Open Access
Add to BibSonomy
Abstract
Magnetorheological polishing (MRF) has emerged as a critical non-contact sub-aperture polishing technology due to its notable attributes of high precision and minimal damage. However, MRF's inherent D-shaped removal function leads to reduced convergence efficiency of surface form error and introduces mid-spatial-frequency (MSF) waviness. To address these challenges, we propose magnetorheological precession finishing (MRPF) technology, which ingeniously combines MRF with bonnet precession polishing to generate a Gaussian-like removal function. A pivotal component of what we believe to be a novel approach is the design and fabrication of a specialized hemispherical magnetorheological precession polishing head. The design process incorporates magnetostatic simulations and magnetic force analysis to determine the optimal generating conditions for magnetorheological ribbons. Spot polishing experiments confirm the suitability of a 30° precession angle. Experimental results demonstrate that 8-step polishing achieves a Gaussian-like removal function. Additionally, uniform polishing of fused quartz surfaces significantly reduces Ra from 0.7 µm to 2.14 nm. This research showcases the feasibility of MRPF as a new technical route to achieve Gaussian-like removal functions and nanometer-scaled surface roughness.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The rapid development of applied optics has increased the demand for ultra-precision optical components in the fields of aerospace, laser fusion [1–3], astronomical observation [4,5], and ultraviolet lithography systems [6–8], etc. Computer-controlled optical surfaces (CCOS) sub-aperture polishing technology is an essential step for obtaining ultra-precision optical surfaces [9], which made it possible to precisely control the material removal distribution during polishing process. Based on CCOS technology, a series of contact and non-contact sub-aperture polishing methods have been developed, such as bonnet precession polishing [3], magnetorheological polishing [10], fluid jet polishing [11], ion beam polishing [12], laser polishing [13] shear-thickening polishing [14] and so on. Among the various traditional sub-aperture polishing tools, magnetorheological finishing (MRF) technology stands out as one of the few capable of ensuring removal accuracy, minimizing damage, and yielding high surface quality [15–17]. Moreover, it proves well-suited for manufacturing a wide range of optical surfaces [18], including flat, spherical, aspherical, and freeform optics. Furthermore, the removal function generated by the MRF exhibits exceptional stability as a result of the continuous renewal of the magnetorheological fluid within the circulation system.
However, the magnetic field intensity distribution and the flow characteristics of the magnetorheological fluid result in a non-central deepest removal point and a D-shaped overall energy density distribution. Consequently, this removal function not only impedes the convergence efficiency of surface form error but also introduces unwanted mid-spatial-frequency (MSF) waviness [19]. On the other hand, the Gaussian-shaped removal function exhibits center rotation symmetry, with the highest energy density precisely located at its center. This feature enables rapid removal of polishing errors by directly aligning with the error position, leading to reduced surface form error convergence rate and superior suppression of MSF waviness caused by polishing paths [20]. In order to attain a Gaussian-like removal function for MRF, Zhang et al. [21] proposed a dual-rotation magnetorheological finishing technique, capable of generating a centrosymmetric removal function that can take on W-shaped or Gaussian-shaped forms. However, achieving the Gaussian-like removal function requires intricate adjustments to the distance between the self-rotation and co-rotation axes, posing considerable challenges in practical optical processing. Consequently, the development of a novel magnetorheological polishing process, offering strong controllability and universality, bears great significance for both the academic and industrial domains.
The “precessions” processing technique, developed by Zeeko Ltd. in the 1990s, has gained widespread adoption for manufacturing high-quality optical components [22–24]. This method employs a unique precession mode, wherein the polishing tool (hemispherical bonnet) rotates around the local normal of the polishing point during its rotation. The motion's advantage lies in obtaining an influence function with near-Gaussian characteristics and generating a surface clutter texture, thereby achieving enhanced surface quality [23]. Nevertheless, bonnet precession polishing is a sub-aperture contact technique, which may result in scratches or abrasive embedding due to direct pad/surface contact. Additionally, the wear of the polishing pad can reduce the stability of the removal function.
