Mid-frequency Errors Research Articles

Multi-dimensional error figuring model for ion beams in X-ray mirrors

X-ray mirrors are core optical elements in synchrotron light sources, which are typically figured by ion beams. However, traditional ion beam figuring (IBF) methods cannot effectively correct both the height and 2D slope errors. Thus, what we believe to be a novel multi-dimensional error figuring model (MEFM) is proposed to integrate the height and 2D slope errors into a linear system of equations for simultaneous multi-dimensional error convergence. The weight values are determined based on specific manufacturing errors. The simulation results show that MEFM can achieve lower 2D slope and height errors than a single height or 2D slope errors in the figuring method. The power spectral density (PSD) curves before and after simulated figuring demonstrate that the low- and mid-frequency errors are corrected simultaneously. Figuring experiments on a 270 mm × 15 mm X-ray reflector showed that the height and 2D slope errors effectively converged. The results of the PSD curves indicate that MEFM is more effective than the traditional height figuring model in correcting mid-frequency errors, which further proves the validity of the solution model. This study provides an algorithmic reference for the IBF of ultra-high precision X-ray reflectors, thereby promoting the development of physics, medicine, materials, and other fields.

Study on the influence of a magnetorheological finishing path on the mid-frequency errors of optical element surfaces

Magnetorheological finishing (MRF) is a deterministic optical processing technique based on CCOS that achieves high removal efficiency and processing accuracy while reducing subsurface damage. This technique still suffers from multiple iterations of processing due to variations in removal efficiency and the inability to fully correct mid-frequency errors below the cut-off frequency of the removal function. For the above problems, this paper attempted to establish the error model of removal function efficiency change for predicting the change of MRF efficiency. Based on the analysis of the distribution of surface shape residuals under different machining paths, a process combining spiral scanning and raster scanning is proposed, which can realize the correction of surface shape and restrain the deterioration of mid-frequency errors. The experimental results show that when the low-frequency errors of fused silica element surface converge rapidly, by optimizing the machining removal coefficient and using the spiral scanning and raster scanning combined method, the PSD analysis results show that the mid-frequency errors of the combined process is lower than the initial value, which expands the process route for the MRF of high-precision optical elements.

Research on the tool influence function characteristics of magnetorheological precession finishing (MRPF).

Magnetorheological finishing (MRF) technology is characterized by its high convergence rate and minimal subsurface damage as advantages. However, the non-Gaussian type tool influence function (TIF) it generates may cause mid-frequency errors and oriented surface texture issues. Magnetorheological precession finishing (MRPF) technology capable of generating Gaussian-like removal functions, lacks a clearly defined removal function model. This study acquired polishing spots in tilted polishing, discrete precession, and continuous precession modes via fixed-point polishing experiments. Using Multiphysics simulation software, stress and velocity distribution in the contact area were simulated. A TIF model, incorporating the synergistic effects of pressure and shear force and multiple influence coefficients, was proposed based on velocity characteristics across the three modes. To accurately predict the TIF, surface topographies with varying coefficients were constructed using this model, analyzing the coefficients' impact on the TIF profile. Optimal coefficients were identified using a least fit error algorithm. Further analysis of the TIF's internal textures revealed that the precession mode of MRPF yields superior surface quality, thereby elucidating the material removal mechanism of MRPF and laying a theoretical groundwork for advancing processing technologies.

Design and frequency control study of small-sized magnetorheological finishing device applied in optical manufacturing

With the continuous development of various advanced optical systems, there is an increasing demand for optical components with small apertures (generally ranging from a few millimeters to tens of millimeters in diameter), steep slopes, or even specific relief structures on their surfaces (such as continuous phase elements). These optical components all require high surface quality and shape accuracy. However, existing magnetorheological finishing (MRF) devices have larger dimensions, and the obtained removal function size is relatively larger than the size of small-diameter optical components, making it difficult to achieve high surface shape accuracy after processing. To achieve high-precision machining of small-aperture optical components and obtain higher frequency control capabilities, this study first designed and optimized a small-size MRF device with a 13 mm polishing wheel. Based on theoretical and finite element simulation analyses, the magnetic pole structure of the small-size MRF device was designed. The orthogonal experimental method was used to optimize the key parameters of the magnetic pole according to the magnetic field design requirements, and the device was constructed. Its performance and stability were experimentally analyzed, and the results showed that the peak magnetic field intensity in the polishing area of the device was about 230mT, which met the polishing requirements, and both its long-term and short-term processing stabilities met the design requirements. In addition, different sizes of removal functions were analyzed for frequency control ability, and theoretical and spectral analyses of the removal function indicated that the small-size removal function had better low-frequency error correction ability, while for mid-frequency band and mid-frequency ripple error, the opposite was true. The experimental results showed that when the optical component was shaped by 20 %, the low-frequency convergence capability of the 100 mm polishing device was only 18.72 %, much lower than that of the 13 mm polishing device, which was 52.51 %.Moreover, the mid-frequency ripple spectrum amplitude for the 13 mm polishing device was more than 15 times higher than that for the 100 mm polishing device when removing 50 nm material, and the mid-frequency root mean square (RMS) increased significantly, deteriorating the surface mid-frequency error of the optical component. Therefore, when performing magnetorheological polishing on an optical component surface, a process of using large-size MRF devices for roughing combined with small-size MRF devices for finishing can ensure machining efficiency while controlling low-frequency and mid-frequency errors well. This study provides theoretical support for the magnetic pole design of MRF devices and broadens the frequency spectrum correction ability and application range of MRF processes, which has great application value.

