Embedded parallel-actuated technology for deformable space segmented mirror.

The deployable segmented space imaging system is an important solution for future ultra-large aperture space optical systems. To achieve the imaging capability of an equivalent aperture monolithic mirror, it requires not only to ensure the positional accuracy in the cophasing process, but also to have extremely high surface accuracy and curvature consistency of the sub-mirrors. However, this work is extremely challenging due to the manufacturing error of the sub-mirrors and the complex space environment. Active optical technology can ensure the surface shape accuracy of the spliced mirror by controlling the mirror surface deformation and compensating for the wavefront aberration. This article compares and analyzes the control ability of two types of deformable mirrors actuated by vertical and parallel methods. We explored the characteristics of the influence function mathematical models of the two types of actuation forms and compared the aberration and curvature correction abilities of them through finite element analysis, summarizing the advantages of the parallel actuation forms. Finally, a 300mm aperture embedded parallel-actuated deformable mirror was designed and manufactured, and relevant experiments were conducted to verify its adjustment ability. By comparing and analyzing the experimental results with the design results, the adjustment ability of the embedded parallel-actuated deformable mirror was verified.

Accurately predicting the tool influence function to achieve high-precision magnetorheological finishing using robots.

Industrial robots with six degrees-of-freedom have significant potential for use in optical manufacturing owing to their flexibility, low cost, and high space utilisation. However, the low trajectory accuracy of robots affects the manufacturing accuracy of optical components when combined with magnetorheological finishing (MRF). Moreover, general robot trajectory-error compensation methods cannot compensate for the running errors of large robots with high precision. To address this problem, a three-dimensional (3D) tool influence function (TIF) model based on inverse distance interpolation is developed in this study to accurately predict the TIF of different polishing gaps. A high-precision robot-MRF polishing strategy based on variable TIFs and surface shape accuracy of polished optics is proposed to achieve high-precision manufacturing without compensating for trajectory errors. Subsequently, the accuracy of a ϕ420 mm fused silica mirror is experimentally verified to be from 0.11 λ RMS to 0.013 λ RMS. This validates that the robot-MRF can achieve high-precision polishing without compensating for trajectory errors. Furthermore, the proposed model will promote the applications of industrial robots in optical manufacturing and will serve as a reference in the field of intelligent optical manufacturing.

Discontinuous phase unwrapping based on the minimization of Zernike gradient polynomial residual.

In many certain optical metrology cases, the pupil is usually divided into multiple connected domains by secondary mirror spiders, thus producing segment piston errors and leaving a false phase unwrapping result. In this paper, a method based on minimization of Zernike gradient polynomial residual (MZGR) is proposed to estimate segment piston errors and correct erroneous phase unwrapping results. Simulations and experiments demonstrated that this method can obtain the segment piston errors precisely under complex aberration forms and varied obscurations, indicating reliable practicality. Comparison to the 4D commercial solution, the RMS (root-mean-square) of the residual decreased from 0.154 λ to 0.020 λ.

High-precision magnetorheological finishing based on robot by measuring and compensating trajectory error.

The 6-DOF industrial robot has wide application prospects in the field of optical manufacturing because of its high degrees of freedom, low cost, and high space utilisation. However, the low trajectory accuracy of robots will affect the manufacturing accuracy of optical components when the robots and magnetorheological finishing (MRF) are combined. In this study, aiming at the problem of the diversity of trajectory error sources of robot-MRF, a continuous high-precision spatial dynamic trajectory error measurement system was established to measure the trajectory error accurately, and a step-by-step and multistage iterations trajectory error compensation method based on spatial similarity was established to obtain a high-precision trajectory. The experimental results show that compared with the common model calibration method and general non-model calibration method, this trajectory error compensation method can achieve accurate compensation of the trajectory error of the robot-MRF, and the trajectory accuracy of the Z-axis is improved from PV > 0.2 mm to PV < 0.1 mm. Furthermore, the finishing accuracy of the plane mirror from 0.066λ to 0.016λ RMS and the finishing accuracy of the spherical mirror from 0.184λ RMS to 0.013λ RMS using the compensated robot-MRF prove that the robot-MRF has the ability of high-precision polishing. This promotes the application of industrial robots in the field of optical manufacturing and lays the foundation for intelligent optical manufacturing.

Stress-induced deformation of the coating on large lightweight freeform optics.