Therefore, this paper introduces the innovative magnetorheological precession finishing (MRPF) process, which combines the benefits of precession polishing for producing Gaussian removal functions with non-contact magnetorheological finishing technology. Firstly, a hemispherical magnetorheological polishing head is designed by analyzing the distribution of magnetic field strength and force, enabling the generation of the ribbon and facilitating precession motion. Subsequently, the optimal precession angle and step number are determined, leading to the generation of a Gaussian-like removal function. Finally, the efficacy of this technology in enhancing surface quality is experimentally validated.
2. Conceptualization and fabrication of MRPF apparatus
2.1 Magnetorheological precession device
A typical precession structure is characterized by the presence of two axes of rotation, along with a spindle axis. The critical requirement is that these three axes intersect at a virtual pivot (VP) point in space. Furthermore, the VP point coincides precisely with the center of a spinning spherical tool, as depicted in Fig. 1(a). During the rotation of the B- and C-axes, the spherical tool's position remains fundamentally unchanged, with only its orientation altering. This design permits meticulous control over the location of the polishing spot (contact area) by affecting the movement of the workpiece along the X, Y, and Z linear axes [25]. Consequently, the MRPF tool head is also devised in a hemispherical configuration, housing the excitation device within it, as illustrated in Fig. 1(b). The role of the excitation device is to establish a gradient magnetic field within the polishing area. This field magnetizes the magnetic particles in the magnetorheological (MR) fluid, forming a flexible solid ribbon that effectively captures abrasive particles to execute material removal from the workpiece surface. The creation of the gradient magnetic field can be achieved through either electromagnet excitation or permanent magnet excitation. Notably, in comparison to the electromagnet, the permanent magnet boasts distinct advantages such as ease of miniaturization due to its uncomplicated structure and the absence of supplementary control necessities like heat dissipation. Consequently, in this study, the permanent magnet is chosen as the excitation device. Relevant magnetic properties are presented in Table 1.
Fig. 1. (a) Typical precession structure; (b) Schematic diagram of hemispheric MRPF tool head (c) Excitation device structure.
Table 1. Magnetic properties of N52 NdFeB magnet
Figure 1(c) portrays the composition of the excitation device, comprising a permanent magnet and a double magnetic pole characterized by extremely high permeability. Both the inner and outer magnetic poles are enveloped by a permanent magnet, with a designated leakage gap existing between the two magnetic poles. This arrangement not only averts the leakage of the ferromagnetic inductance lines from the permanent magnet but also engenders a high-gradient magnetic field within the gap. Consequently, the magnetorheological fluid flowing through this space forms a flexible polishing ribbon. To ensure a uniform magnetic field distribution within the polishing area, the surface curvature of the magnetic pole should be meticulously designed to conform to the curvature of the MRPF tool head.
2.2 Magnetorheological fluid circulation system
The magnetorheological (MR) fluid circulation system consists of a centrifugal pump, a peristaltic pump, an MR fluid stirrer, and delivery hoses, designed to facilitate the continuous replenishment of MR fluid. Given the fluid's suspended nature, an open-turbine impeller with straight blades is employed in the stirring device to achieve homogeneous dispersion of carbonyl iron and abrasive particles within the water-based matrix, as shown in Fig. 2(a). Additionally, compatibility issues with the conventional MR fluid recovery system and the hemispherical polishing head necessitated a redesign of the recycler, as illustrated in Fig. 2(b). The re-engineered recycler features a contour closely matching the curvature of the hemispherical polishing head. Furthermore, it incorporates cylindrical magnets, strategically positioned in a “U-shaped” arrangement. These magnets, possessing weaker magnetic force than annular permanent magnets, are oriented to align with the flow direction of the MR fluid. As the MR fluid rotates into the recycler in synchrony with the polishing tool head, it is subjected to the magnetic force exerted by the cylindrical magnet. This interaction induces the formation of a soft, flexible magnetic cluster brush, effectively trapping the MR fluid within the recycler’s internal cavity. Subsequently, the fluid is returned to the reservoir by the peristaltic pump, which generates the requisite negative pressure.
3. Magnetic field analysis of polishing head
The shape of the magnetorheological fluid ribbons is influenced by the yoke gaps present in the magnetic field generator. To identify the ribbon configurations suitable for polishing applications, it is imperative to first undertake a magnetic field analysis for magnetic field generators with varying yoke gap dimensions.
