# Review on Surface Polishing Methods of Optical Parts

Authors: Mingli Xie; Yipeng Pan; Zijun An; Shijun Huang; Min Dong
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

With the extensive application of optical parts in many high-tech fields such as high-power laser, space optics, and aerospace, the requirements for the surface quality of optical parts are also increasing, which requires not only high surface qualities but also low defects including low subsurface damage and strict wavefront errors. As an essential link in the precision and ultraprecision optical manufacturing, various surface polishing methods and techniques have always attracted researchers’ continuous study and exploration. Considering the development of optical part surface polishing technology in recent years, this study analyzes the principle and development process of typical processing methods represented by each kind of polishing technology, expounds the specific research progress of optical part surface polishing technology, including the iterative renewal of traditional technologies and the research development of new technologies, and gives examples for typical applications. Finally, the development trend of optical part surface polishing technology is prospected, which provides a reference for follow-up intensive research in optical manufacturing.


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## Body

## 1. Introduction

The optical part is the basic unit and an important part of optical related systems such as the laser device and the lithography machine. Optical components with unique physical properties are widely used in aviation, aerospace, electronics, and other fields. With the development of science and technology, the surface accuracy of optical parts tends to be nano and atomized. For example, in the inertial confinement fusion (ICF) system, whether the fusion reaction can be realized mainly depends on the manufacturing level of high light optical elements in the optical path. The pursuit of components with higher surface accuracy and better performance is an eternal topic at the forefront of optical manufacturing. Optical processing is a very complex process. It is difficult to manufacture optical parts that meet various processing quality requirements through a single processing method. For example, for small aperture aspheric surfaces and freeform surfaces, the machining accuracy requires subnanometer, deep subnanometer, or even picometer, and the machined surface is required to be super smooth and free of subsurface damage and ultralow defects. Using ultraprecision diamond turning or ultraprecision grinding can obtain good surface roughness, but it will inevitably cause defects and damage on the surface. Therefore, in actual production, the production process combined with various polishing methods will be used to correct the flaws in the processing process to meet the needs of high-quality workpieces.Ultrasmooth surface optical parts refer to optical components whose RMS deviation of optical surface roughness is less than 1 nm, which have high surface shape accuracy and low surface waviness [1, 2]. To achieve this goal, researchers continue to study and explore the field of ultraprecision optical manufacturing. From the current research, according to whether the workpiece is in contact with the polishing pad, the ultrapolishing methods of optical parts can be divided into three categories: contact polishing, noncontact polishing, and quasicontact polishing. Contact polishing includes bowl feed polishing, bonnet polishing, etc. Noncontact polishing includes ion beam polishing, float polishing, elastic emission machining, plasma-assisted polishing, hydrodynamic suspension polishing, etc. Quasicontact polishing includes magnetorheological polishing, chemical mechanical polishing, etc. This study reviews the above typical superfinishing methods from the aspects of machining principles, key technology research, application, and development process, and it also forecasts the main research direction in the future combined with the current research status.


## 2. Contact Polishing

Contact polishing refers to the processing method, in which the polishing pad contacts the polished surface in the processing process. During processing, the mechanical, chemical, or electrochemical action is used to reduce the surface roughness of the workpiece to obtain a bright and smooth surface. Contact polishing usually exerts a certain pressure on the polished surface, which can achieve high material removal efficiency. It is the most common application form in traditional polishing.


### 2.1. Bowl Feed Polishing

Bowl feed polishing (BFP) is an ultrasmooth surface processing method proposed by Dietz and Bennett based on traditional polishing equipment and techniques to develop UV optics in the United States in the 1960s, and the ultrasmooth surface of RMS 0.3 nm is obtained on fused quartz. As shown in Figure1, the contact surface between the polishing pad and the workpiece is immersed in the polishing fluid, the polishing pad rotates, and the workpiece moves horizontally while rotating to ensure that each point of the polished surface is in random contact with each point of the working surface of the polishing pad. The stirrer keeps stirring to ensure that nearly all of the polishing mixture particles remain suspended, which makes the abrasive particles precipitate continuously on the polishing pad to form a tiny blade to cut the workpiece [3]. In addition, the existence of a large amount of liquid ensures the local temperature balance on the surface of the polishing pad, and the polishing pad is not prone to thermal deformation, which provides the possibility of a high-precision surface. Since it has been found that the wear of the polishing pad, the nature of the abrasive medium, and the polishing time have significant effects on the polished surface quality, subsequent researchers mainly study the relationship between these factors and the machining economy and surface qualities of the parts.Figure 1
Bowl feed polishing principle.


#### 2.1.1. Effect of Polishing Pad Material on Processing Quality

With the increase in the size of the processed parts, the flatness requirements of the polishing pad are also higher. However, under the dual action of abrasive scribing and processing thermal effects in the polishing process, the traditional asphalt polishing pad is easy to deform, resulting in a decline in processing quality. Therefore, finding new materials and producing more stable and durable polishing pads are problems researchers need to solve. Leistner et al. [4] innovatively applied Teflon to prepare polishing pads. Since Teflon itself has the advantages of low-temperature resistance, high-temperature resistance, corrosion resistance, low friction coefficient, etc, the Teflon polishing pad wears very slowly and has strong stability compared with traditional asphalt pads, which makes Teflon polishing pads widely used in subsequent research [5, 6].


#### 2.1.2. Effect of Process Parameters on Polishing Quality

van Wingerden and Johannes [7] systematically studied the effect of polishing time on the surface roughness in BFP, established the best matching relation between the surface target quality and the polishing time, and obtained an ultrasmooth surface with Rq = 0.15 nm through experimental research. Based on previous studies, Meng et al. [8] studied the effects of the abrasive particle size, abrasive concentration and pH value of polishing fluid on the material removal rate, and surface roughness of K9 glass. Finally, they obtained an ultrasmooth surface with a surface roughness of 0.2076 nm through orthogonal experiments. Literature [9, 10] mainly studied the size and particle size uniformity of abrasive particles and selected ceria polishing powder mixed with different particle sizes and different proportions to polish K9 glass, respectively (Table 1). The significance of this study is to establish the polishing abrasive distribution and the corresponding relationship between the particle volume concentration and roughness near the average particle size from the microscopic point of view, which has guiding significance for selecting appropriate polishing abrasives and optimizing machining efficiency according to different target requirements in the actual machining process.Table 1
1.2μm particle size distribution range with different mass ratios and its corresponding workpiece surface roughness values after polishing.
Granularity (μm)Particle size distribution range (μm)Particle volume concentration in 7 intervals near the average particle sizeRMS (nm)1.20.254–4.7556.336.997.467.700.19437.697.436.94—Mass ratio of 1.2μm to 1.6 μm is 3 : 10.22–13.0636.366.897.237.360.28647.276.975.80—Mass ratio of 1.2μm to 1.6 μm is 1 : 10.05–15.9896.076.456.676.720.19156.596.305.85—BFP technology breaks the inherent mode of polishing, provides a new idea for the production and development of other polishing technologies, and promotes the research of polishing fluid. However, in the process of polishing, the surface of the workpiece is in direct contact with the polishing pad, which makes the machined surface more susceptible to subsurface damage, thus directly affecting the imaging quality, antilaser damage threshold, and stability and service life of optical parts, so it needs to be further explored in the manufacture of ultraprecision optical parts. From the current development direction, BFP is mostly combined with chemical polishing, and etching is carried out through the chemical modification of the polishing slurry to reduce the residual subsurface damage on the sample surface after polishing. Meanwhile, hydraulic selection technology is used to control the settlement of abrasive particles to make the particle size distribution more uniform and help obtain lower surface roughness [11–13].


