Surface Shape Error Research Articles

Integration of Metrology in Grinding and Polishing Processes for Rotationally Symmetrical Aspherical Surfaces with Optimized Material Removal Functions

Aspherical surfaces, with their varying curvature, minimize aberrations and enhance clarity, making them essential in optics, aerospace, medical devices, and telecommunications. However, manufacturing these surfaces is challenging because of systematic errors in CNC equipment, tool wear, measurement inaccuracies, and environmental disturbances. These issues necessitate precise error compensation to achieve the desired surface shape. Traditional methods for spherical optics are inadequate for aspherical components, making accurate surface shape error detection and compensation crucial. This study integrates advanced metrology with optimized material removal functions in the grinding and polishing processes. By combining numerical control technology, computer technology, and data analysis, we developed CAM software (version 1) tailored for aspherical surfaces. This software uses a compensation correction algorithm to process error data and generate NC programs for machining. Our approach automates and digitizes the grinding and polishing process, improving efficiency and surface accuracy. This advancement enables high-precision mass production of rotationally symmetrical aspherical optical components, addressing existing manufacturing challenges and enhancing optical system performance.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Poloidal magnetic field reconstruction by laser-driven ion-beam trace probe in spherical tokamak

The poloidal magnetic field ( plays a critical role in plasma equilibrium, confinement and transport of magnetic confinement devices. Multiple diagnostic methods are needed to complement each other to obtain a more accurate profile. Recently, the laser-driven ion-beam trace probe (LITP) has been proposed as a promising tool for diagnosing and radial electric field ( ) profiles in tokamaks [Yang X Y et al 2014 Rev. Sci. Instrum. 85 11E429]. The spherical tokamak (ST) is a promising compact device with high plasma beta and naturally large elongation. However, when applying LITP to diagnosing in STs, the larger invalidates the linear reconstruction relationship for conventional tokamaks, necessitating the development of a nonlinear reconstruction principle tailored to STs. This novel approach employs an iterative reconstruction method based on Newton’s method to solve the nonlinear equation. Subsequently, a simulation model to reconstruct the profile of STs is developed and the experimental setup of LITP is designed for EXL-50, a middle-sized ST. Simulation results of the reconstruction show that the relative errors of reconstruction are mostly below 5%. Moreover, even with 5 mm measurement error on beam traces or 1 cm flux surface shape error, the average relative error of reconstruction remains below 15%, initially demonstrating the robustness of LITP in diagnosing profiles in STs.

A hybrid surface shape control method for optimizing thermal deformation of FEL reflection mirror

The surface shape errors induced by thermal deformation of the free electron lasers (FEL) beamline reflection mirror directly affect the quality of FEL beam. In order to reduce the thermal deformation and meet the stringent requirements of surface shape error of the FEL reflection mirror, this paper proposes a surface shape control method that combines mirror bending and active thermal control (ATC) technique, aiming to minimize surface shape errors and enhance the overall performance of the FEL beamline. A bending mechanism has been designed to achieve a bending sensitivity of 60 nrad RMS/N using only one bending actuator. It does not obstruct the FEL beam with extremely small incident angle. This mechanism can compensate for thermal deformation by eliminating the cylindrical surface component of the thermal deformation. Additionally, a novel ATC algorithm is proposed based on the Tikhonov regularization method. When combined with the bending mechanism, it proves effective in controlling the surface shape of the reflection mirror. The simulation results indicate that this surface control method can effectively reduce the surface shape errors of the reflection mirror. Taking the 3 nm wavelength FEL as an example, the RMS value of surface slope error of the reflection mirror is substantially reduced from 17.1974 μrad (with heat load) to 0.0913 μrad after bending. Based on the bending result, the ATC technique further reduces the slope error to 0.0303 μrad RMS. For 1 nm and 2 nm wavelength FELs, the mirror slope errors ultimately reach 0.0147 μrad RMS and 0.0295 μrad RMS respectively. This surface shape control method ensures that the reflection mirror slope errors meet the beamline requirement, which is 0.05 μrad RMS, thereby guaranteeing the beam quality.