This study, thus, employs COMSOL software for the magnetostatic simulation of the magnetic field generator, sequentially introducing the model and material characteristics. It then refines the computational grid to ultimately determine the spatial distribution of magnetic flux density, as depicted in Fig. 3(a). Given that radial magnetization is applied to the annular permanent magnet, the magnetic field distribution remains consistent across all radial sections, enabling the analysis of simulation results on these radial sections, as illustrated in Fig. 3(b). The magnetic induction line alters direction when it traverses the magnetic leakage gap, thereby generating a gradient magnetic field. To further dissect the gradient distribution of the magnetic leakage field or the polishing area, auxiliary measurement arcs are constructed along the radial section's arc surface. Each auxiliary measurement has an arc spacing of 0.5 mm, facilitating the analysis of the magnetic flux density at the surface distance of the magnetic leakage gap, ranging from 0.5 mm to 6 mm.
It is apparent that the gap between the magnetic poles dictates both the intensity and the distribution scope of the magnetic field during magnetic leakage. Therefore, this study simulates a permanent magnet excitation device with magnetic leakage gaps of 2 mm, 4 mm, and 6 mm respectively. The magnetic flux density distribution corresponding to different gap sizes is presented in Fig. 4(a-c), while the magnetic flux density distribution curve, ranging from 0.5 mm to 6 mm on the magnetic pole surface, is exhibited in Fig. 4(d-e). At a distance of 0.5 mm from the outer surface of the magnetic leakage gap, the magnetic flux density distribution curves produced by the three magnetic field generators exhibit a bimodal nature. This pattern could lead to the formation of two MR fluid ribbon at non-target polishing positions, which is undesirable for efficient polishing. However, as the distance increases, the magnetic flux density distribution curve progressively reveals a strong central region with weaker flanks. At a distance of 2 mm, the magnetic flux density generated by the yokes of 2 mm and 4 mm gaps forms a singular apex at the gap center, whereas the yoke with a 6 mm gap requires a separation of 3 mm to manifest a similar effect. This evolving trend suggests that the MR fluid ribbon will gradually converge with an increased normal distance from the magnetic leakage gap, culminating in a single ribbon protrusion.
Figure 5 depicts the variation curve of magnetic flux density in the normal direction at the magnetic leakage gap. For the yokes with magnetic leakage gaps of 2 mm and 4 mm, the respective magnetic field gradients within their working areas are 51.4 mT/mm and 64.5 mT/mm. The yoke with a magnetic leakage gap of 6 mm forms a single ribbon at a distance of 3 mm, which serves as the initial value for gradient computation, yielding a magnetic field gradient of 50.3 mT/mm. A substantial gradient fosters the accumulation of polishing powder on the ribbon's surface, thereby enhancing the polishing efficiency. Consequently, taking all factors into account, the yoke with a 4 mm magnetic leakage gap is chosen as the optimal magnetic field generator due to its superior gradient.
4. Analytical verification of MR fluid ribbon formation
The MRPF process utilizes a flexible ribbon on the polishing head to shear material off the workpiece surface. Thus, maintaining a stable magnetorheological ribbon is pivotal for efficient finishing. The ribbon's stability largely depends on the magnetic forces acting on the magnetically susceptible particles in the MR fluid, as described by the subsequent equation:
In this equation, $\overrightarrow B$ represents the magnetic flux density, while $\overrightarrow m$ denotes the magnetic dipole moment. The ribbon's behavior can be simulated by calculating the forces exerted on these particles. The magnetically susceptible particles utilized in MR polishing fluid are micron-grade carbonyl iron particles, assumed to be spherical. The magnetic dipole moment applied to these particles, assuming they are ideal spheres, is provided as follows:
In the given equation, V represents the volume of a magnetically susceptible particle, $\overrightarrow M$ denotes the magnetization intensity, µ is the magnetic permeability, µ0 signifies the permeability of a vacuum, while stands for the magnetic field intensity vector at a specific spatial location. By integrating Eq. (2) into Eq. (1), the force exerted on the magnetically susceptible particle associated with the polishing tool head can be ascertained, as detailed in Eq. (3).
