Computer Controlled Optical Surfacing Research Articles

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

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

Compensation of the tool influence function changes under neighborhood effect in atmospheric pressure plasma processing.

Nowadays, computer controlled optical surfacing (CCOS) is greatly developed in the fabrication of ultra-precision optical surfaces. As one of the deterministic CCOS techniques, atmospheric pressure plasma processing (APPP) can achieve the efficient removal based on the chemical reaction. In this process, the temperature rising issue caused by plasma heating is of great importance for accelerating the etching rate, but also increases the difficulty of deterministic removal control, because the tool influence function (TIF) in APPP is no longer time-invariant. In the existing research, the time-variant TIF model can describe the TIF changes to a certain degree, which is considered in the dwell time calculation. However, there inevitably exists the strong neighborhood effect, which indicates that the TIFs of different dwell points are thermally interacted. Thus, the existing time-variant TIF model is no longer accurate for predicting TIF changes, and not suitable for application to further compensation. To solve this, the compensation of TIF changes under neighborhood effect is proposed in this paper. First, the mechanism of TIF changes caused by neighborhood effect is explained in depth. Then, the theoretical analysis is implemented and the compensation method is systematically discussed, encompassing the tool path optimization, model of TIF changes and dwell time calculation. Further, the proposed method is demonstrated and verified by a series of simulations. Finally, the experimental validation is carried out, which proves the capability of achieving high-precision removal and high convergence rate.

B-spline surface approximation method for achieving optimum dwell time in deterministic polishing

In the computer-controlled optical surfacing (CCOS) process, the accurate calculation of the dwell time map is essential for achieving the desired amount of material removal distribution. However, it remains challenging for current methods to generate a smooth dwell time map that reduces the dynamic requirements of machine tools while maintaining the high finishing capability on freeform optics. This paper proposes a B-spline surface approximation method for obtaining the optimum dwell time in deterministic polishing. The B-spline surface representation allows the dwell time map to be expressed by a small number of control points instead of a large number of discrete dwell points. The dwell time deconvolution then becomes a linear least-squares problem with only a few control points as variables, which significantly reduces the scale of the problem. To achieve a more accurate and smoother dwell time map, a knot position optimization algorithm is proposed to adapt the knots to the geometric features of the target removal surface. Simulation results demonstrate that the proposed B-spline-based dwell time algorithm significantly outperforms common dwell time algorithms in terms of the computational accuracy, efficiency, as well as smoothness of the dwell time map. To validate the effectiveness and practicability of the proposed method, experimental polishing of a bi-sinusoidal optical surface has been carried out. The results show that the developed algorithm has greatly reduced the tracking error of the machine tool caused by dwell time fluctuations, and consequently, the corresponding residual error of material removal in deterministic polishing.

Ultra-precision time-controlled grinding for flat mechanical parts with weak stiffness

High-precision flat mechanical parts are widely used, such as in aerostatic bearing, which requires a rather high machining precision. Due to large size, low stiffness and other machining problems, traditional ultra-precision grinding machine tool cannot directly achieve the final precision, so manual grinding is necessary to meet the manufacturing requirements, resulting in low efficiency. Based on the computer-controlled optical surfacing (CCOS) method and the flexible grinding process, the time-controlled grinding method (TCG) is proposed to achieve quantitative material removal at each position on the workpiece. Combined with the material removal mechanism, the removal function with good linearity and stability is extracted by controlling corresponding parameters. By applying a novel measuring and processing method of surface data with high precision and high efficiency, the flatness error and parallelism error are accurately obtained and used as grinding reference to carry out the time-controlled grinding experiment on one spacer ring with a diameter of 190 mm. The final flatness error converges from 1.5–2 μm to 0.6–0.7 μm and parallelism error converges from ~2 μm to ~0.6 μm, while the roughness converges from 273 nm Ra to 65 nm Ra, achieving the goal of ultra-precision digital machining of submicron level. The machining precision is better than traditional ultra-precision grinding machine tool, and the potential for time-controlled grinding method of ultra-precision machining in flat mechanical parts especially with low stiffness is verified.

Statistical Tool Size Study for Computer-Controlled Optical Surfacing

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.

