Surface Figure Error Research Articles

Testing of spherical mirrors with extremely large R numbers using a quasi-autocollimation method.

Spherical mirrors with large R numbers have extreme advantages in optical systems with large apertures and long focus lengths for improving imaging resolution and field of view. Their manufacturing and testing accuracy directly affects the final wavefront aberration of the systems. However, due to the influence of airflow disturbance in the long optical path, testing large R number spherical mirrors with high precision is difficult for the direct testing method. In this paper, a quasi-autocollimation test (QACT) method is proposed based on the consistency and reverse compensation between sphere and paraboloid with large R numbers. In QACT, the length of the testing path is reduced to half, and the test sensitivity of the surface figure error is doubled. According to the Kolmogorov turbulence theory, the suppressed degree of QACT to airflow disturbance is quantitatively evaluated, and QACT can suppress the random error in test to 35%. A comparative experiment between direct test and QACT method is carried out on a ∅100 spherical mirror with 8-meter radius of curvature. Airflow disturbance in the testing environment is calculated by mathematical fitting and the repeated accuracy is improved from 4 nm to 1.4 nm in a single test using the QACT method, which is consistent with theoretical analysis. The research results will provide a new strategy for ultra-precision and efficiency tests of large R number spherical mirrors.

Optimization of the Morphology of the Removal Function for Rotating Abrasive Water Jet Polishing.

Abrasive water jet polishing has significant advantages in the manufacturing of complex optical components (such as high-slope optical component cavities) that require high-precision manufacturing. This is due to its processing process, in which the polishing tool does not make direct contact with the surface of the workpiece, and instead maintains a considerable distance. However, the removal functions of most existing abrasive water-jet polishing technologies do not possess strict symmetry, which significantly impacts the ability to correct surface figure errors. Therefore, this study implements rotating abrasive water-jet polishing based on traditional abrasive water jet processing to optimize the removal function, which turns it into a Gaussian form; thus, obtaining a type of removal function more suitable for CCOS polishing. This paper derives an empirical formula between the distance s' from the peak removal point of the removal function to the stagnation point and the nozzle tilt angle α, based on geometric relationships and experimental results, analyzes the relationship between material removal efficiency, nozzle tilt angle, and standoff distance. Finally, this paper verifies through experiments the validity of this empirical formula under different process parameters. Therefore, this study obtains the process conditions that allow rotating abrasive water-jet polishing technology to achieve a stable Gaussian form removal function, and the appropriate process parameters to be selected in conjunction with polishing efficiency; thereby, effectively improving the removal function's corrective ability and manufacturing efficiency. It provides theoretical support for the processing capability and process parameter selection of abrasive water-jet polishing technology, solves the problem of limited shaping capability of existing abrasive water jet tools, and significantly improves the manufacturing capability of high-end optical components.

Adaptive Petal Reflector: In-Lab Software Configurable Optical Testing System Metrology and Modal Wavefront Reconstruction.

This paper addresses two aspects of the metrology of spherical, petal polymer reflectors which are part of an effort by the European Space Agency (ESA) to develop actively controlled foldable reflectors, enabling larger apertures on CubeSats and small satellites. The first problem is that of measuring the surface figure error of the spherical reflector alone during the development phase, and to assess the quality before assembling the telescope (large stroke, low accuracy). The SCOTS (Software Configurable Optical Testing System) appears to provide a fast and satisfactory solution to this problem. The second problem is the wavefront error reconstruction when the petal reflector is mounted on the telescope, because parts of the petals are obscured by the secondary mirror, in such a way that the petals appear completely disconnected, making the gradient-based metrology impossible. Using the fact that the petals have common mechanical boundary conditions at the central support ring, the problem is solved by using a set of orthogonal modes satisfying the same boundary conditions. The vibration modes are used for this purpose; the modal amplitudes are reconstructed from slope data outside the obstruction, allowing for wavefront error reconstruction over the entire surface.

Highly efficient method for cutting position selection of an x-ray mono-capillary lens based on an improved SCA-CSA algorithm.