As elucidated by the preceding formula, the distribution of the magnetic field intensity vector is indispensable for constructing the magnetic force model. Thus, the magnetic field intensity vector distribution in the y and z directions was derived using COMSOL software, as exhibited in Fig. 6. Firstly, an examination of the Hy distribution demonstrates that as the distance from the yoke surface increases, the magnetic field intensity curve attains a greater degree of symmetry. Upon reaching a distance of 2 mm, Hy becomes negative. This means that at this distance the magnetically sensitive particles will be pressed towards the outer surface of the spherically polished shell. Under the reaction of the supporting force, the magnetically sensitive particles will accumulate on the surface of the shell, and more particles will converge at the center of the yoke. Secondly, according to the Hz distribution, the magnetic field intensity on the left side of the yoke center is all positive, while the right side of the yoke center is all negative, which will cause particles to gather in the center. Lastly, both Hy and Hz curves transition from a rough to a smooth pattern at a distance of 2 mm, thus inducing ribbon smoothness at this particular distance. In conclusion, Hy and Hz, which are more than 2 mm away from the yoke surface, are used to construct the magnetic field force.
The magnetically sensitive particles have a mean diameter of 4 µm and a density of 7.8 × 10^3 kg/m^3. The permeability (µ) of these particles is 1500, and the vacuum permeability (µ0) is 4π×10^-7. Substituting these parameters into Eq. (3) allows for the simulation of the force distribution on magnetically sensitive particles at the cross-section of the polishing head, as conducted in MATLAB, shown in Fig. 7(a). At the magnetic leakage gap, the magnetic field force exerted on the magnetically sensitive particles intensifies significantly, forming a convex, albeit slightly asymmetric, ribbon that leans towards the internal magnetic pole. Figure 7(b) presents the actual ribbon, a single protrusion with a smooth surface, consistent with prior predictions. Furthermore, the actual ribbon exhibits a slight tilt towards the internal magnetic pole's direction. The height of the actual ribbon, approximately 2.2 mm, satisfies the requirement for material removal from the surface of the optical element.
5. Analysis of applicable precession angle for MRPF
5.1 Magnetic field simulation analysis of polishing area
In the MRPF procedure, the spindle's orientation can be adjusted through the B-axis drive, modulating the angle between the workpiece surface's normal and the polishing spindle axis's normal at the polishing point (known as the precession angle). This adjustment ensures that a specific gap is maintained between the polishing head and the workpiece during inclined processing, as depicted in Fig. 1(b). The precession angle, therefore, emerges as a critical parameter for analysis. Magnetostatic simulations of the polishing area on the workpiece surface for a typical precession angle are presented in Fig. 8(a). Notably, the magnetic flux density in the polished area significantly surpasses that in the non-polished regions. Influenced by the magnetic leakage gap's geometry in the magnetic field generator, the polishing area presents a curved contour. This implies that during polishing, the magnetorheological fluid adheres more robustly near the magnetic leakage gap, enabling the ribbon to exert enhanced shear force for material removal, resulting in a curved removal contour. Figure 8(b) illustrates the magnetic flux density curve on a 16mm-wide workpiece surface, centered on the minimal processing clearance, under varying precession angles. As the precession angle diminishes, the peak magnetic field intensity's position gradually transitions across the workpiece, straddling the minimum processing clearance. At a precession angle of approximately 30°, the peak magnetic field intensity aligns with the minimum processing clearance position. Given that this clearance corresponds to the region generating hydrodynamic pressure – a crucial determinant of polishing spot efficacy – a 30° angle is deemed optimal for processing.
Fig. 8. (a) Simulation of magnetic flux density distribution in polishing area, (b) Curve of magnetic flux density under different precession angle.
5.2 Inclined polishing experiments with precession angles
To investigate the impact of precession angles on material removal characteristics, inclined spot polishing experiments were conducted utilizing a single-factor method. Figure 9 displays an inclined polishing experiments photograph. The tilted polishing head allows the ribbon to contact the workpiece, creating a distinct angle from the workpiece's local normal, referred to as the precession angle. The specimen used is a flat fused silica glass, secured onto the working platform with a precision fixture. The composition of the magnetorheological (MR) polishing fluid utilized for the polishing experiments is outlined in Table 2. The cerium oxide abrasive particles exhibit an average diameter ranging from 8 to 10 µm. The parameters governing the experiment can be found in Table 3.
