Computer Controlled Optical Surfacing Research Articles

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.

Theoretical and experimental analysis of material removal and surface generation in novel fixed abrasive lapping of optical surface

Abstract Fixed abrasive machining, which overcomes the lack of determinacy and efficiency of current loose abrasive polishing or lapping processes, is an alternative technology for fabricating large-aperture aspheric surfaces with high finishing efficiency and high-quality surface finish. A novel fixed abrasive lapping (NFAL) tool, which combines computer-controlled optical surfacing and conventional fixed abrasive lapping process, is introduced in this study to produce off-axis aspheric surfaces efficiently while surface state is controlled and subsurface damage (SSD) is avoided. The removal mechanism analysis shows that fused quartz glass is primarily removed in ductile regime and the SSD depth is 14.7 μm when the tool load is 25 N. The material removal volume is linear with the machining time under the ductile removal mode. The material removal and surface generation models are developed on the basis of the calculation of the spatial distribution of abrasive particles, the pad–particle–workpiece interactions, the single-particle abrasion mechanism, and the linearly cumulative removal of surface generation in the NFAL process. The models are verified through a series of spot and surface lapping experiments. Results show that the theoretical model can be successfully used to predict and optimize the NFAL process. The spot lapping experiments indicate that the material removal volume is linear with the rotation speed, and the maximum depth is limited to the specific value that depends on the stiffness of lapping tool. The surface roughness Ra and Rz values of the measured and simulated surface data decrease with the increase in feed rate and increase with the increase in raster spacing. The power spectral density analysis indicates that high feed rate can distinctly improve the high-frequency errors, and the selection of the raster spacing can principally affect the low-frequency and middle-spatial frequency errors.

Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics.

In optics fabrication technologies such as computer controlled optical surfacing (CCOS), accurate computation of the dwell time map plays an essential role in the deterministic performance of the fabrication process. However, it is still difficult for existing methods to derive smooth dwell time maps that reduce dynamic stressing on the machine especially at the aperture edge region, while retaining fine correction capability on freeform optics. To answer these challenges, we propose a new method based on Zernike decomposition and improved differential evolution optimization of the dwell time map, which can be applied to time-dependent optics fabrication processes such as fluid jet machining. Simulations and experiments based on a bi-sinusoidal freeform design were carried out to assess the feasibility of the proposed methodology. With appropriate fluid jet pressure, a bi-sinusoidal optical surface with demanding form error target of sub-100 nm in peak-to-valley was achieved, showing a remarkable improvement on the state-of-the-art, while keeping a good average surface roughness of 2.6 nm Ra on the optical glass.

Theoretical and experimental comparisons of the smoothing effects for different multi-layer polishing tools during computer-controlled optical surfacing.

Optical smoothing is a very effective method to restrict mid-to-high spatial frequency errors generated by computer-controlled sub-aperture polishing technologies. According to Preston's equation, pressure distribution is the key factor in describing the smoothing effect of a tool. Although the classic bridging model can solve pressure distribution during the smoothing process, it is only suitable for a tool that consists of a rigid base, compliant interlayer, thin metal plate, and pitch polishing layer. In this paper, a mathematical model applicable for any multi-layer polishing tool is proposed, which helps to calculate the pressure distribution dependent on the thickness of the layer, mid-spatial frequency errors at different periods, and the structures of polishing tools. Based on the model, the pressure distributions and smoothing rates of a rigid tool and a semi-flexible tool are deduced and compared in detail. Validity and improvement in accuracy are verified by comparison with the finite element model. In addition, three groups of experiments using a rigid tool and a semi-flexible tool for smoothing 4mm and 8mm period errors generated by magnetorheological finishing are carried out to validate the model. The simulation result of the smoothing rates of the errors after every smoothing process matches well with the experiment results.