### 2.2. Bonnet Polishing

In 2000, Zeeko company and Walker et al. in the UK put forward bonnet polishing technology and produced the IRP-200 polishing machine tool. The surface profile accuracy and surface roughness can reach 80 nm (P-V) and 3 nm (Ra) respectively, and the material removal rate of rough polishing can reach 2 mm3/min. The processing principle is shown in Figure 2. The technology uses a spinning, bulged, and compliant tool covered with a suitable polishing surface (cloth, polyurethane, etc.). By controlling the axial position of the tool and its internal pressure, the tool contact area (“spot size”) and polishing pressure can be modulated independently and the process requirements of workpieces with different curved surfaces and sizes can be met, which not only ensures the polishing efficiency but also improves the machining accuracy. It is especially suitable for machining aspheric or freeform surfaces [14]. Subsequently, the team successively developed IRP300 and IRP600 polishing machine tools to expand the size range of the processed workpieces.Figure 2
Bonnet polishing principle.To further improve the surface quality and reduce the edge effect, the team combined slurry jet technology with bonnet polishing to develop a 4 m-class CNC machine tool (Figure3), which extends precession processing to parts with inferior input quality [15]. This is particularly important to large optical large optics where significant volumes of materials may need to be removed and to the creation of more substantial aspheric departures from a parent sphere. Based on this idea, Beaucamp and Namba [16] proposed a two-step freeform surface finishing method to manufacture ultrasmooth aspheric optical devices for X-ray telescopes, which first used fluid jet polishing to remove the turning trace, and the shape error was corrected to less than 50 nm. Then, the continuous precessed bonnet polishing was used to obtain an ultrasmooth surface with a surface roughness of RMS 0.28 nm. Subsequent researchers, based on bonnet polishing technology, have carried out many detailed studies on the microscopic material removal mechanism, edge effect suppression, polishing path planning, etc.Figure 3
Zeeko 4 m-class CNC machine tool, polishing a∼1 m diameter part [15].


#### 2.2.1. Research on Microscopic Material Removal Mechanism

Song et al. [17] studied the effect of different polishing parameters on the material removal rate of spherical optical glass under the different radii of curvature through experiments. The results show that when the spherical workpieces are polished with a smaller curvature radius, it is not proportional to either bonnet decrement or bonnet rotational speed as described by the Preston equation although the removal rate increases as the relative velocity or the applied pressure increases. Therefore, to more accurately calculate the material removal of the spherical workpieces, the Preston equation should be modified and studied further. To more accurately describe the workpiece removal function during bonnet polishing, Wang et al. [18] proposed an improved Preston removal function model based on the finite element analysis method. According to the theory that the stress in the static contact area is a Gaussian distribution, the stress distribution function in the dynamic contact area is derived using the least square method. This further explains the material removal mechanism of bonnet polishing from the perspective of friction and force. Feng et al. [19] further established and optimized the removal function model using finite element analysis based on the velocity and pressure distributions derived from the machining tool motion geometry and Hertzian contact theory. Through the simulation experiments in three modes, the optimal process parameters were obtained. Feng’s research enriched and developed the microscopic removal mechanism of bonnet polishing but did not fully consider the effects of other processing parameters such as pad properties, bonnet features, and processing conditions on the removal function. Shi et al. [20] established a microanalysis model based on the mutual interaction of the slurry, pad, and workpiece among the BP interfaces with microcontact theory and tribology theory. As shown in Figure 4, the model provides a more comprehensive description of the nonPrestonian behavior and helps understand the material removal mechanisms of BP from the perspective of multiple factors.Figure 4
Microtheoretical model of material removal in BP [20].


#### 2.2.2. Polishing Path Planning

In terms of trajectory planning, traditional research primarily focuses on spirals and gratings. The application of the grating path can polish not only the rotating symmetric surface but also the free-form surface. In actual processing, different path methods have a significant impact on the surface texture and processing time. The processing path often adopts the easily controlled equidistant grating path, spiral path, or other regular paths. Due to the periodicity of the path, the machining process is prone to intermediate frequency error during the iterative convolution operation. Walker et al. [21] developed a free path algorithm, which calculates the dwell time by comparing the height error between the actual surface and the target surface and evenly distributes the dwell time to the two cross grating paths on the part. This method can provide controlled local material removal in a predictable manner even over severe and nonuniform aspheric departures. It could swing the debate toward an aspheric design with a fast primary f/F.In recent years, with the development of robot-assisted bonnet polishing technology, most trajectory planning research has been combined with robot technology. The Jishiming team of Zhejiang University of Technology manufactured a 6-DOF robot bonnet polishing system based on the Motoman-HP20 industrial robot and carried out polishing trajectory optimization research with the goal of smooth control and optimal processing time under three different path planning schemes, including direction parallel, contour parallel, and free path. The optimization of line spacing in parallel continuous precession bonnet polishing was investigated by experimental methods. The optimization value of line spacing under the combination of specific process parameters was obtained [22]. Pan et al. [23, 24] reduced the existing errors of precession angle in the polishing process by making micromigration of machining points and realized the real-time and accurate control of the position and attitude of the bonnet on the premise of determining the trajectory, which turned the trajectory research from macropath planning to the micropoint displacement correction control algorithm on the path. In subsequent research work, the team developed a controllable flexible bonnet polishing machine, as shown in Figure 5. The machine tool adopts the precession processing mode, that is, the spindle always forms a fixed precession angle with the local normal of the workpiece during polishing. The two axes Z1 and Z3 control the change in spindle Z2 in space, and the Z1, Z3, and Z2 axes intersect the ball center of the bonnet head. Through the analysis and calculation of the motion space, when Z1 and Z3 are 45° in space, the spatial motion range and stiffness of the whole bonnet polishing tool are the most appropriate.Figure 5
Research on bonnet polishing at Xiamen University [25]. (a) Illustration of bonnet polishing machine and the prototype. (b) Bonnet polishing head. (c) Off-line dressing equipment of bonnet polishing head.
(a)(b)(c)On the machine tool, the mathematical model of fixed-point precession bonnet polishing is established by using the homogeneous coordinate transformation matrices, and the stability of multistep discrete precession polishing under fixed-point polishing is analyzed. The experiments show that the machine tool can meet the continuous precession processing requirements of large-diameter aspheric optical parts, and a better surface accuracy is obtained for the processing of circular planar optical components with a diameter of 320 mm. In addition, the team also developed a flexible bonnet polishing head with built-in steel mesh and off-line dressing equipment and developed an online detection system. The detection system places the laser displacement sensor on the grinding spindle and uses the movement of each axis of the grinder to complete the surface detection of large-diameter aspheric elements, which can realize the full-diameter measurement of large-diameter optical elements. This detection method belongs to the online type. Its characteristic is that it can avoid the clamping and positioning errors introduced by the off-line measurement of the workpiece, realize the measurement of the machining surface accuracy of the workpiece, and provide machining error data for compensated machining. Figure6 shows the surface shape accuracy after original machining and compensated machining of large-aperture aspheric optical elements detected by the online detection system. After three rounds of compensated machining, the shape PV value decreases from 7.77 μm to 4.67 μm [24–27].Figure 6
PV of the original and compensated aspherical surface [25]. (a) Initial processing (PV = 7.77 μm; RMS = 1.35 μm). (b) First compensation processing (PV = 6.39 μm; RMS = 1.24 μm). (c) Second compensation processing (PV = 5.71 μm; RMS = 1.02 μm). (d) Third compensation processing (PV = 4.67 μm; RMS = 0.72 μm).
(a)(b)(c)(d)From the above literature research, it is found that the robot-assisted bonnet polishing technology generally adopts continuous precession processing. However, in the practical work, it is also found that the polishing area of the workpiece is not uniform and the contour line of the cross section of material removal in polishing directions is a wavy line, which indicates the continuous precession processing has bad performance on conformal polishing. The reason is that the dynamic factors of the spindle speed of the polishing tool and the feed speed of the bonnet tool are not incompatible [29]. This phenomenon is particularly obvious when machining high-precision freeform surface optical parts. It is evident that the CAM system alone cannot directly generate an appropriate high-precision tool path without considering dynamics factors.Starting from the machining practice, based on the principle of automatic dynamics analysis of mechanical systems, scholars put forward a tool path generation method for ultraprecision machining of freeform surfaces (Figure7). Considering the dynamics, material and mechanical stiffness, friction, tool, and accuracy of servo components, the toolpath for very complex freeform surfaces is generated by the Newton–Raphson method. Meanwhile, this method also overcomes the problems of shape error and compensation fault in ultraprecision machining of the traditional CAM systems. Considering the influence of friction and contact force on the processing system, a very accurate toolpath curve can be generated [28].Figure 7
Ultraprecision machining principle diagram using multibody TPG [28].Based on the idea of literature [28, 30], the tool influence function of the Gaussian mixture model is proposed in the case of considering the dynamic stress of the bonnet polishing machine and a regional adaptive path planning model that integrates machining depth, TIF volume removal rate, path spacing, and feed rate is established. The optimal feed rate scheduling under the dynamic constraints of the machine tool is realized by establishing the acceptable feed path spacing and feed range, and the stability and utility in deterministic material removal are achieved.