Table 2. Composition of MR fluid
Table 3. Processing parameters for procession angle experiments
Polishing spots at various precession angles are depicted in Fig. 10. Their three-dimensional contours, captured using the Bruker NPFLEX white light interferometer, are presented in Fig. 10(a-c). Corresponding sectional profiles can be seen in Fig. 10(d-f).
Fig. 10. TIF contour of inclined polishing at (a) 25°, (b)30°, (c)35°, (d) Sectional TIF profile along the line shown in (a), (e) Sectional TIF profile along the line shown in (b), (f) Sectional TIF profile along the line shown in (c).
Across these angles, the polishing spots largely exhibit a D-shape with radians, with the most profound point of the tool influence function (TIF) positioned at the termination of the magnetorheological flow direction. Such TIF characteristics indicate that the material removal mechanism of MRPF closely resembles that of MRF, primarily driven by the abrasive particle shear force acting on the target surface in the MR fluid flow direction. However, the resulting TIF is not as symmetric as the TIF produced by MRF. In the conventional MRF process, the principal axis of the polishing wheel is consistently perpendicular to the local normal of the workpiece and intersects the center of the polishing wheel. The location at which the ribbon is generated is always along the diameter of the polishing wheel, as illustrated in Fig. 11(a). Consequently, the flow direction of the ribbon remains symmetrical during spindle rotation, yielding a symmetrical removal function, as depicted in Fig. 11(b). In contrast, during inclined polishing, the principal axis of the hemispherical polishing head forms a specific angle—known as the precession angle—with the local normal of the workpiece. Furthermore, the ribbon is not generated along the diameter of the hemisphere, as shown in Fig. 11(c). As a result, the flow direction of the ribbon undergoes curvature as the spindle rotates, as demonstrated in Fig. 11(d).
Fig. 11. (a) Schematic diagram of the MRF polishing wheel (seen from the x-axis), (b) Ribbon flow direction of MRF (seen from the z-axis), (c) Schematic diagram of the MRPF polishing tool (seen from the x-axis), (d) Ribbon flow direction of MRPF (seen from the z-axis).
Furthermore, a comparison was made between the material removal rates at 25°, 30°, and 35° precession angles, based on their volume removal rate (VRR) and peak removal rate (PRR). The findings are depicted in Fig. 12. At a precession angle of 30°, the average VRR is 0.032mm3/min. In contrast, at angles of 25° and 35°, the VRRs are 0.017mm3/min and 0.014mm3/min, respectively. The 30° angle's VRR exceeds the rates at 25° and 35° by 88% and 128%. Similarly, the average PRRs are 0.452µm/min (30°), 0.294µm/min (25°), and 0.263µm/min (35°), reflecting increases of 53.7% and 71.9%. The increased material removal rate at the 30° precession angle corroborates the analysis presented in the preceding section. When this angle is employed, the most intense local magnetic field is proximate to the narrowest processing gap, coupled with an extensive range of high magnetic flux intensity – factors contributing to heightened material removal. At angles below or above 30°, the local intense magnetic field drifts away from this minimal gap, resulting in a diminished magnetic flux intensity at the polishing spot and subsequently a reduced material removal rate. Thus, considering both the polishing spot shapes and material removal rates, the optimal precession angle for polishing is determined to be 30°.
Fig. 12. Volume removal rate (VRR) and peak removal rate (PRR) comparison between different precession angle.