Development and theoretical analysis of novel center-inlet computer-controlled polishing process for high-efficiency polishing of optical surfaces

Although traditional computer-controlled optical surfacing (CCOS) technology has been successfully developed for polishing large aspheric optics, the polishing process continues to pose several challenges, including polishing tool wear and uneven distribution of polishing particles in contact areas. To improve the efficiency and stability of the polishing process, we present a novel center-inlet computer-controlled polishing (CCCP) process and tool for high-efficiency polishing of large-diameter aspheric optics. Compared with traditional CCOS, the most distinctive feature of CCCP is that the polishing slurry is supplied by the central hole of the polishing tool to improve its utilization efficiency. Moreover, a flexible coupling is used to connect the tool and motorized spindle to keep the tool in parallel with the work surface during the polishing process. The experimental apparatus and optimization design of the CCCP tool were first constructed based on CCOS. Then, the material removal mechanisms were explained by a series of theoretical and experimental studies. Results indicated that CCCP can improve the wear resistance of the polishing pad and make fuller and more even abrasive grain supply compared with traditional CCOS. The innovative theoretical model was verified and used for optimizing the epicyclic tool motion in CCCP. The experiments indicated that CCCP can produce a higher material removal rate and a better surface state than can CCOS.

Development of a Cost-Efficient Computer Controlled Optical Surfacing Process for Correcting Aspheric Lenses using Tool Influence Function based Dwelltime Optimization

A Computer Controlled Optical Surfacing (CCOS) system has been developed for correcting form errors on aspheric surfaces. Experiments were carried out to find the correlation between different polishing parameters and polishing metrics such as removal rate, uniformity etc. Based on established polishing parameters, polishing process is developed to correct surface errors on planar, spherical and aspheric surfaces. A convolution model between TIF and dwell times was developed to simulate and solve for correction polishing. Surface accuracies of peak-to-valley (PV) 141 nm and root-mean-squared (RMS) 22 nm has been achieved for planar surface. For aspheric surface, current accuracy of 662 nm PV and of 115 nm RMS is achieved with further development ongoing.

Modeling and experimentation of dynamic material removal characteristics in dual-axis wheel polishing

CCOS (computer-controlled optical surfacing) approach is widely used in different optical polishing processes for making ultra-precision components with high surface form accuracy requirements. Under the polishing mode using complex tool motions, middle-spatial-frequency errors (MSF, i.e., residual ripples) tend to be generated on the workpiece surface, which would deteriorate the functional performance of the parts. In this paper, a dynamical removal model (DRM) based on the spatial kinematic analysis and polishing material removal theory is proposed, to investigate the actual material removal characteristics in dual-axis wheel polishing (DAWP). The model is developed to calculate the overall material removal profile (low-spatial-frequency error, LSF) and the middle-spatial-frequency errors, simultaneously. The shape and the stability of the tool influence function (TIF) are firstly investigated. A series of straight line path polishing tests on BK7 glass are carried out to investigate the effects of process parameters on the generated MSF errors and also check the validity of the proposed DRM. Uniform polishing tests on 50 × 50 mm BK7 samples are conducted, under different polishing parameters, the power spectral density (PSD) characteristics of the surface are also analyzed. The results show that the proposed model can effectively predict the material removal profile and especially the ripple characteristics generated on the surface, which are not reflected when using the conventional convolution algorithm typically used in a CCOS process. When increasing the ratio of feed velocity to co-rotating speed, the wavelength and amplitude of the residual ripples increase, and the ratio of ripple amplitude to total material removal depth also increases. The level of residual ripples can be effectively restrained by the appropriate setting of the speed ratio (reducing the feed velocity or increasing the co-rotating speed).

Modeling of pad surface topography and material removal characteristics for computer-controlled optical surfacing process

Computer-controlled optical surfacing (CCOS) technology is an advantageous polishing process for producing optical surfaces with high convergence rates and high form accuracy, especially for fabricating hard and brittle materials. However, the optimum control of polishing parameters depends critically on the understanding of polishing mechanisms and modeling of material removal characteristics to achieve a deterministic process with high polishing efficiency. Removal analysis still requires further enhancement due to the multi-disciplinary, multi-scale complexity of the material removal mechanism involved in CCOS. Thus, this study presents a novel statistical asperity model and a material removal model to provide scientific and quantitative knowledge of the material removal mechanisms in CCOS. The model is developed on the basis of the research on statistical method, contact mechanics, iterative algorithm, abrasive wear mechanism, and cumulative removal process in CCOS. Practical experiments with different polishing parameters are performed to verify the theoretical model. Simulation results reasonably agree with measured data. Simulation experiments also show that the proposed model helps clarify the effect of pad surface topography on the micro-contact behavior and the material removal characteristics in CCOS and thus forms the theoretical basis for optimizing the polishing process.

