Wheel-type elastic emission machining (EEM) holds great promise for achieving atomic-level, low-damage optical fabrication. However, existing material removal models fail to account for the inherently coupled physicochemical removal mechanism of EEM, leaving deterministic process control a challenge. In this study, a physicochemical synergistic material removal model was developed for wheel-type elastic emission machining, and an optimal process window was established. A three-dimensional fluid-structure interaction (FSI) simulation model was constructed to resolve the fluid pressure, wall shear stress, and velocity distributions at the polishing interface, while simultaneously capturing the elastic deformation of the polyurethane polishing wheel. The results confirm that the predicted removal profiles are in excellent agreement with the experimental measurements, with coefficients of determination exceeding 0.99 in both the XZ- and YZ-planes. Experimental investigations revealed a three-stage nonlinear response of removal depth to polishing speed, polishing time, and polishing gap. Normalized sensitivity analysis indicated that polishing time is the dominant factor, followed by the polishing gap and polishing speed. A hierarchical optimization framework was adopted, in which efficiency served as a hard constraint and stability was maximized among all qualified candidates. The resulting optimal process window achieves a synergistic balance between high removal efficiency and disturbance rejection. This work provides reliable process guidance for the application of wheel-type EEM to atomic-level fabrication of ultra-precision optical surfaces.

Reaction-bonded silicon carbide (RB-SiC) is the preferred material for space optical systems because of its low density and high specific stiffness. However, its hardness and multi-component properties lead to low efficiency and pit defects during the polishing process, making the fabrication of RB-SiC a significant challenge. This study proposes a high-efficiency and low-defect fabrication method for RB-SiC using center-inlet computer-controlled polishing (CCP). We first investigated the polishing efficiency and surface quality achieved with center-inlet and non-center-inlet liquids. The results show that the defect density under non-center-inlet conditions was positively correlated with process parameters, while fewer defects and higher efficiency could be achieved under center-inlet conditions. Additionally, the efficient removal and defect suppression mechanisms under the center-inlet condition were revealed based on machining force, heat, and defect characterization. Under center-inlet conditions, the friction coefficient is larger and stable, resulting in high removal efficiency. The macro-micro coupled analysis results show that pit defects are generated through the combined action of force and heat, which leads to the thermo-mechanical degradation and shedding of SiC particles due to the temperature increase in the machining zone. The results demonstrate that center-inlet CCP not only ensures sufficient abrasion at the polishing interface to achieve high removal efficiency but also significantly suppresses the processing heat, thereby resulting in a low-defect surface.

The simulation optimization of EUV masks is one of the key technologies in lithography imaging simulation. The internal and external electromagnetic field distribution of a grating mask can be analyzed by using the rigorous coupled-wave analysis method. However, the result obtained by the coupled-wave method alone is a complex amplitude of light, which cannot directly provide the EUV light absorption distribution. Moreover, during the calculation, an energy non-conservation problem at the boundary of the absorption material should be generated by the standard algorithm. To overcome this problem, an extended potential transmittance method to analyze the mask absorption characteristics is introduced in this paper. The potential transmittance method can describe not only the absorptivity of the film system but also the absorptivity and power change of the diffraction lights with different orders of the grating. Assuming the potential transmittance of each diffraction light can be calculated independently, the total absorption of the grating layer can be determined by the sum of the power distribution of all the diffracted light.

A new algorithm to reconstruct rotationally asymmetrical surface deviation is proposed. In planar absolute tests, single-angle iterative algorithm is used to retrieve rotationally asymmetrical surface deviation. However, it always encounters the problem that certain azimuthal frequency terms either do not converge or converge too slowly. In this paper, the convergence characteristics of the single-angle iterative algorithm are analyzed, and it is found that the convergence rate is related to the rotation angle and azimuthal frequency magnitudes. In order to solve the convergence problem, dual-angle iterative algorithm is proposed which uses two rotation measurement data. And the method of obtaining the optimal second rotation angle is presented. Simulation experiments prove that compared to the single-angle iterative algorithm, the dual-angle iterative algorithm can enhance the convergence rate and improve the reconstruction accuracy.

A large-aperture silicon carbide (SiC) aspheric mirror has the advantages of being light weight and having a high specific stiffness, which is the key component of a space optical system. However, SiC has the characteristics of high hardness and multi-component, which makes it difficult to realize efficient, high-precision, and low-defect processing. To solve this problem, a novel process chain combining ultra-precision shaping based on parallel grinding, rapid polishing with central fluid supply, and magnetorheological finishing (MRF) is proposed in this paper. The key technologies include the passivation and life prediction of the wheel in SiC ultra-precision grinding (UPG), the generation and suppression mechanism of pit defects on the SiC surface, deterministic and ultra-smooth polishing by MRF, and compensation interference detection of the high-order aspheric surface by a computer-generated hologram (CGH). The verification experiment was conducted on a Ø460 mm SiC aspheric mirror, whose initial surface shape error was 4.15 μm in peak-to-valley (PV) and a root-mean-square roughness (Rq) of 44.56 nm. After conducting the proposed process chain, a surface error of RMS 7.42 nm and a Rq of 0.33 nm were successfully obtained. Moreover, the whole processing cycle is only about 216 h, which sheds light on the mass production of large-aperture silicon carbide aspheric mirrors.