Effect of Robot Motion Accuracy on Surface Form during Computer-Controlled Optical Surfacing Process

Nowadays, large-aperture optical components are increasingly used in high-power laser systems, remote-sensing satellites, and space-based astronomical telescopes. Fabricating these surfaces with submicron-scale shape accuracy and a nanoscale surface finish has been a great challenge for the optical industry, especially for hard and difficult-to-machine materials. Thus, to achieve the high-efficiency and high-precision polishing of large-aperture aspherical optical parts, this study combined robotic machining technology with computer-controlled optical surfacing (CCOS) technology and investigated the effect of robot motion accuracy on the surface topography of workpieces during polishing. First, a material removal model considering the normal error of the polishing tool was developed based on contact mechanics, kinematic theory, and the abrasion mechanism. Next, in combination with the polishing trajectory, the surface morphology and form accuracy after polishing were predicted under different normal-error conditions. Then, preliminary experiments were conducted to verify the model. The experimental data agreed with the simulation results, showing that as the normal error increased from 0° to 0.5° and 1°, the peak-to-valley (PV) values of the surface profile of the optical element decreased from 5.42, 5.28, and 4.68 μm to 3.97, 4.09, and 4.43 μm, respectively. The corresponding convergence rates were 26.8%, 22.5%, and 5.3%. The root mean square (RMS) values decreased from 0.754, 0.895, and 0.678 μm to 0.593, 0.620, and 0.583 μm, with corresponding convergence rates of 21.4%, 30.7% and 14.0%, respectively. Moreover, a higher motion accuracy enabled the polishing robot to reduce the mid- and high-frequency errors of the optical element.

Nonlinear dwell-time algorithm for freeform surface generation by atmospheric-pressure plasma processing.

Based on deterministic chemical etching, atmospheric pressure plasma processing (APPP) with a high material removal rate and spatial machining resolution, is a promising computer-controlled optical surfacing (CCOS) technique for freeform surface generation. However, the time-variant removal characteristics of APPP induce nonlinearity in the CCOS process, which requires more consideration in the dwell-time calculation. In this paper, the nonlinear dwell-time algorithm based on the concept of controlling volumetric removal is studied. The freeform surface generation by controlling volumetric removal is modeled to provide the theoretical basis for the algorithm. The applicability of the algorithm in freeform generation by APPP with time-varying characteristics is explored through numerical simulations. Finally, a freeform surface is successfully created based on the algorithm and relevant analysis results, which validates the applicability of the algorithm in freeform generation using time-variant tool influence functions.

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.

Genetic algorithm-powered non-sequential dwell time optimization for large optics fabrication.

Computer Controlled Optical Surfacing (CCOS) is widely applied for fabricating large aspheric optical surfaces. For large optics fabrication, various sizes of polishing tools are used sequentially. This raises the importance of efficient and globally optimized dwell time map of each tool. In this study, we propose a GEnetic Algorithm-powered Non-Sequential (GEANS) optimization technique to improve the feasibility of the conventional non-sequential optimization technique. GEANS consists of two interdependent parts: i) compose an influence matrix by imposing constraints on adjacent dwell points and ii) induce the desired dwell time map through the genetic algorithm. CCOS simulation results show that GEANS generates a preferable dwell time map that provides high figuring efficiency and structural similarity with the shape of target removal map, while improving computational efficiency more than 1000 times over the conventional non-sequential optimization method. The practicability of GEANS is demonstrated through error analyses. Random tool positioning error and tool influence function errors are imposed on dwell time maps. Compared to the conventional non-sequential optimization method, the power spectral density values of residual surface error from GEANS remain stable. GEANS also shows superior applicability when the maximum acceleration of a tool is applied.

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.

Study on the Absorption Characteristics and Laser Damage Properties of Fused Silica Optics under Flexible Polishing and Shallow DCE Process.