Theoretical Study of Path Adaptability Based on Surface Form Error Distribution in Fluid Jet Polishing

In the technology of computer-controlled optical surfacing (CCOS), the convergence of surface form error has a close relationship with the distribution of surface form error, the calculation of dwell time, tool influence function (TIF) and path planning. The distribution of surface form error directly reflects the difference in bulk material removal depth across a to-be-polished surface in subsequent corrective polishing. In this paper, the effect of path spacing and bulk material removal depth on the residual error have been deeply investigated based on basic simulation experiments excluding the interference factors in the actual polishing process. With the relationship among the critical evaluation parameters of the residual error (root-mean-square (RMS) and peak-to-valley (PV)), the path spacing and bulk material removal depth are mathematically characterized by the proposed RMS and PV maps, respectively. Moreover, a variable pitch path self-planning strategy based on the distribution of surface form error is proposed to optimize the residual error distribution. In the proposed strategy, the influence of different bulk material removal depths caused by the distribution of surface form error on residual error is compensated by fine adjustment of the path spacing according to the obtained path spacing optimization models. The simulated experimental results demonstrate that the residual error optimization strategy proposed in this paper can significantly optimize the overall residual error distribution without compromising the convergence speed. The optimized residual error distribution obtained in sub-regions of the polished surface is more uniform than that without optimization and is almost unaffected by the distribution of parent surface form error.

Rapid fabrication strategy for Ø1.5 m off-axis parabolic parts using computer-controlled optical surfacing.

Off-axis parabolic parts (OAPs) or quasi-OAPs are mostly frequently used in large optical telescopes. Compared to the stressed mirror polishing, computer-controlled optical surfacing (CCOS) or other computer-controlled subaperture tools provide more flexibility. However, the fabrication efficiency needs to be promoted in tactical ways. In this paper, we present a large aperture CCOS lap equipped with a compound motion unit and go through the grinding and pre-polishing with its figure errors. A CCOS-based heterocercal tool is first used in large optics to restrain the edge effects. In the fine polishing stage, corrective polishing, smoothing, and ion beam figuring are applied in combination to finish. We experimentally test this strategy on an Ø1.5 m OAP, as a part of giant steerable science mirror (GSSM) in the Thirty Meter Telescope. Finally, the surface error of Ø1.5 m OAP is better than 1/50λ RMS (full aperture), and the mid-spatial frequency part is better than 0.64μrad in slope RMS (effective aperture). The effective fabrication duration is reduced to 2 months.

Restraining mid-spatial-frequency error of large-size off-axis parabolic mirrors by multi-tool NC polishing

The mid-spatial-frequency error (MSFR) of large aperture aspherical optical elements have a direct influence on the precision of the beam diffusion function and the energy scattering of the high energy laser. To solve this problem, we put forward a kind of multi-tool NC polishing technology of computer controlled optical surfacing(CCOS) for effective suppression of MSFR. The polishing process of semi-rigid polishing tool is analyzed by finite element methods, and the polishing process is theoretically simulated based on Bridging model. The experimental results show that the MSFR of large aperture aspherical optical elements can be effectively reduced by multi-tool polishing technology. The wavefront PSD1 value of specific spatial frequency has been restrained effectively. For the two finished 460 mm elements，the wavefront PSD1 value has a 70% descend down to 2.835 nm. Besides, the PV value is less than 0.16 (632.8 nm) and the RMS value is less than 0.02.