Higher requirements for monocrystalline silicon x-ray mirrors have been put forward with the development of synchrotron radiation optics. The existing processing technologies limit their efficiency while achieving high-precision manufacturing of x-ray mirrors. Hence, this paper formulates a processing strategy of employing magnetorheological finishing (MRF) to make the precision of x-ray mirrors fully meet the standard. The combination of fine polishing and super-smooth processing can effectively improve the surface quality of mirrors. The residual error, wavefront gradient, and surface roughness of the mirror can reach 7.2 nm, 0.42 µrad, and 0.28 nm, respectively, after several iterations. The research not only indicates that MRF can replace the existing manufacturing method and greatly improve processing efficiency, but also provides technical support for optimizing the processing route of x-ray mirrors.

Conformal vibration polishing (CVP) employing flexible polishing tools is expected to be an efficient means of optical processing, and all current research on it is limited to planar components. Hence, the smoothing characteristics of the middle spatial frequency (MSF) errors and the ability to maintain the surface shape of different types of optics in CVP are analyzed. A combined processing method based on magnetorheological finishing and CVP for full-spatial frequency errors is proposed and verified by experiment. The peak-to-valley value, MSF errors, and surface roughness of the large-diameter component can reach 75 nm, 1.1 nm, and 0.37 nm after 9 h of processing. The research not only demonstrates the excellent removal characteristics of CVP and the effectiveness of the proposed method but also provides an additional choice for the high-precision manufacturing of optics.

Magnetorheological finishing (MRF) has become the mainstream method for ultra-precision manufacturing of optics due to its high certainty and low damage. However, there are still some gaps in the research on the characteristics of the tool influence function for the MRF method, which makes the parameter optimization and quality improvement lack effective theoretical support. To solve this problem, this paper demonstrates the mapping relationship between various process parameters and the evaluation indexes of the influence function based on the orthogonal test. A characteristic length coefficient is proposed to characterize the suppression effect of the tool influence function on the ripple errors. The uniform removal experiment shows that selecting reasonable characteristic length coefficient and line spacing can significantly suppress the generation of ripple errors and obtain the optimal parameters under a comprehensive consideration. Finally, a component with a size of 400 mm x 280 mm is deterministically finished and a high-quality optical surface is obtained. The theoretical analysis and experiment data carried out in this work can effectively improve the final quality of components and provide certain theoretical support for parameter optimization.

Freeform surfaces play an important role in modern optical systems with compactness and better performance. The fabrication tools tend to impart a structured signature on optical surfaces, called ripple errors, during the freeform surface manufacturing process. The description and extraction of ripple errors for freeform surface fabrication and testing have attracted extensive attention. In this paper, we develop a fast and accurate method to describe ripple errors for the large aperture based on Fourier model coupling. The polynomial expression is transformed into Fourier series form and surface errors are reconstructed by frequency feature extraction combining with the least square method. The high accuracy and efficiency of the proposed method for representing and filtering ripple errors consuming little computer memory are demonstrated using real experimental data. The proposed method offers a robust and powerful tool not only suitable for surface error characterization but also for image filtering and analysis.

By combining the conformal polishing method with short stroke vibration, a novel, to the best of our knowledge, conformal vibration polishing (CVP) method is proposed. The CVP method is expected to be an efficient means of optical processing by its high material removal rate and smoothing characteristics of mid-spatial frequency (MSF) errors. A quantitative time-domain smoothing model and a convergence factor (${\rm CF}_C$) are presented based on the research of smoothing characteristics. The motion mechanism, material removal ability, solution, and expansion of the smoothing model are demonstrated theoretically and experimentally. The experimental results exhibited good agreement with the theoretical predictions for the proposed method. The research provides a certain theoretical foundation for parameter selection and process optimization of the CVP method.

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

Magnetorheological finishing (MRF) has been widely used in the field of modern optical machining due to the high certainty of processing. In the processing of spherical components, the detection means and sample preparation limit the acquisition of magnetorheological spherical tool influence function. In order to realize the high precision manufacturing of spherical components, the spherical removal function in the magneto-rheological polishing process is simulated and applied in practice. Based on the Preston equation, the material removal of the planar component was analyzed and the plane tool influence function model was established. On this basis, the correlation between spherical removal and plane removal was analyzed, and a simplified spherical tool influence function simulation method was proposed, and its accuracy was verified by experiments. Aiming at the processing of spherical components, the processing technology was improved and the actual processing was carried out. After processing, the PV value of the transmitted wavefront was 0.09λ, and the RMS value was 3.2 nm. The experimental results show that the spherical tool influence function simulated in this paper can be applied in actual processing and obtain a high-quality optical surface.