Surface shape error modeling in optical machining and tolerance analysis of mosaic aperture telescopes

In the simulation and tolerance analysis of mirror-based optical systems, the magnitude distribution of the surface shape error of each mirror must be established under certain values. Thus, in this study, several large-diameter meter-scale spherical mirrors were statistically processed, and a surface shape error model was constructed to control the RMS, PV, and PV/RMS of the surface shape error in Monte Carlo experiments. The findings show an improved system qualification probability from 69.2% to 99.4%. The proposed method considers the maximum evaluation of the sub-wavefront that eliminates the final co-phase adjustment for individual segments.

Mask-Moving-Lithography-Based High-Precision Surface Fabrication Method for Microlens Arrays.

Microlens arrays, as typical micro-optical elements, effectively enhance the integration and performance of optical systems. The surface shape errors and surface roughness of microlens arrays are the main indicators of their optical characteristics and determine their optical performance. In this study, a mask-moving-projection-lithography-based high-precision surface fabrication method for microlens arrays is proposed, which effectively reduces the surface shape errors and surface roughness of microlens arrays. The pre-exposure technology is used to reduce the development threshold of the photoresist, thus eliminating the impact of the exposure threshold on the surface shape of the microlens. After development, the inverted air bath reflux method is used to bring the microlens array surface to a molten state, effectively eliminating surface protrusions. Experimental results show that the microlens arrays fabricated using this method had a root mean square error of less than 2.8%, and their surface roughness could reach the nanometer level, which effectively improves the fabrication precision for microlens arrays.

Investigation into the Co-Phase Detection Methodology for Segmented Plane Mirrors Utilizing Grazing Incidence Interferometry

Segmented plane mirrors constitute a crucial component in the self-aligned detection process for large-aperture space optical imaging systems. Surface shape errors inherent in segmented plane mirrors primarily manifest as tilt errors and piston errors between sub-mirrors. While the detection and adjustment techniques for tilt errors are well-established, addressing piston errors poses a more formidable challenge. This study introduces a novel approach to achieve long-range, high-precision, and efficient co-phase detection of segmented plane mirrors by proposing a segmented plane mirror shape detection method based on grazing incidence interferometry. This method serves to broaden the detection range of piston errors, mitigate the issue of the 2π ambiguity resulting from piston errors in co-phase detection, and extend the detection capabilities of the interferometer. By manipulating the incident angle of the interferometer, both rough and precise adjustments of the segmented plane mirrors can be effectively executed.

Bidirectional two-degree-of-freedom grating interferometer with biased Littrow configuration

Traditional grating interferometer with Littrow configuration suffer from low optical subdivision factor and high grating base surface shape error. To solve these problems, a grating interferometer with bidirectional Littrow configuration is proposed. Using a high linear density grating of 1800 gr/mm with quadruple optical subdivision is achieved on the optical path. A three-dimensional contour analysis method is proposed to calculate the influence of surface shape error. The experimental result shows that the error of the 10 mm/2 mm displacement test in the X/Z direction fluctuates in the range of ±25 nm, and the actual resolution in the X and Z direction is all 1.5 nm. In summary, the system has good repeatability and high resolution, and can achieve nanoscale displacement measurement in the X/Z direction, and has broad application prospects in the field of precision machining and manufacturing.