6. MRPF process experiments
6.1 Process experiments for precession-steps number
Precession polishing typically occurs from multiple angles, with the total count referred to as the precession-steps number. The optimal count dictates the contour of the removal function. Therefore, the multi-step polishing is carried out from 4 and 8 directions respectively. Table 4 provides the conditions for these experiments. The polishing spots are measured by the Zygo NewView 8200 white-light interferometer, as shown in Fig. 13. The 4-step process yielded a rectangular spot due to the considerable angle between consecutive steps, resulting in incomplete coverage of the full 360° area and uneven material removal, as seen in Fig. 13(a). In contrast, the 8-step spot was nearly symmetrical about its center of rotation, with X and Y removal profiles closely aligning to form a Gaussian shape, and the diameter of the TIF is approximately 17.3 mm. This suggests that an 8-step dynamic magnetorheological polishing can efficiently produce a Gaussian-like, rotationally symmetric removal function, as displayed in Fig. 13(b). Furthermore, the PRR of 4-step is 0.53µm/min, and that of 8-step is 0.49µm/min, the VRR of 4-step is 0.033mm3/min, and that of 8-step is 0.030 mm3/min, which are similar to the PRR and VRR of the previous section, indicating that the removal function of the device is stable.
Table 4. Processing parameters for precession-steps number experiments
Fig. 13. TIFs of precession-steps number experiments: (a) 4 steps, (b) 8 steps; Cross-sectional of TIFs:(c) 4 steps, (d) 8 steps.
6.2 Experiments for improving surface quality
To assess the processing capability of the MRPF (8 steps) technology in enhancing surface quality, we conducted uniform polishing experiments on a 50mm × 50mm × 10 mm planar fused quartz substrate using a raster path with a 1 mm interval and a polishing feed rate of 0.1 mm/s. The tool influence function (TIF) commenced scanning from the initial point in the 0° direction (step 1), then rotated by 45° for subsequent scanning (step 2), continuing this sequence until the completion of the 8-step polishing, as illustrated in Fig. 14. The post-finishing surface morphology was examined using the VHX-1000E optical microscope, as illustrated in Fig. 15. The initial workpiece surface, depicted in Fig. 15(a), exhibited numerous pits. While MRPF polishing left residual defects in the workpiece's edge area due to its under-polishing, the central region displayed a considerably smoother surface. Additionally, the workpiece's surface roughness underwent quantitative analysis. The initial roughness was gauged using the Taylor Hobson roughness profiler (PGI 1240), while the polished surface's roughness was assessed with a white light interferometer (Bruker NPFLEX), as presented in Fig. 16. Results indicated a reduction in surface roughness from an initial Ra of 0.7 µm to a final Ra of 2.14 nm. This notable improvement in both surface roughness values and morphology underscores the MRPF process's efficacy in refining surface quality.
Fig. 14. Schematic of surface generation process by 8 steps MRF precession polishing along raster path.
Fig. 15. Surface morphology measurement results. (a) initial surface, (b) edge area, (c) middle area.
7. Conclusion
This research introduces an innovative magnetorheological precession polishing technique designed to achieve a Gaussian-like removal function. The development process commenced with the design of a hemispherical magnetorheological polishing head, informed by magnetostatic simulations and magnetic force analyses related to a ring magnet. This design enables the magnetorheological fluid to manifest as a singer MR fluid ribbon. Further analysis of the magnetic field distribution within the workpiece's polishing region, combined with a single-point polishing experiment, established that the optimal precession angle is 30 degrees. Utilizing this angle and through an 8-step rotation of the A-axis, the sought-after Gaussian-like removal function was achieved. Subsequent experiments employing the TIFs revealed a significant decrease in the roughness of the silica plane surface from an initial Ra 0.3 µm to a refined 2.1 nm. Given its design, this polishing head can seamlessly integrate into the spindle of existing bonnet polishing machines, thus offering the potential for concurrent bonnet and magnetorheological polishing, and broadening machining capabilities. The primary significance of this research lies in the development of a novel polishing technique that promises enhanced efficiency and precision in optical manufacturing.