Large aperture, lightweight optics are frequently utilized in modern optical systems. However, despite the use of advanced techniques for developing their materials, fabrication, and mechanical structure, the coatings placed on the substrates induce slight lattice mismatches and increase the thin film stress on polished surfaces. This significantly distorts nano-accuracy optical surfaces, especially on lightweight freeform surfaces. In this study, we construct a finite element model (FEM) and a ray tracing model to estimate the impact of the stress-induced deformation of the coating on a 1.5m class lightweight silicon carbine (SiC) mirror with a freeform surface. Our simulation results are within 10% deviation from the experimental results, and the deformation texture map matches these results as well. We discuss several possible strategies to overcome stress-induced deformation, including fabrication pre-compensation, lightweight structure redesign, and an inverse print-through effect.

Equivalent thin-plate method for stressed mirror polishing of an off-axis aspheric silicon carbide lightweight mirror.

No physical model of stressed mirror polishing, based on the small deflection and deformation of elastic thin plates, has been applied in processing lightweight mirrors. We propose an equivalent thin-plate method for the stressed loading of lightweight mirrors for the first time. Stressed loading and polishing of an aspheric lightweight mirror are simulated using the small-deflection deformation theory of an elastic thin plate. We simulate off-axis aspheric silicon carbide (SiC) lightweight mirrors with three different structures, determining the corresponding equivalent thickness plate in a lightweight structure with a nearly uniform surface density distribution and isotropic bending properties. We then establish a residual removal model of a stressed polishing surface, design the stressed loading equipment, and propose an iterative method for stressed polishing of an off-axis aspheric SiC lightweight mirror. The results demonstrate that it is feasible to choose a lightweight structure that performs full-aperture stressed polishing on off-axis aspheric lightweight mirrors consisting of SiC or other materials.

Distribution model of the surface roughness in magnetorheological jet polishing.

Magnetorheological jet polishing (MJP) plays an important role in polishing complex cavities and special optical elements with high precision. However, the roughness distribution function that describes the variation with polishing time of the roughness value of every area in the polishing area has not been studied deeply. In this paper, the influence of the roughness distribution on the removal function of MJP in optics (with a roughness of less than 10 nm) and its evolution model in the spatial and time domains are studied. With the increase of polishing time, the surface roughness of the central area linearly increases, forming surface defects, such as pits. The roughness of the polishing area exhibits a limited growth trend. Verification experiments are carried out on BK7 glass. The results of the roughness distribution on the removal function prove the correctness of the model. The model laid a foundation; therefore, it has important guidance and reference value for the application to the whole aperture polishing.

Comprehensive study of the rapid stressed mirror polishing method for off-axis aspheric SiC thin-plate mirrors.

In this study, the stressed mirror polishing technique is used to perform off-axis aspheric silicon carbide (SiC) mirror full-aperture polishing for the first time. Mechanical and optical parameter analysis methods have been proposed. A medium-diameter off-axis aspheric SiC thin-plate mirror is used as a scaling model for an optical system mirror. A full diameter polishing simulation was completed, and a conceptual design for stress loading equipment is presented. An initial aspheric surface method for stressed mirror polishing of an off-axis aspheric SiC thin-plate mirror, providing a reference for rapid stress mirror polishing of SiC mirrors, is also proposed.

Distortion measurement of optical system using phase diffractive beam splitter.

Traditional methods for distortion measurement of large-aperture optical systems are time-consuming and ineffective because they require each field of view to be individually measured using a high-precision rotating platform. In this study, a new method that uses a phase diffractive beam splitter (DBS) is proposed to measure the distortion of optical systems, which has great potential application for the large-aperture optical system. The proposed method has a very high degree of accuracy and is extremely economical. A high-precision calibration method is proposed to measure the angular distribution of the DBS. The uncertainty analysis of the factors involved in the measurement process has been performed to highlight the low level of errors in the measurement methodology. Results show that high-precision measurements of the focal length and distortion were successfully achieved with high efficiency. The proposed method can be used for large-aperture wide-angle optical systems such as those used for aerial mapping applications.

Designing a hydraulic support system for large monolithic mirror's precise in-situ testing-polishing iteration.