Phase retrieval is an attractive optical testing method with a simple experimental arrangement. The sampling grids wave propagation computation based on the FFT operations is usually involved in each iterative process for the classical phase retrieval model. In this paper, a novel non-propagation optimization phase retrieval technique with the FFT-based basis function is proposed to accelerate wavefront measurement. The sampling grids wave diffraction propagation computation is converted to matrix-vector products that have small dimensions to reduce the computational burden. The diffraction basis function based on generalized numerical orthogonal polynomial and two-step Fresnel propagation is deduced, which is suitable for the generally shaped pupil. This paper provides a universal non-propagation framework to accelerate phase retrieval which is applicable to the arbitrarily shaped wavefront measurement.

Due to the complexity and inhomogeneity of the distribution of the middle-spatial frequency errors (MSFE), the existing theoretical models cannot realize the manufacturability prediction of the smoothing process for the MSFE on the largeaperture optical components. Therefore, based on the parameterized time-domain smoothing model and the idea of regional division, a prediction algorithm suitable for the smoothing process of the MSFE in complex periods is proposed in this paper. The relevant verifiable experiments are carried out. The prediction results are in good agreement with the real data, which indicates that the prediction algorithm proposed in this paper can be applied to predict the smoothing process of the MSFE of large-aperture optical components and guide the polishing process.

Subsurface damage (SSD) is the fracture and deformation near the surface of brittle optical materials, caused by surface lapping or grinding. The existence of SSD dramatically influences the performance of optical glass and reduces the laser-induced damage threshold. Subsurface cracks of borosilicate glass can be spontaneously healed when heated under appropriate conditions. In this paper, thermal healing experiments of borosilicate glass (BK7) subsurface cracks are conducted on typical cracks induced by an indentation process, and the effects of the Beilby layer, temperature, crack depth, and water vapor pressure are studied. A semi-empirical relation is obtained through the regression of experimental results to describe the variation of subsurface crack length. Finally, a healing experiment is performed on the subsurface damage formed by grinding. The detection results show both the damage density and maximum damage depth have been reduced after heat treatment, demonstrating the effectiveness of the thermal healing method on eliminating glass subsurface damage.

The specification and characterization of mid-spatial-frequency (MSF) ripples for the large-square-aperture optical elements, typically used in high-power laser systems, have received considerable critical attention. It is necessary to resort to a simple and robust way to characterize error surfaces for facilitating prediction of performance degradation and guiding the fabrication and tolerance settings. In this paper, we characterize residual periodic surface undulations called ripple errors for the large square aperture generated from modern subapertures and deterministic optical fabrication techniques through two methods, taking a step from qualitative judgment to quantitative analysis. The cross artifact reduction technology, instead of traditional windowed preprocessing, is introduced into power spectral density to suppress spectrum leakage while retaining the information about the part. An efficient algorithm to generate Legendre moments for two-dimensional Legendre polynomials is proposed to quantify ripple errors. This work contributes to understanding the optical degradation caused by MSF errors and associating the design and performance index with surface parametric description.

A conformal vibration polishing method combining high-frequency short-stroke vibration for efficiently manufacturing optics is introduced. The efficient removal characteristics and excellent smoothing ability of the method were verified by theoretical derivation and verification experiments.

The mid-spatial frequency error and high-spatial frequency error on the optical glass component surface limit the development of high-power laser devices. By heat-treatment in wet atmosphere, the surface can be smoothed spontaneously under the action of capillary force, which is positive to improve the quality of optical components. In this paper, the finite element simulation model of the glass surface smoothing process is established based on the level-set method. The factors affecting the smoothing process, such as morphology wavelength and viscosity, are analyzed by simulation. A series of surface smoothing heat-treatment experiments for borosilicate glass were carried out to verify the effectiveness of improvement on surface quality through heat-treatment. Finally, the reasons for the discrepancy between theory and experiment are investigated through the simulation, and the effects of wavelength and the water content in the material are further investigated.

In the Multi-intensities phase retrieval processing, the measurement uncertainty of the defocus distance undermines its measurement accuracy. In this paper, using a general phase retrieval experimental arrangement, we propose an adaptive autofocusing nonlinear optimization phase retrieval algorithm based on the extended Nijboer-Zernike (ENZ) theory. This method concurrently accomplishes correction of defocusing position error and the wavefront measurement requiring without additional facility. The numerical experiments show that the proposed method accuracy searching for the optimal defocusing position is superior to 10 μm among different measurement planes. The numerical experiments show that the wavefront measurement accuracy with the proposed method is superior to λ/100 , RMSE.

The tool influence function of magnetorheological finishing which is widely used in optical machining due to its high efficiency and determinism, directly affects the final processing effect of optical components. Due to the existence of curvature effect in magnetorheological finishing, the existing tool influence function models cannot predict the tool influence functions of various positions in the machining process of aspheric or free-form components. Viewing this, this paper carried out the correlation analysis of the tool influence function models corresponding to different types of components and presented a novel interactive regionalized modeling approach of tool influence function for the processing of aspherical optics. Tool influence function was modelled based on the regionalization of component and the solution of the nearest spherical radius. The verification experiments show that the simulated tool influence functions based on this model agree well with the actual measured tool influence functions. Therefore, the modeling method proposed in this paper can effectively obtain the aspheric tool influence functions and accurately predict the material removal in magnetorheological finishing.