Research on the influence of the non-stationary effect of the magnetorheological finishing removal function on mid-frequency errors of optical component surfaces.

With the continuous development of modern optical systems, the demand for full spatial frequency errors of optical components in the system is increasing. Although computer-controlled sub-aperture polishing technology can quickly correct low-frequency errors, this technology significantly worsens the mid-frequency errors on the surface of the component, which greatly inhibits the improvement of optical system performance. Therefore, we conducted in-depth research on the non-stationary effect of the removal function caused by the fluctuation in magnetorheological polishing and their influence on the mid-frequency errors of the component surface. We established a non-stationary profile model of the removal function and applied this model to simulate the distribution of mid-frequency errors on the surface of the processed component, considering the non-stationary effect. The simulation results showed that the non-stationary effect of the removal function weaken the mid-frequency ripple errors but increase other mid-frequency errors. Therefore, we first proposed the optimal single-material removal thickness corresponding to the non-stationary effect and experimentally verified the effectiveness of the optimal material removal thickness in suppressing mid-frequency errors. The experimental results showed that when the magnetorheological finishing single-material removal thickness is set to the optimal value, both the mid-frequency ripple errors and the mid-frequency RMS on the surface significantly decrease. Therefore, this work provides a basis for improving the existing magnetorheological finishing process and effectively suppressing the mid-frequency errors on the surface of processed components. It also provides theoretical and technical support for the magnetorheological processing and manufacturing of high-precision optical components. At the same time, the non-stationary effect and the corresponding analytical models has the potential to be extended to other polishing tools.

A tool-path planning method used in computer controlled optical surfacing based on improved prim algorithm

In view of the disadvantages of existing planning methods used in CCOS techniques, such as low efficiency and workpieces containing obvious mid-frequency error after polishing, a new tool-path planning method based on improved Prim algorithm is presented. The core idea of method consists of the following steps: surface data reading, mesh generation, distribution of resident points determining, and polishing path generating. Then, comparison of raster path and the path based on improved Prim algorithm are carried out by simulations from aspects of path length and polishing texture. The results indicate that the path based on improved Prim algorithm can shorten path length as well as increase polishing efficiency; moreover, both the texture and mid-frequency errors can be improved by using the path presented. Finally, the processing experiments of raster path and the path presented are carried out. The experimental results show that the polishing efficiency and precision are improved by using the proposed method. Moreover, it can reduce the mid-frequency error of workpiece effectively. Thus, the experimental results which are in good agreement with the simulation results prove the feasibility of proposed method.

Multi-tool selection model for the error control of mid-to-high frequency and rapid fabrication on large-scale aspheric optics

Aspheric optics has been widely used in the space telescope system. The large amount of material removal and mid-frequency errors district the high-precision and high-efficiency fabrication of large-scale aspheric optics. On the basis of parsing the figuring ability of tool influence functions (TIFs) and principles of smoothing polishing technology, the multi-TIFs process is proposed in this paper. Then the selection principle and replacement time of TIFs have been discussed. Furthermore, the multi-TIFs process is optimized with frequency filtering method. This filtering method with multi-TIFs can obtain better surface accuracy in a faster way compared to the traditional method. Finally, a Φ540mm SiC off-axis aspheric mirror is polished to verify the proposed method.

Fabrication of electroless nickel plated aluminum freeform mirror for an infrared off-axis telescope.

Freeform mirrors can be readily fabricated by a single point diamond turning (SPDT) machine. However, this machining process often leaves mid-frequency errors (MFEs) that generate undesirable diffraction effects and stray light. In this work, we propose a novel thin electroless nickel plating procedure to remove MFE on freeform surfaces. The proposed procedure has a distinct advantage over a typical thick plating method in that the machining process can be endlessly repeated until the designed mirror surface is obtained. This is of great importance because the sophisticated surface of a freeform mirror cannot be optimized by a typical SPDT machining process, which can be repeated only several times before the limited thickness of the nickel plating is consumed. We will also describe the baking process of a plated mirror to improve the hardness of the mirror surface, which is crucial for minimizing the degradation of that mirror surface that occurs during the polishing process. During the whole proposed process, the changes in surface figures and textures are monitored and cross checked by two different types of measurements, as well as by an interference pattern test. The experimental results indicate that the proposed thin electroless nickel plating procedure is very simple but powerful for removing MFEs on freeform mirror surfaces.