Funding
Key Research and Development Program of Hunan Province of China (No. 2023GK2069); National Natural Science Foundation of China (No. 52075463); Shenzhen Technical Project (JCYJ20210324122001003).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. Q. Liu, Z. Liao, and D. Axinte, “Temperature effect on the material removal mechanism of soft-brittle crystals at nano/micron scale,” Int. J. Mach. Tool Manufact. 159, 103620 (2020). [CrossRef]
2. T. He, C. Wei, Z. Jiang, et al., “Super-smooth surface demonstration and the physical mechanism of CO2 laser polishing of fused silica,” Opt. Lett. 43(23), 5777–5780 (2018). [CrossRef]
3. R. Pan, B. Zhong, D. Chen, et al., “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018). [CrossRef]
4. A. Lu, T. Jin, Q. Liu, et al., “Modeling and prediction of surface topography and surface roughness in dual-axis wheel polishing of optical glass,” Int. J. Mach. Tool Manufact. 137, 13–29 (2019). [CrossRef]
5. J. Angel, “Very large ground-based telescopes for optical and IR astronomy,” Nature 295(5851), 651–657 (1982). [CrossRef]
6. Y. Xu, J. Lu, X. Xu, et al., “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018). [CrossRef]
7. C. Wagner and N. Harned, “Lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010). [CrossRef]
8. X. Liu, Y. Chen, D. Li, et al., “Nearly lattice-matched molybdenum disulfide/gallium nitride heterostructure enabling high-performance phototransistors,” Photonics Res. 7(3), 311 (2019). [CrossRef]
9. DD Walker, R Freeman, R Morton, et al., “Use of the ‘Precessions’™ process for prepolishing and correcting 2D & 2½D form,” Opt. Express 14(24), 11787 (2006). [CrossRef]
10. Xianyun Zhong, Bin Fan, and Fan Wu, “High-accuracy process based on the corrective calibration of removal function in the magnetorheological finishing,” Opt. Eng. 56(08), 1 (2017). [CrossRef]
11. OW Fähnle, BH Van, and HJ Frankena, “Fluid jet polishing of optical surfaces,” Appl. Opt. 37(28), 6771 (1998). [CrossRef]
12. CR Giuliano, “Laser-induced damage in transparent dielectrics: ion beam polishing as a means of increasing surface damage thresholds,” Appl. Phys. Lett. 21(1), 39–41 (1972). [CrossRef]
13. A. Lamikiz, JA Sánchez, López de Lacalle LN, et al., “Laser polishing of parts built up by selective laser sintering,” Int. J. Mach. Tool Manufact. 47(12-13), 2040–2050 (2007). [CrossRef]
14. Z. H. Zhu, P. Huang, S. To, et al., “Fast-tool-servo-controlled shear-thickening micropolishing,” Int. J. Mach. Tool Manufact. 184, 103968 (2023). [CrossRef]
15. N. Savage, “Optical polishing equipment,” Nat. Photonics 4(12), 880–881 (2010). [CrossRef]
16. M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008). [CrossRef]
17. J. Seok, Y. Kim, K. Jang, et al., “A study on the fabrication of curved surfaces using magnetorheological fluid finishing,” Int. J. Mach. Tool Manufact. 47(14), 2077–2090 (2007). [CrossRef]
18. V.K. Jain, A. Sidpara, R. Balasubramaniam, et al., “Micromanufacturing: a review—part i,” Proc. IME B J. Eng. Manufact. 228(9), 973–994 (2014). [CrossRef]
19. N Zhou J, C Cao Z, P Zhang J, et al., “Development and theoretical analysis of novel surface adaptive polishing process for high-efficiency polishing of optical freeform surface,” J. Manuf. Process 80, 874–886 (2022). [CrossRef]
20. Y. Han, C. Liu, M. Yu, et al., “Material removal characteristics in submerged pulsating air jet polishing process,” Int. J. Mech. Sci. 257, 108534 (2023). [CrossRef]
21. Yun Zhang and Zhi Jing Feng, “Optimization of the Removal Function of Dual-Rotation Magnetorheological Finishing,” Mater. Sci. Forum 874, 70–78 (2016). [CrossRef]
22. RG Bingham, DD Walker, DH Kim, et al., “Novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000). [CrossRef]
23. DD Walker, D Brooks, A King, et al., “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003). [CrossRef]
24. X. Su, P. Ji, K. Liu, et al., “Combined processing chain for freeform optics based on atmospheric pressure plasma processing and bonnet polishing,” Opt. Express 27(13), 17979–17992 (2019). [CrossRef]
25. J Guo, A Beaucamp, and S Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017). [CrossRef]