Theoretical and experimental investigations on conformal polishing of microstructured surfaces

Microstructured surfaces play a pivotal role in various fields, notably in lighting, diffuser devices, and imaging systems. The performance of these components is intricately related to the accuracy of their shapes and the quality of their surfaces. Although current precision machining technologies are capable of achieving conformal shapes, the post-machining surface quality often remains uncertain. To appropriately address this challenge, this paper introduces a novel conformal polishing methodology, specifically designed to enhance the surface quality of microstructured surfaces while maintaining their shape accuracy. As part of the investigations, specialized tools, namely the damping tool and profiling damping tool, are methodically developed for polishing rectangular and cylindrical surfaces. A shape evolution model is established based on the simulation of individual microstructures, incorporating the concept of finite-slip on the microstructured surface. The findings reveal that principal stresses and velocities experience abrupt variations at the convex and concave corners of rectangular surfaces as well as at the ends of cylindrical surfaces. The numerically predicted surface shape errors after polishing demonstrate reasonably good agreement with experimental results such that their discrepancies are less than 1 μm. Additionally, this method is able to successfully eradicate pre-machining imperfections such as residual tool marks and burrs on the microstructured surfaces. The arithmetic roughness (Ra) of the rectangular surface is measured to be an impressively low 0.4 nm, whereas the cylindrical surface exhibits Ra = 6.2 nm. These results clearly emphasize the effectiveness of the conformal polishing method in achieving high-quality surface finishes.

An Intelligent Detection System for Surface Shape Error of Shaft Workpieces Based on Multi-Sensor Combination

As the main components of mechanical products and important transmission components of mechanical motion, shaft workpieces (SW) need to undergo high-speed motion while also withstanding high torque motion, which has high processing requirements. At the same time, the processing quality of the workpieces determines the success of the entire processing process, and the quality-inspection methods and the accuracy of the technology directly affect the evaluation of the product. This paper designs an intelligent detection system for the surface shape error (SSE) of SW that combines multiple sensors. Based on the principle of sensor use and specific experimental status, the overall scheme of the detection system is designed, followed by research on the spatial positioning algorithm and surface measurement algorithm of the workpiece to be tested. We then compensate and correct the errors with the algorithm. The effectiveness of the system is verified by measuring the surface size of the workpiece. Finally, the radial circular runout error is taken as an example to verify the detection system. The results show that the measurement error is less than 5%, and the accuracy of the system is high.

Surface modeling and influencing factors for microlens array by slow tool servo machining

Microlens arrays (MLAs) are widely used in a variety of important fields due to their unique optical properties. Slow tool servo machining (STSM)technology is a manufacturing technology for machining non-rotationally symmetric surfaces. In order to solve the problems of many influencing factors of STSM machining quality, high experimental trial and error cost, and mutual limitation of accuracy and efficiency, on the basis of analyzing and determining reasonable tool trajectories, a microlens array machining surface morphology prediction model is established from the theoretical point of view, and the prediction model is optimized by combining the two-dimensional Gaussian filtering method, and the surface accuracy and roughness are used to evaluate the processing quality. The prediction model is used to analyze the influence, like feed per revolution, radius of tool tip, and tool setting error on the surface quality. After the Microlens machining experiments, the results are matched with the simulation, which shows us the model is correct, and the MLAs were machined by the optimal parameters with the surface shape error PV = 0.741 μm, surface roughness Sa = 22 nm, Sq = 28 nm, and Sz = 59 nm.

Nano-Precision Processing of NiP Coating by Magnetorheological Finishing.

NiP coating has excellent physicochemical properties and is one of the best materials for coating optical components. When processing NiP coatings on optical components, single-point diamond turning (SPDT) is generally adopted as the first process. However, SPDT turning produces periodic turning patterns on the workpiece, which impacts the optical performance of the component. Magnetorheological finishing (MRF) is a deterministic sub-aperture polishing process based on computer-controlled optical surface forming that can correct surface shape errors and improve the surface quality of workpieces. This paper analyzes the characteristics of NiP coating and develops a magnetorheological fluid specifically for the processing of NiP coating. Based on the basic Preston principle, a material removal model for the MRF polishing of NiP coating was established, and the MRF manufacturing process was optimized by orthogonal tests. The optimized MRF polishing process quickly removes the SPDT turning tool pattern from the NiP coating surface and corrects surface profile errors. At the same time, the surface quality of the NiP coating has also been improved, with the surface roughness increasing from Ra 2.054 nm for SPDT turning to Ra 0.705 nm.