Path planning and parameter optimization of uniform removal in active feed polishing

A high-quality ultrasmooth surface is demanded in short-wave optical systems. However, the existing polishing methods have difficulties meeting the requirement on spherical or aspheric surfaces. As a new kind of small tool polishing method, active feed polishing (AFP) could attain a surface roughness of less than 0.3 nm (RMS) on spherical elements, although AFP may magnify the residual figure error or mid-frequency error. The purpose of this work is to propose an effective algorithm to realize uniform removal of the surface in the processing. At first, the principle of the AFP and the mechanism of the polishing machine are introduced. In order to maintain the processed figure error, a variable pitch spiral path planning algorithm and the dwell time-solving model are proposed. For suppressing the possible mid-frequency error, the uniformity of the synthesis tool path, which is generated by an arbitrary point at the polishing tool bottom, is analyzed and evaluated, and the angular velocity ratio of the tool spinning motion to the revolution motion is optimized. Finally, an experiment is conducted on a convex spherical surface and an ultrasmooth surface is finally acquired. In conclusion, a high-quality ultrasmooth surface can be successfully obtained with little degradation of the figure and mid-frequency errors by the algorithm.

Analysis of corrective characteristics of various polishing methods for mid-frequency errors

The theoretical analysis of corrective characteristics of three kinds of polishing methods for mid-frequency errors was studied, which was aimed to confirm the possibility that computer control optical surfacing and computer control active-lap can be replaced by bonnet polishing in the machining process. The first step was to calculate the removal functions of three kinds of polishing technologies and use fast Fourier transform to figure out the frequency spectrum of each method. After that, according to the frequency spectra, curves of cut-off frequencies related to the working ranges of spatial frequencies errors were obtained. It revealed that the affected scope of spatial frequencies is determined by the polishing method, diameter size of polishing tool and shape of removal function. Moreover, only low-frequency errors could be modified and mid-frequency errors could not be corrected or created by computer control active-lap, and computer control optical surfacing can correct part of the mid-frequency errors and low-frequency errors in the polishing process, but at the same time can produce some new mid-frequency errors; as for bonnet polishing, it can be computer control active-lap-like in smoothing which only modified and created the low-frequency errors or computer control optical surfacing-like which corrected and created the mid-frequency errors in local polishing. Otherwise, the efficiency of bonnet polishing is higher than the other two methods. As a result, seen from the point of correction ability of mid-frequency or polishing efficiency, bonnet polishing could replace computer control active-lap and computer control optical surfacing for finishing two polishing stages by only one tool, which is significant to extending the application of bonnet polishing in optical manufacturing.

被动半刚性磨盘在平滑中频误差中的应用

被动半刚性磨盘在平滑中频误差中的应用

Toward the Accurate Coverage of Aspheric Surfaces Using Two-Dimensional Scanning Paths for Minimizing Regular Errors

This paper describes a two-dimensional tool-path planning model for minimizing the regularly distributed errors or mid-frequency errors during computer controlled optical surfacing (CCOS) by optimally connecting different tool-path segments. The model was established based on a neuro-fuzzy algorithm, a path neighborhood function which is defined as a victorious output element calculated in a self-organization way, then, the optimum material removal function with a modified weight was derived. The material removal function was studied theoretically and the results of simulation present a Gaussian distribution feature. Discrete removal points and optimized tool-path grid were simulated. Finally, an experiment involving a parabolic mirror was performed for residual error removal and the two-dimensional tool-path planning algorithm was found to be valid.

Performance of ion-figured silicon carbide SUMER telescope mirror in the vacuum ultraviolet

Measured and theoretical encircled energy and small-angle scatter of the telescope mirror (SST) of the solar ultraviolet measurements of emitted radiation (SUMER) instrument are compared at the wavelength of 123.6 nm. Mirror performance modeling was accomplished with the Optical Surface Analysis Code software package. The modeling is based on measured mirror-surface figure error data and roughness characteristics covering all important spatial frequencies that affect imaging in the vacuum ultraviolet wavelength region. Mirror-surface errors were measured with a Zygo Mark IV interferometer, Bauer Model 200 Profiler, and WYKO Topo 2-D (two-dimensional) interferometer. Performance of the SST mirror, including encircled energy and small-angle scatter, was also directly measured. A good agreement is found between measured and theoretical encircled energy within 6 arcsec and small-angle scatter up to ~50 arcmin from the peak. The 80% encircled energy diameter of the SST mirror is ~1.9 arcsec, and the amount of scattered light drops to approximately 1.0 × 10(-10) of peak irradiance (normalized to 1 arcsec(2) in the focal plane) 50 arcmin from the peak. Vacuum ultraviolet performance of the mirror is degraded primarily by midfrequency errors.

Processing of interferometric fringe scanner data for the AXAF/TMA x-ray telescope

An interferometric fringe scanner was used for the Technology Mirror Assembly (TMA) x-ray telescope, built by Perkin-Elmer as a technology demonstration for the Advanced X-Ray Astrophysics Facility (AXAF). We discuss advanced data processing features, implemented during a follow-on project to improve the mirror's midfrequency errors still further. Data processing techniques include interleaving of multiple scans, and optimal smoothing and interpolation of the interleaved data onto a uniform grid. We discuss the underlying mathematics behind the processes, the motivation in terms of recovering the highest possible spatial frequencies from the data, and some sample results.