The enhancement of laser damage resistance of fused silica optics was a hotspot in scientific research. At present, a variety of modern processes have been produced to improve the laser induced damage threshold (LIDT) of fused silica optics. They included pre-treatment processes represented by flexible computer controlled optical surfacing (CCOS), magnetorheological finishing (MRF), ion beam finishing (IBF), and post-treatment processes represented by dynamic chemical etching (DCE). These have achieved remarkable results. However, there are still some problems that need to be solved urgently, such as excessive material removal, surface accuracy fluctuation in the DCE process, and the pollution in MRF process, etc. In view of above problems, an MRF, CCOS, IBF and shallow DCE combined technique was used to process fused silica optics. The surface morphology could be greatly controlled and chemical etching depth was reduced, while the LIDT increased steadily. After processing by this combined technique, the LIDT increased to 12.1 J/cm2 and the laser damage resistance properties of fused silica were significantly enhanced. In general, the MRF, IBF, CCOS and shallow DCE combined technique brought much help to the enhancement of laser damage resistance of fused silica, and could be used as a process route in the manufacturing process of fused silica.

Investigation of the tool influence function neighborhood effect in atmospheric pressure plasma processing based on an innovative reverse analysis method.

Ultra precision optical surfaces can be efficiently manufactured using a computer-controlled optical surfacing (CCOS) process. Based on the chemical reaction, atmospheric pressure plasma processing (APPP) is a promising deterministic CCOS technique and has great application prospect for the figuring processing as well as freeform generation. However, the plasma jet also works as the heat source, leading to the variation of substrate temperature field. This way, the tool influence function (TIF) is continuously changed, which leads to the nonlinear removal characteristic. Especially, it becomes much more complex when considering the neighboring dwell points, because they are thermally interacted. The conventional time-variant TIF model cannot accurately describe the practical TIF changes. In this paper, an innovative reverse analysis method is proposed to derive the practical TIF changes in APPP. First, the special problem of the TIF neighborhood effect is pointed out. The limitation of the conventional TIF model is analyzed with the assisted thermal model. Then, an innovative reverse analysis method is presented to derive the TIF changes from the practical removal, which is demonstrated with the simulation. Further, the proposed method is applied to the analysis of the TIF changes in APPP. To verify its feasibility, the experimental validation is undertaken, which proves its capability of deriving complex TIF changes.

Generic model of time-variant tool influence function and dwell-time algorithm for deterministic polishing

In computer-controlled optical surfacing (CCOS) techniques, the tool influence function (TIF) is generally assumed to be time-invariant; thus, two-dimensional convolution can be employed to compute the dwell time. However, the material removal rate is time-variant in some CCOS processes. This time-variant material removal rate makes it difficult to accurately model the TIF and leads to impracticality of the two-dimensional convolution algorithm. We herein establish a novel modelling framework of the TIF considering the time-variant material removal rate in CCOS based on a partial differential equation. An updated dwell-time algorithm is also proposed to address the inverse problem of freeform surface generation by using the established TIF. The proposed modelling technique is well demonstrated in magnetically driven internal finishing and abrasive jet machining. The results demonstrate that the model can precisely predict the polished profile against the polishing time, and the novel dwell-time algorithm outperforms the conventional convolution algorithm in terms of efficiency and accuracy. The modelling framework enables localised freeform surface generation and corrective polishing on internal surfaces. The proposed TIF model and dwell-time algorithm may be extended to other CCOS techniques to achieve better figuring accuracy, such as bonnet polishing, ion beam figuring, and plasma jet machining.

Analysis of the misalignment effect and the characterization method for imprinting continuous phase plates.

Continuous phase plates (CPPs) are increasingly being used to realize beam shaping and smoothing in high-power laser systems. With computer controlled optical surfacing (CCOS) technology, CPPs can be imprinted with high accuracy by a series of processing iterations, in which the characterization of the imprinted CPP surface plays a key role. However, the form accuracy evaluation is sensitive to the misalignment caused by the difference between the designed and measured coordinates. In this paper, the matching problem, which is the critical part of characterization, is first summarized as a least squares problem in accordance with the processing principle of CPPs. Then, the misalignment effect on the form error evaluation is analyzed. Necessary attention is paid to the CPP features and the sensibility analysis for different misalignments is conducted. To improve the efficiency and accuracy, an automatic characterization method based on image registration and nonlinear optimization is presented. Considering the smoothness of the CPP surface, the height difference tracing method is proposed to evaluate the matching performance and embedded into the characterization method. Finally, a series of simulations and experiments were undertaken to verify the performance of the proposed characterization method. The results demonstrated the feasibility of the proposed method, indicating that it can provide the reliable form error evaluation with sub-nanometer accuracy for imprinted CPPs.