Modeling and Experimental Verification of Time-Controlled Grinding Removal Function for Optical Components.

As a flexible grinding method with high efficiency, abrasive belt grinding has been widely used in the machining of mechanical parts. However, abrasive belt grinding has not been well applied in the field of ultra-precision optical processing, due to the lack of a stable and controllable removal function. In this paper, based on the idea of deterministic machining, the time-controlled grinding (TCG) method based on the abrasive belt as a machining tool was applied to the deterministic machining of optical components. Firstly, based on the Preston equation, a theoretical model of the TCG removal function was established. Secondly, removal function experiments were carried out to verify the validity and robustness of the theoretical removal model. Further, theoretical and actual shaping experiments were carried out on 200 mm × 200 mm flat glass-ceramic. The results show that the surface shape error converged from 6.497 μm PV and 1.318 μm RMS to 5.397 μm PV and 1.115 μm RMS. The theoretical and experimental results are consistent. In addition, the surface roughness improved from 271 to 143 nm Ra. The results validate the concept that the removal function model established in this paper can guide the actual shaping experiments of TCG, which is expected to be applied to the deterministic machining of large-diameter optical components.

Surface generating mechanism in surface shape error control for thin copper plate with large-diameter based on chemical mechanical lapping

As metal plane flyer, pure copper thin plate is required with extremely low surface shape error. To achieve this goal, some researchers make a significant attempt to develop a deterministic full-aperture polishing/lapping process. However, the detail relationship of surface shape error and vital machining parameter such as machining time which benefits machining efficiency promotion is not given. Besides, the error rate of surface shape error prediction is high. To solve this problem, the surface shape prediction model considering the influence of pressure and relative velocity distribution on material removal amount is established for thin copper plate. Through the product of pressure distribution, relative velocity distribution, Preston coefficient k and machining time T, material removal distribution is obtained. According to initial surface shape characteristic, through targeted adjustment of eccentricity, lapping pad rotation speed, workpiece rotation speed to control pressure and relative velocity distribution, suitable material removal distribution is formed to smooth surface radial profile, realizing deterministic control of surface shape error. By above method, the flatness of pure copper thin plate (Φ200 mm × 2.2 mm) decreases from PV 54.8 μm to PV 1.9 μm with mean error rate of surface shape error prediction <10 %, realizing deterministic control of surface shape error.

Innovative process for precise grinding of optical free-form elements

The aim of the presented article is to share experience gained throughout the course of two projects focused on precise grinding of a free-form glass optical element with the objective of achieving a surface shape error of less than approximately 10 μm PV before the subsequent polishing phases. Compared to spheres or aspheres machining, it is considerably more demanding, mainly due to the impossibility of using rotationally symmetric shape corrections. The developed and tested process combines a mechanical engineering approach based on the use of the current Computer Aided Design and Computer Aided Manufacturing software with their respective strengths and weaknesses and an optical engineering approach, for which the employment of CNC machines featuring precise control but low flexibility is typical. Therefore, attention is paid mainly to the description of particular process steps like CAD construction and CNC grinding step programming with regard to the necessary software and data handling, as well as the required parametrisation of the used machine equipment.

Compensation machining of freeform based on fast tool servo system.

With the advantages of large field of view, low cost and simple structure, the freeform optical system has extensive requirements in space exploration and other fields. However, the current machining methods for freeform are difficult to meet the requirements of optical use. Based on a developed fast servo tool (FTS) device, this paper proposes an error compensation turning method for freeforms. Firstly, the Zernike polynomial fitting method is used to reconstruct the freeform surface shape error obtained from off-line measurement, and the offset compensation is used to correct the tool path. Then, the compensation processing physical system is built to simulate the off-line compensation processing of the workpiece to verify the feasibility of compensation processing. Finally, the turning compensation processing of convex freeform aluminum mirror is carried out, and the surface accuracy of the workpiece meets the requirements of visible band. The research results have important practical significance for realizing the fast response machining of free-form surface mirror.