## 2.1. Bowl Feed Polishing

Bowl feed polishing (BFP) is an ultrasmooth surface processing method proposed by Dietz and Bennett based on traditional polishing equipment and techniques to develop UV optics in the United States in the 1960s, and the ultrasmooth surface of RMS 0.3 nm is obtained on fused quartz. As shown in Figure1, the contact surface between the polishing pad and the workpiece is immersed in the polishing fluid, the polishing pad rotates, and the workpiece moves horizontally while rotating to ensure that each point of the polished surface is in random contact with each point of the working surface of the polishing pad. The stirrer keeps stirring to ensure that nearly all of the polishing mixture particles remain suspended, which makes the abrasive particles precipitate continuously on the polishing pad to form a tiny blade to cut the workpiece [3]. In addition, the existence of a large amount of liquid ensures the local temperature balance on the surface of the polishing pad, and the polishing pad is not prone to thermal deformation, which provides the possibility of a high-precision surface. Since it has been found that the wear of the polishing pad, the nature of the abrasive medium, and the polishing time have significant effects on the polished surface quality, subsequent researchers mainly study the relationship between these factors and the machining economy and surface qualities of the parts.Figure 1
Bowl feed polishing principle.


### 2.1.1. Effect of Polishing Pad Material on Processing Quality

With the increase in the size of the processed parts, the flatness requirements of the polishing pad are also higher. However, under the dual action of abrasive scribing and processing thermal effects in the polishing process, the traditional asphalt polishing pad is easy to deform, resulting in a decline in processing quality. Therefore, finding new materials and producing more stable and durable polishing pads are problems researchers need to solve. Leistner et al. [4] innovatively applied Teflon to prepare polishing pads. Since Teflon itself has the advantages of low-temperature resistance, high-temperature resistance, corrosion resistance, low friction coefficient, etc, the Teflon polishing pad wears very slowly and has strong stability compared with traditional asphalt pads, which makes Teflon polishing pads widely used in subsequent research [5, 6].


### 2.1.2. Effect of Process Parameters on Polishing Quality

van Wingerden and Johannes [7] systematically studied the effect of polishing time on the surface roughness in BFP, established the best matching relation between the surface target quality and the polishing time, and obtained an ultrasmooth surface with Rq = 0.15 nm through experimental research. Based on previous studies, Meng et al. [8] studied the effects of the abrasive particle size, abrasive concentration and pH value of polishing fluid on the material removal rate, and surface roughness of K9 glass. Finally, they obtained an ultrasmooth surface with a surface roughness of 0.2076 nm through orthogonal experiments. Literature [9, 10] mainly studied the size and particle size uniformity of abrasive particles and selected ceria polishing powder mixed with different particle sizes and different proportions to polish K9 glass, respectively (Table 1). The significance of this study is to establish the polishing abrasive distribution and the corresponding relationship between the particle volume concentration and roughness near the average particle size from the microscopic point of view, which has guiding significance for selecting appropriate polishing abrasives and optimizing machining efficiency according to different target requirements in the actual machining process.Table 1
1.2μm particle size distribution range with different mass ratios and its corresponding workpiece surface roughness values after polishing.
Granularity (μm)Particle size distribution range (μm)Particle volume concentration in 7 intervals near the average particle sizeRMS (nm)1.20.254–4.7556.336.997.467.700.19437.697.436.94—Mass ratio of 1.2μm to 1.6 μm is 3 : 10.22–13.0636.366.897.237.360.28647.276.975.80—Mass ratio of 1.2μm to 1.6 μm is 1 : 10.05–15.9896.076.456.676.720.19156.596.305.85—BFP technology breaks the inherent mode of polishing, provides a new idea for the production and development of other polishing technologies, and promotes the research of polishing fluid. However, in the process of polishing, the surface of the workpiece is in direct contact with the polishing pad, which makes the machined surface more susceptible to subsurface damage, thus directly affecting the imaging quality, antilaser damage threshold, and stability and service life of optical parts, so it needs to be further explored in the manufacture of ultraprecision optical parts. From the current development direction, BFP is mostly combined with chemical polishing, and etching is carried out through the chemical modification of the polishing slurry to reduce the residual subsurface damage on the sample surface after polishing. Meanwhile, hydraulic selection technology is used to control the settlement of abrasive particles to make the particle size distribution more uniform and help obtain lower surface roughness [11–13].


## 2.1.1. Effect of Polishing Pad Material on Processing Quality

With the increase in the size of the processed parts, the flatness requirements of the polishing pad are also higher. However, under the dual action of abrasive scribing and processing thermal effects in the polishing process, the traditional asphalt polishing pad is easy to deform, resulting in a decline in processing quality. Therefore, finding new materials and producing more stable and durable polishing pads are problems researchers need to solve. Leistner et al. [4] innovatively applied Teflon to prepare polishing pads. Since Teflon itself has the advantages of low-temperature resistance, high-temperature resistance, corrosion resistance, low friction coefficient, etc, the Teflon polishing pad wears very slowly and has strong stability compared with traditional asphalt pads, which makes Teflon polishing pads widely used in subsequent research [5, 6].