Research and application on the key techniques of conformal vibration polishing on optics

In computer controlled optical surfacing (CCOS), the small-sized polishing tools make the process exhibit a weaker material removal capability and exacerbate the deterioration of mid-spatial frequency (MSF) errors. Consequently, this paper presents a full-aperture conformal vibration polishing method incorporating short-stroke forced vibration. The realization mechanism, removal ability and machining effect of it were expounded separately, and verified by experiments. The experimental results show that conformal vibration polishing can achieve uniform smoothing of the MSF errors without destroying the original surface shape while efficiently removing the materials. The conformal vibration polishing proposed in this paper not only extends the existing processing field, but also provides a new approach for the suppression of MSF errors.

An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing.

The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr150 = 0.028 λ and PVcr100 = 0.014 λ respectively.

Rapid and Non-Destructive Repair of Fused Silica with Cluster Damage by Magnetorheological Removing Method.

The damage repair of fused silica based on the CO2 laser repair technique has been successfully applied in high-power laser systems in the controllable nuclear fusion field. However, this kind of repairing technique mainly focuses on large-scale laser damage with sizes larger than 200 μm, but ignores the influence of cluster small-scale damage with sizes smaller than 50 μm. In order to inhibit the growth of small-scale damage and further improve the effect of fused silica damage repair, this paper carried out a study on the repair of fused silica damage using the magnetorheological (MR) removing method. The feasibility of fused silica damage repairing was verified, and the evolution law of the number, morphology, and the surface roughness of small-scale damage were all analyzed. The results showed that the MR removing method was non-destructive compared to traditional repairing technologies. It not only effectively improved the whole damage repairing rate to more than 90%, but it also restored the optical properties and surface roughness of the damaged components in the repairing process. Based on the study of the MR removing repair law, a combined repairing process of 4 μm MR removal and 700 nm computer controlled optical surfacing (CCOS) removal is proposed. A typical fused silica element was experimentally repaired to verify the process parameters. The repairing rate of small-scale damage was up to 90.4%, and the surface roughness was restored to the level before repairing. The experimental results validate the effectiveness and feasibility of the combined repairing process. This work provides an effective method for the small-scale damage repairing of fused silica components.

A predictable smoothing evolution model for computer-controlled polishing

Quantitative prediction of the smoothing of mid-spatial frequency errors (MSFE) is urgently needed to realize process guidance for computer controlled optical surfacing (CCOS) rather than a qualitative analysis of the processing results. Consequently, a predictable time-dependent model combining process parameters and an error decreasing factor (EDF) were presented in this paper. The basic smoothing theory, solution method and modification of this model were expounded separately and verified by experiments. The experimental results show that the theoretical predicted curve agrees well with the actual smoothing effect. The smoothing evolution model provides certain theoretical support and guidance for the quantitative prediction and parameter selection of the smoothing of MSFE.

Optimized strategy to restrain the mid-spatial-frequency surface error in computer-controlled optical surfacing

In computer-controlled optical surfacing (CCOS), the paths of the lap tools are limited inside the optical surface; this restricts convolution in the dwell-time algorithm and causes mid-spatial-frequency surface errors. An optimized strategy ensuring relatively complete convolution of the dwell-time algorithm is developed to control the mid-spatial-frequency surface error and simultaneously ensure high optical manufacturing efficiency. Different-sized lap tools are then introduced to correct the surface error in different areas of the optics. Simulations and experiments using a large off-axis SiC mirror demonstrate the validity of the strategy, and it could be widely applied to CCOS in grinding or polishing processes.

Pseudo-random Path Generation Algorithms and Strategies for the Surface Quality Improvement of Optical Aspherical Components

This study proposes two path generation algorithms to diminish the superposition of the convolution effect on the polishing path in computer-controlled optical surfacing. According to the polishing of aluminum-alloy based hyperboloid optical components, different proportions of polishing agents were blended. Then, the surface roughness of the optical components were determined through a validation experiment of the algorithms. Furthermore, the relationship between surface roughness and the polishing agent concentration, and the compensation strategies for surface roughness were analyzed. The results show that the two algorithms effectively compensated for surface waviness. The findings support the strategies for improving the surface quality of optical components with aspherical surfaces.