In order to improve the fabrication efficiency and testing accuracy of meter-scale, large monolithic mirrors, hydraulic support units (HSUs) are commonly used. However, the challenges to reduce the disparity of the HSUs' stiffness and keep the stability of the mirrors' altitude are hard to resolve, especially for large-scale mirrors. In this paper, we found the air ratio of the working fluid for HSUs is a key factor for designing the HSUs to resolve the challenges from the analytical solution that we derived for supporting large mirrors. Here we designed, tested and fabricated dozens of HSUs and used a four-meter SiC mirror, the world's largest monolithic SiC reported in public, as a study case. It shows that the stiffness values of grouped HSUs vary within ± 3%, and the mirror's reference surface PV is less than 20 µm in 10 days, producing a mirror tip/tilt angle less than 1.5″. The surface error of the supported mirror is about 20 nm, which is very close to the ideal case where uniform stiffness exists, for randomly distributed stiffness values. The repeatability of the in-situ interferometric test with 0.019 λ RMS of the mirror surface demonstrates the supporting system in a high precision. With such a supporting system, the fabrication process of this mirror was estimated to be sped up by 47% compared to the typical fabricating iteration. With minor modifications and easy extensions, such a novel supporting system could be used widely for many in-situ, high-quality fabricating-testing processes.

Multi-beam array stitching method based on scanning Hartmann for imaging quality evaluation of large space telescopes.

To test large-aperture space optical systems in a simple and highly efficient manner, the scanning Hartmann test (SHT) has been used to measure the sub-aperture wavefront slopes of optical systems by scanning with a collimated beam followed by retrieval of the overall wavefront form. However, the use of such a method contains a crucial flaw in that pointing errors of the translation stage can severely affect the test accuracy. Therefore, a multi-beam stitching method is proposed to correct pointing errors by stitching together data obtained by successive sub-aperture acquisition. In this paper, a test principle and a data processing method are detailed. Simulation results theoretically verify a high precision for the stitching algorithm. Furthermore, a multi-beam array stitching test system (MASTS) is developed and used to successfully test an actual space optical system of ∅800 mm. The MASTS shows a deviation of 1/50 λ (λ = 632.8 nm) root mean square (RMS) from the interferometric results and a repeatability of 1/80 λ RMS, which demonstrates high precision, high repeatability and low sensitivity to air turbulence compared to interferometric measurement. In future engineering applications, the MASTS has great potential to solve the test problems of space optical systems using ultra-large apertures.

Mapping distortion correction in freeform mirror testing by computer-generated hologram.

Distortion can be introduced in null testing using computer-generated holograms for off-axis aspheres or freeforms with significant deviation. It leads to the failure of testing results to guide deterministic optical processing. In this paper, based on ray tracing and calibration marks applied to a mirror surface, a high-accuracy method is proposed to correct the distortion. The correction error is less than 1 mm. Second and fourth mirrors of a reflective telescope prototype with an F number of 6.5 and field of view of 76° are polished. In the process, distortion is corrected, and the position misalignment error is as small as 0.783 mm. For the sake of alignment, the two mirrors are fixed on a 790 mm×390 mm SiC substrate. The root-mean-square value of the mirror surface error is 0.0433λ (λ=0.6328 µm) after ion beam finishing.

Ultra-precision fabrication of a nickel-phosphorus layer on aluminum substrate by SPDT and MRF.

Metal mirrors are rarely used in visible or ultraviolet systems due to the ultra-precision fabrication difficulties. In this work, a plane aluminum alloy substrate (ϕ100 mm) surface deposited with a nickel-phosphorus (NiP) layer by the electroless deposition technique is prepared. The NiP layer is processed by single point diamond turning (SPDT) technology to the accuracy of 60 nm in RMS, and the surface roughness reaches 4.157 nm in Ra. A kind of water-based magnetorheological polishing fluid for the ultra-precision of the NiP layer is developed, and magnetorheological finishing (MRF) is applied to the final finishing of the mirror. The developed fluid that contains small size (1.5 µm) carbonyl iron powder (CIP) and 50 nm nano-cerium possesses material removal of 1.8 µm/min, and surface roughness of 1 nm is determined as the optimal fluid formula. The surface residual error is improved from 60 to 10 nm, and the surface roughness decreases from 4.157 to 0.851 nm after MRF in 1.5 h with one polishing cycle with the developed MR polishing fluid. Finally, the surface quality after MRF is tested by SEM and XRD, and the results manifest that the periodical tool mark is swiped out and the surface is not contaminated by MR polishing fluid. The experiment results and theoretical analysis of this work prove that MRF can satisfy the ultra-precision fabrication of NiP film on the metal mirror, and the surface quality can be applied in a visible or even ultraviolet optical system by using suitable MR polishing fluids.

Fabrication of a high-accuracy phase-type computer-generated hologram by physical vapor deposition.