In order to efficiently select the optimal cutting position of x-ray mono-capillary lenses, an improved sine cosine algorithm-crow search algorithm (SCA-CSA) algorithm is proposed, which combines the sine cosine algorithm with the crow search algorithm, with further enhancements. The fabricated capillary profile is measured using an optical profiler; then the surface figure error for interest regions of the mono-capillary can be evaluated using the improved SCA-CSA algorithm. The experimental results indicate that the surface figure error in the final capillary cut region is about 0.138µm, and the runtime is 2.284s. When compared with the traditional metaheuristic algorithm, the particle swarm optimization algorithm, the improved SCA-CSA algorithm, enhances the surface figure error metric by two orders of magnitude. Furthermore, the standard deviation index of the surface figure error metric for 30 runs also improves by more than 10 orders of magnitude, demonstrating the superior performance and robustness of the algorithm. The proposed method provides significant support for the development of precise cuttings of mono-capillaries.

Surface figure compensation of the primary mirror in a Ritchey-Chrétien space telescope by spring preloads.

To reduce the surface figure error induced by mechanical strains during the integration process of a high-precision mirror, a cost-efficient compensation method by spring preloads is proposed. The study is based on the primary mirror of a Ritchey-Chrétien space telescope with a focal length of 1200mm. First, the surface figure degradation of the mirror during the assembly process is expressed and analyzed. Then, a finite element model of the mirror and its mounting structure is established, and surface deformations caused by different preloading forces are simulated. An optimized combination of different preloads was obtained through data fitting, and the influence of the combined preload on the mirror was analyzed. The simulation results show that ring preloads mainly affect spherical aberration and high-order spherical aberrations, while quadrupole preloads mainly affect astigmatism, and the optimized preload can compensate for the surface figure error from 0.120λ RMS to 0.088λ RMS. Last, the surface figure error of the mirror is measured by experiments under optimized preloads, and the result is 0.084λ RMS, which verifies the correctness of the analysis process and effectiveness of the compensation method.

Challenges and strategies in high-accuracy manufacturing of the world’s largest SiC aspheric mirror

In the process of manufacturing the world’s largest silicon carbide (SiC) aspheric mirror, the primary difficulties are mirror blank preparation, asphere fabrication, and testing, as well as cladding and coating. Specifically, the challenges include the homogeneity of the complicated structure casting, accuracy and efficiency of the fabrication process, print-through effect, fidelity and precision of test procedure, stress and denseness of cladding process, the dynamic range of interferometric measurement, and air turbulence error due to the long optical path. To break through such a barrier of difficulties, we proposed the water-soluble room temperature vanishing mold and gel casting technology, homogeneous microstructure reaction-formed joint technology, nano-accuracy efficient compound fabrication, gravity unloading technology, high-denseness low-defect physical vapor deposition (PVD) Si-cladding technology, test data fusion method, and time-domain averaging method, etc. Based on the proposed technologies and methods, we have accomplished the world’s largest SiC aspheric mirror with a size of ⌀4.03 m. The impressive performance of the SiC aspheric mirror is validated by the characteristics of the fabricated SiC aspheric mirror. The aerial density of the SiC blank is less than 120 kg/m2, surface shape test accuracy is better than 6 nm RMS, thickness inhomogeneity of the cladding layer is less than 5%, and the final surface figure error and roughness are 15.2 nm RMS and 0.8 nm RMS, respectively.

Local tolerance and quality evaluation for optical surfaces

The manufacture of high-precision surfaces is the foundation of building high-performance optical systems. For over 50 years, the tolerance for optical surfaces has been specified by the root-mean-square (rms) or peak-to-valley (PV) value over the entire surface geometry. However, different regions on optical surfaces do not contribute equally to image quality and, thus, can tolerate different levels of errors. A global tolerance described by a single or few parameters cannot precisely provide the manufacturing requirements of each region on the surface, which may result in unnecessary accuracy specifications for surfaces. Furthermore, the components with the same PV or rms figure errors can produce different imaging qualities; however, this difference cannot be distinguished by the conventional figure of merit. To address these problems, a framework that includes a local tolerance model and a quality merit function for optical surfaces is proposed. The local tolerance model can provide an accurate tolerance for each region on the surface so the targeted wave aberration requirements are met during components manufacturing. More importantly, the proposed merit function closely ties the surface figure error to imaging performance, e.g., the findings can explain that the component with lower geometric accuracy may produce better imaging quality. This framework provides new insights into optical design, manufacture, and metrology and especially paves the way for the manufacture of high-precision large-aperture systems.

