removed by either using smaller tools sequentially or randomizing the tool path. However, the existing tool-path solutions can hardly adapt to different surface aperture shapes and localized surface errors. Process efficiency and accuracy are also not well considered in tool-path planning. We propose an innovative zonal Random Adaptive Path (RAP) to solve these problems in this study. Firstly, RAP can be flexibly adapted to different surface aperture shapes by introducing part boundary. Secondly, an average threshold strategy is used in the RAP planning to improve efficiency, enabling the surface errors to be selectively corrected. Finally, the threshold is performed in several passes within one processing cycle, each with its RAP, until the desired residual is achieved. The performance of the proposed RAP is studied by comparing it with the conventional tool paths. The results demonstrated that RAP takes the least processing time and achieves the best surface quality, which verifies the effectiveness of RAP in deterministic optics fabrication.

Universal dwell time optimization for deterministic optics fabrication.

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.

Parametric removal rate survey study and numerical modeling for deterministic optics manufacturing.

Surface errors directly affect the performance of optical systems in terms of contrast and resolution. Surface figure errors at different surface scales are deterministically removed using controlled material removal rate (MRR) during a precision optics fabrication process. We systematically sectioned the wide range of MRR space with systematic parameters and experimentally evaluated and mapped the MRR values using a flexible membrane-polishing tool. We performed numerical analysis with a tool influence function model using a distributed MRR-based Preston's constant evaluation approach. The analysis procedure was applied to a series of experimental data along with the tool influence function models to evaluate removal rates. In order to provide referenceable survey data without entangled information, we designed the experiments using Taguchi's L27 orthogonal array involving five control parameters and statistically analyzed a large number of programmatic experiments. The analysis of variance showed that the most significant parameters for achieving a higher MRR are the spot size and active diameter.