## 2.1.2. Effect of Process Parameters on Polishing Quality

van Wingerden and Johannes [7] systematically studied the effect of polishing time on the surface roughness in BFP, established the best matching relation between the surface target quality and the polishing time, and obtained an ultrasmooth surface with Rq = 0.15 nm through experimental research. Based on previous studies, Meng et al. [8] studied the effects of the abrasive particle size, abrasive concentration and pH value of polishing fluid on the material removal rate, and surface roughness of K9 glass. Finally, they obtained an ultrasmooth surface with a surface roughness of 0.2076 nm through orthogonal experiments. Literature [9, 10] mainly studied the size and particle size uniformity of abrasive particles and selected ceria polishing powder mixed with different particle sizes and different proportions to polish K9 glass, respectively (Table 1). The significance of this study is to establish the polishing abrasive distribution and the corresponding relationship between the particle volume concentration and roughness near the average particle size from the microscopic point of view, which has guiding significance for selecting appropriate polishing abrasives and optimizing machining efficiency according to different target requirements in the actual machining process.Table 1
1.2μm particle size distribution range with different mass ratios and its corresponding workpiece surface roughness values after polishing.
Granularity (μm)Particle size distribution range (μm)Particle volume concentration in 7 intervals near the average particle sizeRMS (nm)1.20.254–4.7556.336.997.467.700.19437.697.436.94—Mass ratio of 1.2μm to 1.6 μm is 3 : 10.22–13.0636.366.897.237.360.28647.276.975.80—Mass ratio of 1.2μm to 1.6 μm is 1 : 10.05–15.9896.076.456.676.720.19156.596.305.85—BFP technology breaks the inherent mode of polishing, provides a new idea for the production and development of other polishing technologies, and promotes the research of polishing fluid. However, in the process of polishing, the surface of the workpiece is in direct contact with the polishing pad, which makes the machined surface more susceptible to subsurface damage, thus directly affecting the imaging quality, antilaser damage threshold, and stability and service life of optical parts, so it needs to be further explored in the manufacture of ultraprecision optical parts. From the current development direction, BFP is mostly combined with chemical polishing, and etching is carried out through the chemical modification of the polishing slurry to reduce the residual subsurface damage on the sample surface after polishing. Meanwhile, hydraulic selection technology is used to control the settlement of abrasive particles to make the particle size distribution more uniform and help obtain lower surface roughness [11–13].


## 2.2. Bonnet Polishing

In 2000, Zeeko company and Walker et al. in the UK put forward bonnet polishing technology and produced the IRP-200 polishing machine tool. The surface profile accuracy and surface roughness can reach 80 nm (P-V) and 3 nm (Ra) respectively, and the material removal rate of rough polishing can reach 2 mm3/min. The processing principle is shown in Figure 2. The technology uses a spinning, bulged, and compliant tool covered with a suitable polishing surface (cloth, polyurethane, etc.). By controlling the axial position of the tool and its internal pressure, the tool contact area (“spot size”) and polishing pressure can be modulated independently and the process requirements of workpieces with different curved surfaces and sizes can be met, which not only ensures the polishing efficiency but also improves the machining accuracy. It is especially suitable for machining aspheric or freeform surfaces [14]. Subsequently, the team successively developed IRP300 and IRP600 polishing machine tools to expand the size range of the processed workpieces.Figure 2
Bonnet polishing principle.To further improve the surface quality and reduce the edge effect, the team combined slurry jet technology with bonnet polishing to develop a 4 m-class CNC machine tool (Figure3), which extends precession processing to parts with inferior input quality [15]. This is particularly important to large optical large optics where significant volumes of materials may need to be removed and to the creation of more substantial aspheric departures from a parent sphere. Based on this idea, Beaucamp and Namba [16] proposed a two-step freeform surface finishing method to manufacture ultrasmooth aspheric optical devices for X-ray telescopes, which first used fluid jet polishing to remove the turning trace, and the shape error was corrected to less than 50 nm. Then, the continuous precessed bonnet polishing was used to obtain an ultrasmooth surface with a surface roughness of RMS 0.28 nm. Subsequent researchers, based on bonnet polishing technology, have carried out many detailed studies on the microscopic material removal mechanism, edge effect suppression, polishing path planning, etc.Figure 3
Zeeko 4 m-class CNC machine tool, polishing a∼1 m diameter part [15].


### 2.2.1. Research on Microscopic Material Removal Mechanism

Song et al. [17] studied the effect of different polishing parameters on the material removal rate of spherical optical glass under the different radii of curvature through experiments. The results show that when the spherical workpieces are polished with a smaller curvature radius, it is not proportional to either bonnet decrement or bonnet rotational speed as described by the Preston equation although the removal rate increases as the relative velocity or the applied pressure increases. Therefore, to more accurately calculate the material removal of the spherical workpieces, the Preston equation should be modified and studied further. To more accurately describe the workpiece removal function during bonnet polishing, Wang et al. [18] proposed an improved Preston removal function model based on the finite element analysis method. According to the theory that the stress in the static contact area is a Gaussian distribution, the stress distribution function in the dynamic contact area is derived using the least square method. This further explains the material removal mechanism of bonnet polishing from the perspective of friction and force. Feng et al. [19] further established and optimized the removal function model using finite element analysis based on the velocity and pressure distributions derived from the machining tool motion geometry and Hertzian contact theory. Through the simulation experiments in three modes, the optimal process parameters were obtained. Feng’s research enriched and developed the microscopic removal mechanism of bonnet polishing but did not fully consider the effects of other processing parameters such as pad properties, bonnet features, and processing conditions on the removal function. Shi et al. [20] established a microanalysis model based on the mutual interaction of the slurry, pad, and workpiece among the BP interfaces with microcontact theory and tribology theory. As shown in Figure 4, the model provides a more comprehensive description of the nonPrestonian behavior and helps understand the material removal mechanisms of BP from the perspective of multiple factors.Figure 4
Microtheoretical model of material removal in BP [20].