Modelling and simulation of mid-spatial-frequency error generation in CCOS

BackgroundThe computer-controlled optical surfacing (CCOS) technology, which has advantages of high certainty and high convergence rate for surface error correction, has been widely applied in the manufacture of large-aperture optical elements. However, due to the convolution effect, the mid-spatial-frequency (MSF) errors are difficult to be restrained in CCOS.MethodsConsequently, this paper presents a theoretical and experimental investigation on the generation of MSF errors, aiming to reveal its main influencing factors, and figure out the optimized parameters and the controlling strategies for restraining MSF errors. A surface topography simulation model for the generation of MSF errors was established first. Based on which, orthogonal simulation experiments were designed and conducted for the following three parameters, i.e., tool influence function (TIF), path type, and path spacing. Subsequently, the proposed model was verified through the practical polishing experiments.Results and conclusionsThe results demonstrated the influencing degree of the parameters and the optimized combination of parameters, and provided process guidance for restraining MSF errors in CCOS.

Characterization of the tool influence function in a dual-axis wheel polishing process to achieve high material removal rates

Various computer controlled optical surfacing (CCOS) processes have been proposed and developed in previous researches for producing ultra-precision optical surfaces, based on the fundamental CCOS principles, i.e., predictable material removal and dwell-time based process control. The main limitation for using the CCOS processes in real industrial applications, however, is the low material removal rates related with most of the CCOS processes, due to the ‘gentle’ tool-workpiece contact feature, resulting in very slow material removal and long process cycle time. This paper presents a novel dual-axis wheel polishing (DAWP) technology using a semi-rigid polishing wheel, designed to achieve high material removal rates and high convergence rates of surface roughness. Modeling for the tool influence function (TIF) was carried out based on the finite element analysis (FEA) and the results of the material property tests, for predicting and characterizing the material removal behavior of the DAWP. Fixed spot polishing experiments on BK7 glass and fused silica were carried out using the DAWP tool, to verify the validity of TIF models and to acquire the variation of TIF and material removal rate under different processing parameters. The experimental results show that the measured and theoretical TIFs match rather well, and the DAWP tool can realize much higher material removal rates on both materials. A BK7 ground flat surface was polished to validate the actual polishing performance of the DAWP tool. After one pass polishing, excellent surface quality was obtained. The preliminary study in this paper shows that, the DAWP tool has a good potential to be used for making large size optical components, significantly increasing the polishing efficiency and reducing the process cycle time.

Positive dwell time algorithm with minimum equal extra material removal in deterministic optical surfacing technology.

In deterministic computer-controlled optical surfacing, accurate dwell time execution by computer numeric control machines is crucial in guaranteeing a high-convergence ratio for the optical surface error. It is necessary to consider the machine dynamics limitations in the numerical dwell time algorithms. In this paper, these constraints on dwell time distribution are analyzed, and a model of the equal extra material removal is established. A positive dwell time algorithm with minimum equal extra material removal is developed. Results of simulations based on deterministic magnetorheological finishing demonstrate the necessity of considering machine dynamics performance and illustrate the validity of the proposed algorithm. Indeed, the algorithm effectively facilitates the determinacy of sub-aperture optical surfacing processes.

Development of multi-pitch tool path in computer-controlled optical surfacing processes

BackgroundTool path in computer-controlled optical surfacing (CCOS) processes has a great effect on middle spatial frequency error in terms of residual ripples. Raster tool path of uniform path pitch is one of the mostly adopted paths, in which smaller path pitch is always desired for restraining residual ripple errors. However, too dense paths cause excessive material removal in lower removal regions deteriorating the form convergence.MethodsWith this in view, we propose a novel tool path planning method named multi-pitch path. With the path, the material removal map is divided into several regions with varied path pitches according to the desired removal depth in each region. The path pitch is designed larger at low removal regions while smaller at high removal regions, and the feeding velocity of the tool is maintained at high level when scanning the whole surface.Results and conclusionsExperiments were conducted to demonstrate this novel tool path planning method, and the results indicate that it can successfully restrain the residual ripples, and meanwhile guarantee favorable convergent rate of form error.

Experimental power spectral density analysis for mid- to high-spatial frequency surface error control.

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of only a few millimeters may degrade the performance of an optical system, causing background noise from scattered light and reducing imaging contrast for large optical systems. Conventionally, the microsurface roughness is often given by the root mean square at a high spatial frequency range, with errors within a 0.5×0.5 mm local surface map with 500×500 pixels. This surface specification is not adequate to fully describe the characteristics for advanced optical systems. The process for controlling and minimizing mid- to high-spatial frequency surface errors with periods of up to ∼2-3 mm was investigated for many optical fabrication conditions using the measured surface power spectral density (PSD) of a finished Zerodur optical surface. Then, the surface PSD was systematically related to various fabrication process parameters, such as the grinding methods, polishing interface materials, and polishing compounds. The retraceable experimental polishing conditions and processes used to produce an optimal optical surface PSD are presented.