Adaptive Deployable Thin Spherical Shell Reflectors

This paper begins with a quick survey of potential space applications and a brief review of previous experiments on the shape control of a spherical shell reflector with a thin film of PVDF-TrFE. Next, the problem of thermal sensitivity is addressed numerically; it is found that, because of the large thermal expansion of the active material, the surface figure error generated by a linear thermal gradient on a unimorph reflector is considerable and its correction requires large control voltages. The surface figure accuracy can be greatly improved by a balanced design (i.e., adding a passive layer symmetrical to the PVDF-TrFE layer) and using a low CTE substrate. Finally, the paper considers a petal reflector; the unimorph design is even more sensitive than the full reflector to the thermal gradient, but the balanced design turns out to be better than the full reflector, both from the point of view of the surface figure error and the control voltages.

Three orientations method for extracting zero-gravity surface figure of a mirror

Zero-gravity surface figure testing is important for space optical elements. We propose the three orientations method (TOM) to achieve this goal. The optical element is rotated according to the proposed degree of freedom, and we calculate its zero-gravity surface figure by any three rotation angles (θ1, θ2, and θ3) and their corresponding surface figures (S1, S2, and S3). The algorithm of TOM can also be applied to the face-up/face-down test and horizontal rotation test. Theoretically, TOM can get an absolute zero-gravity surface figure; however, a rotation angle error can result in a zero-gravity surface figure error. The surface figure model (SFM) and gravity-included angle model (GAM) are proposed to analyze the relationship between the rotation angle error and zero-gravity surface figure error. For numerical results, SFM is equivalent to GAM. In addition, GAM addresses the zero-gravity surface figure error, which is induced by the rotation angle error, also being regarded as a surface figure, which is caused by a certain amount of gravity. For all models, we provide both theoretical derivations and numerical examples.

Astigmatism correction of convex aspheres using the subaperture stitching hindle test

We propose an astigmatism correction method for the subaperture stitching Hindle test to measure hyperbolic convex aspheres. Astigmatic wavefront errors arise from misaligned Hindle setups, mechanical runout errors of the rotational motion for stitching, and the surface error of the target itself. Because these errors are combined, they cannot be separated in the conventional subaperture stitching Hindle tests. We exploited the rotational periodicity of each error to distinguish the surface figure error from other astigmatic error sources and rectified the Hindle test results with a third-order astigmatism. Using the subaperture stitching Hindle test, we averaged two sets of measurement data with a 180° rotational phase difference between them to calculate the astigmatic surface error. The proposed method was verified experimentally by comparing it with the results from a commercial stitching interferometer from QED Technologies; only subnanometer differences in the root-mean-square values were obtained. Therefore, the proposed method calibrated the system errors from the test surface wedge and the rotational decenter easily, thereby reducing the mechanical costs and alignment efforts and making it more accessible than a sophisticated mechanism.

Surface form error measurement for rough surfaces using an infrared lateral shearing interferometry

The fabrication of a large monolithic mirror or a segmented mirror requires a high throughput that satisfies the time-cost requirement. Particularly, the rough surface properties of grinding pose a challenge for accurate measurement of the surface figure error (SFE). If the SFE during grinding is as small as possible, the material removal volume in the figuring process gets reduced, and the total required time of the fabrication is greatly minimized. In this paper, we propose a new metrology tool called intermediate surface figure error measurement (ISFEM) that can be applied to measurement of SFE for rough surfaces. It consists of a CO2 laser of wavelength 10.6 µm as a light source, a lateral shearing interferometer as a wavefront sensor, and several optical components for beam shaping and imaging. The ISFEM demonstrated its ability to measure the microns to sub-micron rms SFE of the ground surface by testing the samples with a 0.59 µm -1.56 µm rms of surface roughness and a large SFE of about 3 µm rms. The system was applied to the fabrication of an off-axis parabolic mirror of diameter 1.1 m, where it successfully performed as an intermediate metrology between laser tracker measurement for the rough surface and interferometric measurement for the polished surface. The ISFEM obtained measurements from 3.88 µm rms SFE during the fine grinding process and down to 0.38 µm rms during the polishing process. Therefore, we confirmed that the ISFEM provides a unique solution for high throughput for the fabrication of large or multiple segmented mirrors.