### 2.2.2. Polishing Path Planning

In terms of trajectory planning, traditional research primarily focuses on spirals and gratings. The application of the grating path can polish not only the rotating symmetric surface but also the free-form surface. In actual processing, different path methods have a significant impact on the surface texture and processing time. The processing path often adopts the easily controlled equidistant grating path, spiral path, or other regular paths. Due to the periodicity of the path, the machining process is prone to intermediate frequency error during the iterative convolution operation. Walker et al. [21] developed a free path algorithm, which calculates the dwell time by comparing the height error between the actual surface and the target surface and evenly distributes the dwell time to the two cross grating paths on the part. This method can provide controlled local material removal in a predictable manner even over severe and nonuniform aspheric departures. It could swing the debate toward an aspheric design with a fast primary f/F.In recent years, with the development of robot-assisted bonnet polishing technology, most trajectory planning research has been combined with robot technology. The Jishiming team of Zhejiang University of Technology manufactured a 6-DOF robot bonnet polishing system based on the Motoman-HP20 industrial robot and carried out polishing trajectory optimization research with the goal of smooth control and optimal processing time under three different path planning schemes, including direction parallel, contour parallel, and free path. The optimization of line spacing in parallel continuous precession bonnet polishing was investigated by experimental methods. The optimization value of line spacing under the combination of specific process parameters was obtained [22]. Pan et al. [23, 24] reduced the existing errors of precession angle in the polishing process by making micromigration of machining points and realized the real-time and accurate control of the position and attitude of the bonnet on the premise of determining the trajectory, which turned the trajectory research from macropath planning to the micropoint displacement correction control algorithm on the path. In subsequent research work, the team developed a controllable flexible bonnet polishing machine, as shown in Figure 5. The machine tool adopts the precession processing mode, that is, the spindle always forms a fixed precession angle with the local normal of the workpiece during polishing. The two axes Z1 and Z3 control the change in spindle Z2 in space, and the Z1, Z3, and Z2 axes intersect the ball center of the bonnet head. Through the analysis and calculation of the motion space, when Z1 and Z3 are 45° in space, the spatial motion range and stiffness of the whole bonnet polishing tool are the most appropriate.Figure 5
Research on bonnet polishing at Xiamen University [25]. (a) Illustration of bonnet polishing machine and the prototype. (b) Bonnet polishing head. (c) Off-line dressing equipment of bonnet polishing head.
(a)(b)(c)On the machine tool, the mathematical model of fixed-point precession bonnet polishing is established by using the homogeneous coordinate transformation matrices, and the stability of multistep discrete precession polishing under fixed-point polishing is analyzed. The experiments show that the machine tool can meet the continuous precession processing requirements of large-diameter aspheric optical parts, and a better surface accuracy is obtained for the processing of circular planar optical components with a diameter of 320 mm. In addition, the team also developed a flexible bonnet polishing head with built-in steel mesh and off-line dressing equipment and developed an online detection system. The detection system places the laser displacement sensor on the grinding spindle and uses the movement of each axis of the grinder to complete the surface detection of large-diameter aspheric elements, which can realize the full-diameter measurement of large-diameter optical elements. This detection method belongs to the online type. Its characteristic is that it can avoid the clamping and positioning errors introduced by the off-line measurement of the workpiece, realize the measurement of the machining surface accuracy of the workpiece, and provide machining error data for compensated machining. Figure6 shows the surface shape accuracy after original machining and compensated machining of large-aperture aspheric optical elements detected by the online detection system. After three rounds of compensated machining, the shape PV value decreases from 7.77 μm to 4.67 μm [24–27].Figure 6
PV of the original and compensated aspherical surface [25]. (a) Initial processing (PV = 7.77 μm; RMS = 1.35 μm). (b) First compensation processing (PV = 6.39 μm; RMS = 1.24 μm). (c) Second compensation processing (PV = 5.71 μm; RMS = 1.02 μm). (d) Third compensation processing (PV = 4.67 μm; RMS = 0.72 μm).
(a)(b)(c)(d)From the above literature research, it is found that the robot-assisted bonnet polishing technology generally adopts continuous precession processing. However, in the practical work, it is also found that the polishing area of the workpiece is not uniform and the contour line of the cross section of material removal in polishing directions is a wavy line, which indicates the continuous precession processing has bad performance on conformal polishing. The reason is that the dynamic factors of the spindle speed of the polishing tool and the feed speed of the bonnet tool are not incompatible [29]. This phenomenon is particularly obvious when machining high-precision freeform surface optical parts. It is evident that the CAM system alone cannot directly generate an appropriate high-precision tool path without considering dynamics factors.Starting from the machining practice, based on the principle of automatic dynamics analysis of mechanical systems, scholars put forward a tool path generation method for ultraprecision machining of freeform surfaces (Figure7). Considering the dynamics, material and mechanical stiffness, friction, tool, and accuracy of servo components, the toolpath for very complex freeform surfaces is generated by the Newton–Raphson method. Meanwhile, this method also overcomes the problems of shape error and compensation fault in ultraprecision machining of the traditional CAM systems. Considering the influence of friction and contact force on the processing system, a very accurate toolpath curve can be generated [28].Figure 7
Ultraprecision machining principle diagram using multibody TPG [28].Based on the idea of literature [28, 30], the tool influence function of the Gaussian mixture model is proposed in the case of considering the dynamic stress of the bonnet polishing machine and a regional adaptive path planning model that integrates machining depth, TIF volume removal rate, path spacing, and feed rate is established. The optimal feed rate scheduling under the dynamic constraints of the machine tool is realized by establishing the acceptable feed path spacing and feed range, and the stability and utility in deterministic material removal are achieved.


## 2.2.1. Research on Microscopic Material Removal Mechanism

Song et al. [17] studied the effect of different polishing parameters on the material removal rate of spherical optical glass under the different radii of curvature through experiments. The results show that when the spherical workpieces are polished with a smaller curvature radius, it is not proportional to either bonnet decrement or bonnet rotational speed as described by the Preston equation although the removal rate increases as the relative velocity or the applied pressure increases. Therefore, to more accurately calculate the material removal of the spherical workpieces, the Preston equation should be modified and studied further. To more accurately describe the workpiece removal function during bonnet polishing, Wang et al. [18] proposed an improved Preston removal function model based on the finite element analysis method. According to the theory that the stress in the static contact area is a Gaussian distribution, the stress distribution function in the dynamic contact area is derived using the least square method. This further explains the material removal mechanism of bonnet polishing from the perspective of friction and force. Feng et al. [19] further established and optimized the removal function model using finite element analysis based on the velocity and pressure distributions derived from the machining tool motion geometry and Hertzian contact theory. Through the simulation experiments in three modes, the optimal process parameters were obtained. Feng’s research enriched and developed the microscopic removal mechanism of bonnet polishing but did not fully consider the effects of other processing parameters such as pad properties, bonnet features, and processing conditions on the removal function. Shi et al. [20] established a microanalysis model based on the mutual interaction of the slurry, pad, and workpiece among the BP interfaces with microcontact theory and tribology theory. As shown in Figure 4, the model provides a more comprehensive description of the nonPrestonian behavior and helps understand the material removal mechanisms of BP from the perspective of multiple factors.Figure 4
Microtheoretical model of material removal in BP [20].