Optimization technique for rolled edge control process based on the acentric tool influence functions.

In the process of computer controlled optical surfacing (CCOS), the uncontrollable rolled edge restricts further improvements of the machining accuracy and efficiency. Two reasons are responsible for the rolled edge problem during small tool polishing. One is that the edge areas cannot be processed because of the orbit movement. The other is that changing the tool influence function (TIF) is difficult to compensate for in algorithms, since pressure step appears in the local pressure distribution at the surface edge. In this paper, an acentric tool influence function (A-TIF) is designed to remove the rolled edge after CCOS polishing. The model of A-TIF is analyzed theoretically, and a control point translation dwell time algorithm is used to verify that the full aperture of the workpiece can be covered by the peak removal point of the tool influence functions. Thus, surface residual error in the full aperture can be effectively corrected. Finally, the experiments are carried out. Two fused silica glass samples of 100 mm×100 mm are polished by traditional CCOS and the A-TIF method, respectively. The rolled edge was clearly produced in the sample polished by the traditional CCOS, while residual errors do not show this problem the sample polished by the A-TIF method. Therefore, the rolled edge caused by the traditional CCOS process is successfully suppressed during the A-TIF process. The ability to suppress the rolled edge of the designed A-TIF has been confirmed.

Distortion of removal function based on the local asphericity of aspheric surface and the viscoelasticity of polishing tool in computer-controlled optical surfacing

In the process of large aspheric optical surfaces fabrication, the distortion of the removal function is a big problem that affects the producing efficiency and accuracy, due to the misfit between the tool and the aspheric surface in the contact region. Consequently, this paper aims to find out the influence factors and the distortion rule of aspheric removal function in the computer-controlled optical surfacing. Firstly, based on the analysis of the sub-aperture polishing technology for the large aspheric optical surfaces, the local asphericity of aspheric surface and the viscoelasticity of polishing tool are supposed to be the main sources. After that, a method to calculate the local asphericity considering the misfit between the tool and the aspheric surface is proposed based on the least square method, and the viscoelasticity of the polishing tool is obtained through viscoelastic experiment. Subsequently, combining the results of the local asphericity of aspheric surface and the viscoelasticity of polishing tool, the prediction of the distortion rule of aspheric removal function is presented. Finally, the comparative experiment is carried out, and the removal function on different regions of the aspheric surface is obtained. The experimental result indicated that the distortion of the removal function is consistent with the theoretical result. Through this study, the distortion rule of aspheric removal function in the computer-controlled optical surfacing with pitch tool is finally mastered, which provides a theoretical guidance for the computer-controlled optical surfacing process optimization.

Edge control in a computer controlled optical surfacing process using a heterocercal tool influence function.

Edge effect is regarded as one of the most difficult technical issues in a computer controlled optical surfacing (CCOS) process. Traditional opticians have to even up the consequences of the two following cases. Operating CCOS in a large overhang condition affects the accuracy of material removal, while in a small overhang condition, it achieves a more accurate performance, but leaves a narrow rolled-up edge, which takes time and effort to remove. In order to control the edge residuals in the latter case, we present a new concept of the 'heterocercal' tool influence function (TIF). Generated from compound motion equipment, this type of TIF can 'transfer' the material removal from the inner place to the edge, meanwhile maintaining the high accuracy and efficiency of CCOS. We call it the 'heterocercal' TIF, because of the inspiration from the heterocercal tails of sharks, whose upper lobe provides most of the explosive power. The heterocercal TIF was theoretically analyzed, and physically realized in CCOS facilities. Experimental and simulation results showed good agreement. It enables significant control of the edge effect and convergence of entire surface errors in large tool-to-mirror size-ratio conditions. This improvement will largely help manufacturing efficiency in some extremely large optical system projects, like the tertiary mirror of the Thirty Meter Telescope.