Multi-Objective Parametric Optimization Design for Mirrors Combined with Non-Dominated Sorting Genetic Algorithm

The process of intelligent multi-objective parametric optimization design for mirrors is discussed in detail in this paper, with the error of the mirror surface shape and the total mass being examined as the optimization objectives. The establishment of complex objective functions for solving the optimization problem of the mirror surface shape error was realized, and manual modification of the model was avoided. Moreover, combining this with a non-dominated sorting genetic algorithm (NSGA) helped the Pareto front move towards an ideal optimal set of solutions. To verify the effectiveness of the proposed method, an aluminum alloy mirror with an aperture of 140 mm was taken as an example. The Pareto optimal solution set of the mass and surface shape error under 1 g gravity was obtained for finding the required solution and satisfying the optimization goal. In addition, this method is applicable to other complex structural design problems.

Technology for developing a high-aperture four-mirror lens with aspherical mirrors

Subject of study: Methods for optimizing the design, assembly, and alignment of a high-aperture wide-angle four-mirror axisymmetric lens are presented. Aim of study: The aim is the development of a high-tech lens design considering the relationship between the calculated tolerances for the decentering of mirrors and the technological capabilities of their fabrication, assembly, and alignment. Method: The methods include selection of an image quality criterion and calculation of its permissible decrease, distribution of the fabrication errors between the decentering errors and surface shape errors, and calculation of the tolerances based on the obtained ratios. Moreover, the motivation for choosing a lens design with a minimum number of adjustment stages based on the optimization of the calculated permissible decentering is provided considering the technological tolerances for positioning the optical elements. In addition, the possibilities of the scheme to compensate for the residual aberrations resulting from the fabrication and positioning of the mirrors are investigated. At the final stage, the method of reducing the evaluation function for the final adjustment of the optical elements in the lens is used. Main results: The design and technological solutions enabling the optimization of the requirements for the tolerances for deviation of the surface shape of the mirrors from their calculated profile, as well as decentering of the optical elements considering the technological capabilities of production, are examined. The criteria for the distribution of tolerances for permissible deviations of optical system parameters affecting the image quality are formulated. The possibility of designing a high-tech drop-in structure of a high-aperture four-mirror lens comprising a case of two blocks and a single linear adjustment stage of the second mirror to compensate for residual aberrations is demonstrated using the proposed method. Practical significance: The proposed technical solutions were tested by designing a high-resolution lens comprising four aspherical mirrors. The positive results of fabricating a lens with a high aperture and resolution allow the proposed solutions to be used for the design of multimirror axisymmetric lenses.

The measurement method of heliostat surface shape error based on photogrammetry

The measurement method of heliostat surface shape error based on photogrammetry

Design of a metal-based deformable mirror for orthogonal beam deflection and highly dynamic beam oscillation.

We report on an opto-mechanical metal mirror design for highly dynamic, diffraction-limited focus shifting. Here, the mechanical geometry of the membrane is of crucial interest as it must provide sufficient optical performance to allow for diffraction limited focussing and have a high mechanical eigenfrequency to provide dynamic motions. The approach is the analytical consideration of the plate theory and provides the basis for a parameterized finite element model. By means of an finite element analysis (FEA), essential steps for the optimization of the mirror design with respect to a wide range of optical power and a high operating frequency are shown. To verify the results of the FE analysis, the deformed surface is decomposed into Zernike coefficients. An analysis of the point spread function is performed to evaluate the optical performance. For dynamic evaluation a modal and a harmonic vibration analysis are conducted. The opto-mechanical design allows a biconical deformation of the mirror surface, enabling the generation of a diffraction-limited spot diameter in the adjustment range of ±1.2 dpt. The surface shape error in this range is 53 nm. The dynamic analysis shows the first excited eigenfrequency at 21.6 kHz and a diffraction-limited operation frequency at 9.5 kHz. This paper provides an alternative design approach for highly dynamic beam oscillation in the Z direction, forming a complement to highly dynamic X-Y scanning systems.