## 2.2.2. Polishing Path Planning

In terms of trajectory planning, traditional research primarily focuses on spirals and gratings. The application of the grating path can polish not only the rotating symmetric surface but also the free-form surface. In actual processing, different path methods have a significant impact on the surface texture and processing time. The processing path often adopts the easily controlled equidistant grating path, spiral path, or other regular paths. Due to the periodicity of the path, the machining process is prone to intermediate frequency error during the iterative convolution operation. Walker et al. [21] developed a free path algorithm, which calculates the dwell time by comparing the height error between the actual surface and the target surface and evenly distributes the dwell time to the two cross grating paths on the part. This method can provide controlled local material removal in a predictable manner even over severe and nonuniform aspheric departures. It could swing the debate toward an aspheric design with a fast primary f/F.In recent years, with the development of robot-assisted bonnet polishing technology, most trajectory planning research has been combined with robot technology. The Jishiming team of Zhejiang University of Technology manufactured a 6-DOF robot bonnet polishing system based on the Motoman-HP20 industrial robot and carried out polishing trajectory optimization research with the goal of smooth control and optimal processing time under three different path planning schemes, including direction parallel, contour parallel, and free path. The optimization of line spacing in parallel continuous precession bonnet polishing was investigated by experimental methods. The optimization value of line spacing under the combination of specific process parameters was obtained [22]. Pan et al. [23, 24] reduced the existing errors of precession angle in the polishing process by making micromigration of machining points and realized the real-time and accurate control of the position and attitude of the bonnet on the premise of determining the trajectory, which turned the trajectory research from macropath planning to the micropoint displacement correction control algorithm on the path. In subsequent research work, the team developed a controllable flexible bonnet polishing machine, as shown in Figure 5. The machine tool adopts the precession processing mode, that is, the spindle always forms a fixed precession angle with the local normal of the workpiece during polishing. The two axes Z1 and Z3 control the change in spindle Z2 in space, and the Z1, Z3, and Z2 axes intersect the ball center of the bonnet head. Through the analysis and calculation of the motion space, when Z1 and Z3 are 45° in space, the spatial motion range and stiffness of the whole bonnet polishing tool are the most appropriate.Figure 5
Research on bonnet polishing at Xiamen University [25]. (a) Illustration of bonnet polishing machine and the prototype. (b) Bonnet polishing head. (c) Off-line dressing equipment of bonnet polishing head.
(a)(b)(c)On the machine tool, the mathematical model of fixed-point precession bonnet polishing is established by using the homogeneous coordinate transformation matrices, and the stability of multistep discrete precession polishing under fixed-point polishing is analyzed. The experiments show that the machine tool can meet the continuous precession processing requirements of large-diameter aspheric optical parts, and a better surface accuracy is obtained for the processing of circular planar optical components with a diameter of 320 mm. In addition, the team also developed a flexible bonnet polishing head with built-in steel mesh and off-line dressing equipment and developed an online detection system. The detection system places the laser displacement sensor on the grinding spindle and uses the movement of each axis of the grinder to complete the surface detection of large-diameter aspheric elements, which can realize the full-diameter measurement of large-diameter optical elements. This detection method belongs to the online type. Its characteristic is that it can avoid the clamping and positioning errors introduced by the off-line measurement of the workpiece, realize the measurement of the machining surface accuracy of the workpiece, and provide machining error data for compensated machining. Figure6 shows the surface shape accuracy after original machining and compensated machining of large-aperture aspheric optical elements detected by the online detection system. After three rounds of compensated machining, the shape PV value decreases from 7.77 μm to 4.67 μm [24–27].Figure 6
PV of the original and compensated aspherical surface [25]. (a) Initial processing (PV = 7.77 μm; RMS = 1.35 μm). (b) First compensation processing (PV = 6.39 μm; RMS = 1.24 μm). (c) Second compensation processing (PV = 5.71 μm; RMS = 1.02 μm). (d) Third compensation processing (PV = 4.67 μm; RMS = 0.72 μm).
(a)(b)(c)(d)From the above literature research, it is found that the robot-assisted bonnet polishing technology generally adopts continuous precession processing. However, in the practical work, it is also found that the polishing area of the workpiece is not uniform and the contour line of the cross section of material removal in polishing directions is a wavy line, which indicates the continuous precession processing has bad performance on conformal polishing. The reason is that the dynamic factors of the spindle speed of the polishing tool and the feed speed of the bonnet tool are not incompatible [29]. This phenomenon is particularly obvious when machining high-precision freeform surface optical parts. It is evident that the CAM system alone cannot directly generate an appropriate high-precision tool path without considering dynamics factors.Starting from the machining practice, based on the principle of automatic dynamics analysis of mechanical systems, scholars put forward a tool path generation method for ultraprecision machining of freeform surfaces (Figure7). Considering the dynamics, material and mechanical stiffness, friction, tool, and accuracy of servo components, the toolpath for very complex freeform surfaces is generated by the Newton–Raphson method. Meanwhile, this method also overcomes the problems of shape error and compensation fault in ultraprecision machining of the traditional CAM systems. Considering the influence of friction and contact force on the processing system, a very accurate toolpath curve can be generated [28].Figure 7
Ultraprecision machining principle diagram using multibody TPG [28].Based on the idea of literature [28, 30], the tool influence function of the Gaussian mixture model is proposed in the case of considering the dynamic stress of the bonnet polishing machine and a regional adaptive path planning model that integrates machining depth, TIF volume removal rate, path spacing, and feed rate is established. The optimal feed rate scheduling under the dynamic constraints of the machine tool is realized by establishing the acceptable feed path spacing and feed range, and the stability and utility in deterministic material removal are achieved.


## 3. Noncontact Polishing

Noncontact polishing refers to a polishing method, in which the polishing pad does not contact the polished surface. It mainly depends on the polishing fluid or ions to erode the machined surface to obtain high surface accuracy and improve subsurface damage. This type of technology is characterized by getting a complete lattice structure without mechanical damage, low surface roughness, and high surface precision. It is currently the most active in the field of precision manufacturing of optical parts [31].


### 3.1. Ion Beam Polishing

Ion beam polishing (IBP) is a process of deterministic shape modification polishing through surface shape error corrections, which is developed based on atomic sputtering theory. Its principle is shown in Figure8. In the vacuum environment, the ion source controlled by the numerical control system emits ions with a specific energy to bombard the polished surface. These ions continuously collide with the shallow atoms of the polished surface for the energy exchange. When the polished surface atoms obtain the energy to get rid of the lattice binding, the physical sputtering effect occurs to realize the atomic level machining of the workpiece.Figure 8
Ion beam polishing principle.In 1967, Narodny and Tarasevich used an argon ion beam to process a parabolic mirror with a diameter of 100 mm F/6D to form the prototype of IBP [32]. Bruce et al. [33] further studied IBP and realized structural defect treatment and surface cleaning on alkali halide single crystal materials. This work lays a foundation for the systematic study of IBP technology theory. In 1988, based on previous studies, Wilson et al. [34] systematically proposed the theory and critical methods of IBP technology for the first time and converged the fused quartz optical plane with a surface accuracy of RMS 259.45 nm to RMS 26.58 nm, which laid a foundation for the commercial application of IBP technology. In the late 1980s, Kodak company of the United States developed the world’s first IBP machine for machining large-diameter (2500 mm) off-axis aspheric surfaces. This is also the first time that an IBP machine has been reported for a large-diameter off-axis aspheric surface, which is of great significance for applying IBP technology in the field of optical machining. With the development of IBP technology, as a powerful tool for material surface polishing, the technology has been constantly improving and perfecting. Researchers in various countries have conducted a large amount of in-depth research in this field.


#### 3.1.1. Study on the Mechanism of Material Removal

As a noncontact machining method, IBP is different from the traditional polishing process and cannot be modeled by the Preston equation. The emergence of Sigmund’s linear cascade collision theory makes up for this deficiency. Sigmund’s theory points out that the energy scattering of incident ions in the element follows a Gaussian distribution, puts forward a quantitative description of the ion sputtering process, and widely applies it to the calculation of the sputtering yield, which is very important for the establishment of an IBP removal function model [35, 36]. Based on Sigmund’s sputtering theory, Liao [37] studied the effect of the incident angle on the removal rate, revealed the nonlinear relationship between the removal rate and the incident angle, and established a mathematical model of the removal function. Zhang [38] further improved the model of the removal function by the current density distribution parameter. In addition, Zhang [39] studied the microscopic behavior of material removal and optimized the function removal model based on Sigmund’s sputtering theory and BH theory. At present, the research on the evolution of the surface microstructure under ion beam is still in the primary stage, and there is still a lack of theoretical analysis and systematic verification. The quantitative analysis of the surface microstructure change needs to be further studied.


#### 3.1.2. Study on the Effects of Process Parameters on Polishing Quality

References [40–46] systematically studied the effect of various process parameters on the polishing process in IBP and determined that the ion beam energy, beam voltage, and incident angle are the main factors affecting the removal function. The research shows that the relationship between the incident angle and the sputtering yield is nonlinear under different energies. Therefore, how to optimize the incident angle and improve the machining efficiency is the difficulty of the current research. With the development of artificial intelligence in recent years, neural networks have been widely used in engineering because of their substantial advantages in dealing with complex nonlinear problems. References [47, 48] established the relationship between the ion beam energy, incident angle, and sputtering yield using a neural network, solved the problem of ignoring the effect of the incident angle on the removal function when solving the dwell time function in the traditional process, and provided theoretical guidance for realizing the angle control of the removal function. However, this research only focuses on the angle and sputtering yield under single energy. When the energy changes, massive calculations need to be performed to modify the neural network. Therefore, how to correlate the energy and other parameters needs further research. Based on these previous studies, the literature [49, 50] selects the ion beam energy, incident angle, and sputtering yield as the sample data for the training and testing of the neural network and selects the Gaussian function as the radial basis function of the RBF neural network to establish a three-layer RBF neural network. By solving the dwell time, the feasibility of solving the dwell time by the LSQR algorithm is verified, and the edge effect of the dwell time solution is eliminated by edge continuation.