Atmospheric Plasma Jet processing for figure error correction of an optical element made from S-BSL7

To meet the increasing market demand for optical components, Plasma Jet Machining (PJM) of Borosilicate Crown Glass (BCG), which can be an alternative to Fused Silica, is presented. Surface figure error correction was performed by applying reactive plasma jet etching, where a fluorine-containing microwave driven plasma jet is employed to reduce the figure error in a deterministic dwell-time controlled dry etching process. However, some of the glass constituents of BCG cause the formation of a residual layer during surface treatment which influences the local material removal. By heating the substrate to about TS = 325 °C to 350 °C during processing, the etching behavior can clearly be improved. Geometric conditions of the optical element nevertheless lead to a characteristic temperature distribution on the substrate surface, which requires an adjustment of the local dwell times in order to obtain the required material removal. Furthermore, the resulting local surface roughness is also influenced by the surface temperature distribution. It is shown that figure error can be significantly reduced by taking the local temperature distribution and resulting local etching rates into account. A subsequent polishing step smoothens roughness features occurring during etching to provide optical surface quality.

Optimization design of an ultralight large-aperture space mirror.

The ultralight space mirror has long been a hot topic in the research field of space telescopes. In this paper, an ultralight mirror is designed by obtaining the structure and parameters of a mirror with an aperture of 2 m through experimental design and multiobjective integrated optimization. Specifically, the materials near the neutral surface were replaced with elliptical holes. The back of the mirror was supported at three points. Finite-element analysis shows that the mirror had a surface figure error of 10.4 nm under 1 g in the x direction (gravity direction), which is sufficiently high to be applied to visible light optical systems. Further, the eigenfrequencies of mirror components were obtained through finite-element analysis: 70 Hz in the x direction, 70 Hz in the y direction, and 90 Hz in the z direction. The results demonstrate the excellent dynamics performance of the designed mirror. Compared with test results, the relative error of eigenfrequencies was within 4%. Hence, our ultralight design outputs reliable optimization results and applies to the development of large-aperture ultralight space mirrors. Finally, the ultralight mirror was prepared from reaction-bonded silicon carbide. The mass and surface density of the prepared mirror were 105 kg and 34kg/m2, respectively. The mirror mass was 50% lighter than that of the mirrors designed by traditional lightweight methods.

Measuring large amplitude surface figure error using coordinate metrology

Advances in optical testing are as important as advances in fabrication because one can make only what one can measure. A high-precision metrology capability is utilized to close the gap between interferometric testing and lower precision metrology, laser radar, or contact-probe-based coordinate measuring machines (CMM) to accurately measure surfaces with large form error. This nearly universal optical testing method employs a precision CMM equipped with a non-contact, confocal probe. This technique was developed to characterize and align a broad spectrum of optical surfaces including ones with high slopes that are nearly impossible to measure using traditional interferometric testing without custom-made optics. Optical components covering a wide range of prescriptions, such as large convex conics, high-sloped aspherics, grazing-incidence x-ray optics, and highly deformed flats, were successfully measured. The resulting data were processed using custom-developed routines to determine the optic’s alignment, the departure from design surface, and the as-built prescription parameters. This information was used to verify and guide the development and fabrication of novel optics.

Interferometric measurement of high-order aspheric surface parameter errors based on a virtual-real combination iterative algorithm.

Aspheric surface parameters, including vertex radius of curvature, conic constant, and high-order aspheric coefficients, decide the optical properties of aspheric surfaces. The measurement of aspheric surface parameter errors (SPEs) is a substantial issue for the fabrication of aspheric surfaces. Interferometry is a mature high-accuracy method in aspheric surface figure error measurement, but challenges still exist in the measurement of SPEs for high-order aspheric surfaces or convex aspheric surfaces. We propose an interferometric measurement method for high-order aspheric SPEs based on a virtual-real combination iterative algorithm (VRCIA). We also propose a recommended measurement system including a partial compensation interferometer to obtain the partial compensated wavefront and a laser differential confocal system to obtain the best compensation distance for calculating SPEs through the VRCIA. A high-order convex aspheric surface is measured to demonstrate the feasibility of the method. The relative accuracy of vertex radius of curvature error, conic constant error and fourth-order aspheric coefficient error can reach 0.025%, 0.095% and 3.02%, respectively.