With the development of optical systems used in astronomical and earth observation, aspherical and free-form surfaces are increasingly used because they are lightweight and have improved image quality. As a highly accurate, aberrationless technique, computer-generated hologram (CGH) plays an important role in wavefront testing. At present, the main way to fabricate phase CGH is reactive ion etching, which suffers from low accuracy. To improve the accuracy, physical vapor deposition (PVD) is applied in the fabrication of phase CGH. The wavefront errors of PVD-fabricated phase CGH were analyzed. Testing results indicate that the wavefront error of the CGH is 0.020λ root mean square (RMS), mainly caused by the machine tool orthogonality error rather than the PVD process. The diffraction efficiency of the +1st order is 22.4%.

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 0.64 µrad in slope RMS (effective aperture). The effective fabrication duration is reduced to 2 months.

Modified surface testing method for large convex aspheric surfaces based on diffraction optics.

Large convex aspheric optical elements have been widely applied in advanced optical systems, which have presented a challenging metrology problem. Conventional testing methods cannot satisfy the demand gradually with the change of definition of "large." A modified method is proposed in this paper, which utilizes a relatively small computer-generated hologram and an illumination lens with certain feasibility to measure the large convex aspherics. Two example systems are designed to demonstrate the applicability, and also, the sensitivity of this configuration is analyzed, which proves the accuracy of the configuration can be better than 6 nm with careful alignment and calibration of the illumination lens in advance. Design examples and analysis show that this configuration is applicable to measure the large convex aspheric surfaces.

Effects of the gap slope on the distribution of removal rate in Belt-MRF.

Belt magnetorheological finishing (Belt-MRF) is a promising tool for large-optics processing. However, before using a spot, its shape should be designed and controlled by the polishing gap. Previous research revealed a remarkably nonlinear relationship between the removal function and normal pressure distribution. The pressure is nonlinearly related to the gap geometry, precluding prediction of the removal function given the polishing gap. Here, we used the concepts of gap slope and virtual ribbon to develop a model of removal profiles in Belt-MRF. Between the belt and the workpiece in the main polishing area, a gap which changes linearly along the flow direction was created using a flat-bottom magnet box. The pressure distribution and removal function were calculated. Simulations were consistent with experiments. Different removal functions, consistent with theoretical calculations, were obtained by adjusting the gap slope. This approach allows to predict removal functions in Belt-MRF.

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.

Large-aperture space optical system testing based on the scanning Hartmann.

Based on the Hartmann testing principle, this paper proposes a novel image quality testing technology which applies to a large-aperture space optical system. Compared with the traditional testing method through a large-aperture collimator, the scanning Hartmann testing technology has great advantages due to its simple structure, low cost, and ability to perform wavefront measurement of an optical system. The basic testing principle of the scanning Hartmann testing technology, data processing method, and simulation process are presented in this paper. Certain simulation results are also given to verify the feasibility of this technology. Furthermore, a measuring system is developed to conduct a wavefront measurement experiment for a 200 mm aperture optical system. The small deviation (6.3%) of root mean square (RMS) between experimental results and interferometric results indicates that the testing system can measure low-order aberration correctly, which means that the scanning Hartmann testing technology has the ability to test the imaging quality of a large-aperture space optical system.

Ion beam figuring approach for thermally sensitive space optics.

During the ion beam figuring (IBF) of a space mirror, thermal radiation of the neutral filament and particle collisions will heat the mirror. The adhesive layer used to bond the metal parts and the mirror is very sensitive to temperature rise. When the temperature exceeds the designed value, the mirror surface shape will change markedly because of the thermal deformation and stress release of the adhesive layer, thereby reducing the IBF accuracy. To suppress the thermal effect, we analyzed the heat generation mechanism. By using thermal radiation theory, we established a thermal radiation model of the neutral filament. Additionally, we acquired a surface-type Gaussian heat source model of the ion beam sputtering based on the removal function and Faraday scan result. Using the finite-element-method software ABAQUS, we developed a method that can simulate the thermal effect of the IBF for the full path and all dwell times. Based on the thermal model, which was experimentally confirmed, we simulated the thermal effects for a 675 mm×374 mm rectangular SiC space mirror. By optimizing the dwell time distribution, the peak temperature value of the adhesive layer during the figuring process was reduced under the designed value. After one round of figuring, the RMS value of the surface error changed from 0.094 to 0.015λ (λ=632.8 nm), which proved the effectiveness of the thermal analysis and suppression method.