#### 3.1.3. IBP Combined with Chemical Etching

With the development of IBP technology, the content of the technology is also enriched. Generally, the physical sputtering technology is used in IBP. Still, if the physical sputtering polishing is continued in the processing of superhard materials (e.g., diamond, CBN, and SiC), the material removal rate will be significantly reduced. After the exploration of researchers from various countries, a chemical etching polishing method using oxygen ions was developed [51]. Hirata et al. [52] found that when the surface of a diamond film was processed by an ion beam, the removal efficiency of the oxygen ion was higher than that of the argon ion. Bovard et al. [53] used an oxygen-ion beam to reduce the surface roughness of diamond with a diameter of 5 cm to RMS 5.5 nm, which proved the feasibility of ion beam etching for polishing diamond films. Mahmud et al. [54] used ion beam processing technology to smooth the surface of a synthetic single crystal diamond chip (100). When a 1.0 keV Ar+ ion beam was used for normal incidence, a super smooth surface with a surface roughness of RMS 0.10 nm and waviness of RMS 0.12 nm was obtained. To improve the processing speed, a 0.5 keV O2+/O+ beam was used to smooth the diamond surface at the normal incidence angle. When the dose of the 0.5 keV O2+/O+ beam was much lower than that of 1 keV Ar+, a super smooth surface with ultrasmooth RMS 0.1 nm was obtained. In recent years, Russian scholars Ieshkin et al. [55] used a gas-cluster ion beam to polish the surface of superhard materials and obtained the smooth surfaces with a surface roughness of RMS 1.09 nm and 1.62 nm on SiC and diamond, respectively, which proved that the surface irradiation with gas-cluster ions does not introduce defects into the crystalline structure of irradiated materials. Mi et al. [56] proposed a modeling method of treating a brittle substrate by ion beam etching. Based on the inverse cone model of the surface pit, the relationship between the taper χ of the model and the incident angle θ was analyzed for the first time. The etching rate of the sidewall relative to that on the planar top surface at different depths was calculated. The results are shown in Figure 9. The results show that a larger incident angle can improve the removal effect. To quantitatively describe the removal process, a 2D axisymmetric simulation method was used to reveal the cross-section profile evolution in time during IBE treatment with sample rotation. Through the polishing experiment of single-crystal diamond and the simulation of the polishing process, it is found that 95% of the dent depth is removed in 30 minutes, and the method is proved to be flexible and suitable for various materials.Figure 9
(a): Sidewall etch rate relative to the planar top surface etch rate. (b): Temporal evolution of the cross-section profile of a pit withh = 100 nm and χ = 0.4 [56].
(a)(b)From the current research situation, IBP technology has made some progress and research results in theory and practice. Some breakthroughs have been made in improving the IBP on the surface roughness of optical parts, the numerical simulation, the study of technological parameters, and the establishment of physical models of the temperature field and stress field. IBP equipment has been developed in many countries (the United States, Germany, China, etc; Figure10). IBF series machine tools developed by NTG company in Germany have surface accuracy up to 6.33 nm and surface roughness better than RMS 1 nm; IFS300 series machine tools developed by Chinese AFiSy company based on the CCOS technology can converge the quartz material with an initial surface roughness of RMS 38.60 nm to RMS 4.43 nm after one iterative processing; German SCIA company and American AJA company have developed their ion beam etching system and magnetron sputtering coating system, which has the world-leading level in ion beam sputtering film deposition, large-area ion beam etching, and high-precision ion beam processing. However, IBP technology is not fully mature. According to the discipline research status and future industrial development needs, it is necessary to study IBP in the following aspects further:①
The effect of ion beam post-treatment on the surface roughness of optical films needs to be further explored. Revealing the relationship between the surface roughness of optical films and the ion beam post-treatment process is of great practical significance for preparing high-quality optical films with ultrasmooth and low scattering loss.②
After obtaining the dwell time matrix of IBP, there are few reports on how to divide the trajectory segment and its feed speed solution algorithm more quickly, efficiently, and accurately, which is also one of the follow-up research directions.Figure 10
Ion beam polishing equipment. (a) NGT IBF-450. (b) SCIA mill 150. (c) AFiSy IFS300. (d) AJA SI500.
(a)(b)(c)(d)


### 3.2. Float Polishing

In 1977, Namba of Osaka University first proposed float polishing (FP) technology (Figure11) and obtained a surface quality with a surface accuracy of 31.64 nm and a surface roughness Rz less than 1 nm on single crystals sapphire (α-Al2O3). In 1987, Namba et al. carried out float polishing on various single-crystal materials and obtained an ultrasmooth surface with a surface roughness better than 0.2 nm RMS. In the same year, the team developed the first ultraprecision floating polishing machine. After polishing workpieces of various materials with a diameter of 180 mm, they obtained an ultrasmooth surface of varying degrees of RMS 0.1–0.2 nm [57–59].Figure 11
Float polishing principle.FP technology is an improved result of traditional mechanical polishing. In the machining process, the workpiece and the polishing pad rotate stably. The hydrodynamic pressure caused by the polishing fluid creates a layer of liquid film between the workpiece and the polishing pad, and the abrasives move in the liquid film. The atoms on the surface of the workpiece drop off under the impact of abrasive particles, and then the material is removed [60]. In its research and development, it has gone through two stages: the first stage focuses on the processing of optical parts, focusing on the effect of processing parameters on the polished surface quality. The second stage is represented by compound polishing, which combines FP with magnetic flow control technology and pneumatic pressure technology to realize flexible polishing of large-size workpieces.


#### 3.2.1. Study on the Technological Properties of FP

As a typically hard and brittle material, optical parts often appear to subsurface damage such as plastic deformation, fracture, and crystal structure changes in the traditional machining process. These subsurface damages have a significant impact on the performance of optical parts. Therefore, reducing or removing subsurface damage is an essential goal of optical components or semiconductor manufacturing [61]. Reicher et al. [62] found that there was no sign of crack propagation on the polished workpiece surface in the process of FP, the surface defects disappeared with the removal of the material surface, and the subsurface damage of the workpiece was significantly reduced, which verified the technical feasibility of FP in removing the subsurface damage of the workpiece. In 1992, the Changchun Institute of Optics and Mechanics began to study FP technology and established a laboratory. Experiments such as wet polishing, abrasive paste polishing, and liquid FP were carried out on the FPJ-1 polishing machine. An ultrasmooth surface with a surface roughness of less than RMS 1 nm was successfully processed on K9 glass [63]. Based on slip-line theory, Xu et al. [64] analyzed the contact stress between the crystal and the workpiece. They explained the relationship between the material removal and the contact pressure from a mechanical perspective. In addition, aiming at the effect of process parameters on the polishing surface roughness, the team also established the process parameter database, designed the float three-polishing pad polishing machine, studied its polishing law, and provided the data reference for follow-up float polishing technology research [65]. Using this technology, Chi et al. [66, 67] carried out float polishing on a GCr15 bearing steel workpiece, and obtained a metal nanoultrasmooth surface.