Design method of wide field-of-view imaging systems using Gaussian radial basis functions freeform surfaces.

High optical performance systems with wide field-of-view (FOV) have important applications in remote sensing. The radial basis functions, which have a prominent local characteristic in surface description, have attracted much attention in recent years. In this paper, an effective design method for the wide FOV imaging system using Gaussian radial basis function freeform surfaces is proposed. The FOV of the optical system is extended from a relatively small value to a larger one, and the Gaussian radial basis function surfaces are extended stepwise based on certain criteria. A high image quality and small distortion off-axis freeform three-mirror system with a wide FOV (${{60}}^\circ \times {0.6}^\circ$) is designed as an example. Tolerance analysis considering both surface figure error and assembly error is performed. The design results demonstrate the effectiveness of the proposed method.

Active alignment of complex perturbed pupil-offset off-axis telescopes using the extension of nodal aberration theory

This paper presents an optical alignment strategy for complex perturbed pupil-offset off-axis reflective telescopes, based on the extension of nodal aberration theory (NAT). First, the direct expansion of the wave aberration function in the vector form for perturbed off-axis systems is given, which is especially convenient for the expansion of the corresponding higher-order terms. The inherent vector relationships between the contributions generated by the aberrations of the on-axis parent systems through pupil transformation are disclosed in detail, which is helpful to understand the aberration behavior of off-axis systems. Then, according to the inherent vector relationships, an analytical alignment model based on NAT for complex cases of perturbed off-axis telescopes is established. It can quantitatively separate the effects of misalignments and surface figure errors from the total aberration fields. The alignment model is solved by using particle swarm optimization algorithm. Then, an optical alignment example of the off-axis three-mirror anastigmatic telescope with misalignments and complex surface figure errors based on the proposed method is demonstrated. After correction, the perturbed telescope can be nearly restored to the nominal states. Finally, Monte Carlo simulations are carried out to show the effectiveness and accuracy of the proposed method.

Calculation of Effect Ratio of 21 Geometric Errors and Detection of Surface Figure Error

Traditionally, a machine tool is regarded as a rigid-multi body system, and it is studied by integrated geometric error modeling. Considering a three axis-machine, this study introduced the ratio and effects of the geometric errors on the surface figure error. First, based on synchronous iteration location, a surface matching model was employed to assess the coordinate measurement result. Subsequently, considering all the geometric error functions having the same parameters, the effect ratio and the surface figure error of a single geometric error were obtained. Concurrently, based on the effect ratio and surface figure error results, the main geometric errors were obtained, such as EZX, EZY, EAX, and COY. Moreover, the proposed method and the main errors were experimentally verified. By compensating the main errors, the sphere accuracy was improved by 53.4% and the flat accuracy by 70.0%. Additionally, the method proposed in this paper could be utilized to detect the surface figure error.

Simultaneous phase-shifting interferometer with a monitored spatial light modulator flexible reference mirror.

A simultaneous phase-shifting interferometer with a monitored spatial light modulator (SLM) flexible reference mirror is proposed to balance the flexibility and accuracy of aspheric-surface in-process measurements. In this method, polarization simultaneous phase-shifting camera systems are applied to reduce the influence of environmental vibrations on the in-process measurements. An SLM reference mirror is employed to improve the flexibility of in-process measurements. A device is integrated to monitor the SLM surface in order to improve measurement accuracy caused by the spatial phase nonuniformity and modulation instability of the SLM. Thus, the SLM surface is monitored and the aspheric surface is measured simultaneously in only one interferometer, which presents the advantages of a compact structure and simple calibration. A flat acrylic mirror with an unknown surface figure error is measured by the proposed interferometer. Cross tests demonstrate the feasibility of this interferometer.

Study of Epoxy Bonding

Bonding is used widely when the optical glasses are connected with metal structures. It plays a very important role in the design of space telescope. Improper bonding may induce great surface figure error for optics in telescope. Milbond and EC2216 are the most popular epoxies that are used in optics. Bubbles usually exist in the epoxy when two components are mixed or translated to syringe. In this paper, the methods and experiments of adhesive mixture and injection in vacuum environment were explained to reduce the bonding surface figure of the mirror. The results show that adhesive mixture and injection in vacuum environment can dramatically decrease the bubble in the epoxy and greatly reduce the bonding surface figure error.