#### 3.2.2. Research on FP Compound Machining

As shown in Figure12, Shimada et al. [68, 69] innovatively introduced magnetic compound fluid into FP technology, using a magnetic fluid with a shear thickening effect as the polishing fluid, forming a liquid film between the polishing surface of the grinding head and the workpiece to isolate the grinding head from the workpiece. The grinding head floats above the surface of the workpiece and finally reaches a state of automatic balance. In the polishing area, the convex peak of the rough surface of the workpiece produces resistance to the fluid, which causes the solid particles to tightly wrap the abrasive particles, form particle clusters, and produce solid-like particles, thus shearing the convex peak and removing the material on the workpiece surface.Figure 12
Schematic diagram of float polishing using MCF [68].Aiming at the problem of low machining surface quality caused by unstable grinding of the existing suspension polishing device, Yuan et al. [70] proposed an anticollision suspension polishing method based on air pressure floating (Figure 13), which adjusts the axial pressure distribution of the polishing device through an adaptive anticollision device, thereby improving the surface polishing quality. However, many experiments have shown that the surface roughness is saturated with the increase of the polishing solution exposure time or polishing time. Once the saturation limit is reached, a further reduction in surface roughness without the modification of processing conditions and the size of the abrasive particles is not possible. Therefore, the literature [71, 72] proposed a combination of jet technology and float polishing (Figure 14). This method establishes the characteristic relationship between the velocity and the angle of attack when the abrasive particles collide with the workpiece surface and uses the DCFP distribution curve to obtain the most matching FJP distribution curve under the float polishing condition. This research is expected to control the surface roughness of large-scale aspheric optical devices below 0.1 nm RMS, making up for the deficiency of float polishing in processing optical parts with large or curved surfaces.Figure 13
Schematic diagram of anticollision suspension polishing device based on air pressure floating [70]. 1, U-shaped polishing pad; 2, compressed gas inlet; 3, anti-collision device; 4, orifice; 5, gap gas film; 6, driving shaft; 7, polishing pad; 8, polishing fluid; 9, suspended base plate.Figure 14
Proposed plan for a novel “hybrid” finishing process [71].From these studies, float polishing has been dramatically improved in processability and machine tool structure. Practice shows that this technology can be used to process fused quartz and similar optical materials and can obtain small subsurface damage and an atomic level super smooth surface with a roughness of 0.2 nm and flatness of up to 31.64 nm. However, the polishing pad of the polishing equipment is difficult to make, and the requirements for the operating environment and spindle accuracy are high. Therefore, the technology is mainly used for plane processing. With the increase in processing demand for special-shaped optical elements such as large-size off-axis aspheric surfaces, using float polishing technology to polish large-scale freeform surface optical parts poses a challenge to researchers. The literature [73] reduced the friction coefficient and wear rate by adding a mixture of graphene and ethanol, and the results showed that the smooth surface was easier to obtain lower friction coefficient and wear rate under water lubrication conditions. This provides a new idea for researchers to think about how to control the friction behavior of the workpiece surface after mixing the polishing liquid with the abrasive particles to achieve the microremoval of materials. In addition, in the processing of freeform surface optical parts, the small residual roughness is in the form of long surface spatial wavelength waviness, which can probably be reduced even further if the optimum polishing conditions can be achieved. To control the surface topography, the lap flatness and temperature control of the polishing machine are very essential. Thus, it is unrealistic to consider polishing very large or curved optical parts without precise temperature control of the working area and polishing fluid. The technology for these tasks remains to be developed.


### 3.3. Elastic Emission Machining

To obtain ultrasmooth surfaces without surface defects, Japanese researchers Mori et al. [74] proposed elastic emission machining (EEM) in 1977. As shown in Figure 15, based on the principle of hydrodynamic pressure, the technology relies on highly rotating polyurethane polishing balls to drive the nanopolishing particles to collide with the workpiece surface to realize the atomic material removal and obtain a high-quality surface without subsurface damage, lattice dislocation, and other defects [75, 76].Figure 15
Elastic emission machining principle.


#### 3.3.1. Research on the Mechanism of Material Removal

The research on the material removal mechanism of EEM technology generally focuses on three aspects: chemical characteristics, fluid characteristics, and particle motion characteristics. Mori discussed the mechanism of the material removal from the perspective of the interaction between the material surface and the powder particle surface. Through experimental observations, the luminescence spectrum of the optical parts is consistent with that obtained by chemical processing. It is considered that the process of removing surface atoms by EEM is similar to chemical etching. Yamauchi et al. [78] of Osaka University further improved this theory and studied the surface effect in EEM by employing the first principles of molecular dynamics (MD). Through the solid-phase chemical interaction between the ultrafine powder and the workpiece surface, the removal of atoms can be achieved. On this basis, reference [77] further found the effect of the oxygen atom content of nanosilicon oxide polishing particles on material removal. As shown in Figure 16, the angle of the Si-O-Si bond increases with the decrease of oxygen atoms, and the bond energy gradually increases, making it easier to tear the first layer of atoms on the surface of the optical parts to achieve material removal, which confirms that the processing performance largely depends on the matching degree between the polishing particles and optical parts and that the polishing particle structure also has a significant effect on the material removal. In terms of fluid characteristics, reference [79] established a mathematical model of liquid film thickness in EEM based on electrohydrodynamic lubrication theory. By machining fused silica optical parts with colloidal silica particles, it was found that the removal function contours all have an inverse pattern of the fluid film thickness distribution. In the aspect of particle movement characteristics, Kanaoka et al. [80] analyzed the relationship between the force and removal efficiency of polished particles in detail. Xu [81] further studied the trajectory of polished particles based on solid-liquid two-phase flow theory and tested K9 glass under different conditions by using the EEM test-bed with pressure feedback and online adjustment. It is found that the polishing particles reaching the surface of the optical parts are mainly concentrated in the front part of the lowest point of the polishing tool.Figure 16
MD calculation results for different structures. (a) (OH)3Si-O-Si(OH)3. (b) (OH)3Si-O-Si(OH)2. (c) (OH)3Si-O-Si(OH)1 [77].


#### 3.3.2. Processing Device

In the past ten years, great changes have taken place in the device structure and processing mode of EEM, as shown in Figure17. Mori et al. initially used the cross spring to regulate the EEM machining clearance (Figure 17(a)). When the machining clearance changes, the axial and transverse forces of the horizontal spring will change, and the length will be adjusted through the spring deformation to keep the clearance constant. This device has the advantage of a simple structure. Still, when the clearance accuracy requirements are very high, it is difficult to maintain an accurate and rapid response to the clearance using the stiffness and deformation of the spring itself. Therefore, subsequent researchers have performed much research work on the clearance adjustment. With the development of industrial robots, a polishing machine tool with constant clearance is developed using intelligent manipulators to simplify the polishing device. Zhang [82] uses a 6-Dof joint robot to control the polishing clearance, and the XY worktable provides feed in the processing process to realize workpiece processing (Figure 17(b)). Zhang et al. [83] designed a relatively complete EEM CNC system (Figure 17(c)), in which sensors are installed for online measurement of the total load in the contact area, and the contact state between the tool and the workpiece can be adjusted by the combined control with the machine tool feed system. Takei and Mimura [84] proposed the method of controlling the shape of a stationary spot profile by realizing a focusing-flow state between the nozzle outlet and the workpiece surface in EEM (Figure 17(d)). The team developed an EEM nozzle with less than 60 μm and obtained a fixed spot with a diameter of 100 μm. This technology successfully solved the problem of unsatisfactory machining of steep curved surfaces by rotating ball EEM. An ultrasmooth surface of RMS 0.16 nm was obtained on a slender glass column using EEM. Meanwhile, the applicability of EEM to extreme ultraviolet and soft X-ray optical devices with complex surfaces such as ellipsoid mirrors has also been proved [85, 86]. References [87, 88] designed a double rotating wheel elastic emission processing device (Figure 17(e)). Under the combined action of rotation and revolution of the polishing wheel, the ultrasmooth surface of quartz glass of RMS 0.0801 nm and monocrystalline silicon of RMS 0.151 nm was obtained.Figure 17
Development of processing device in EEM. (a) Cross spring-type EEM. (b) Robotic type EEM. (c) Structural schematic diagram of elastic constrained-free abrasive particle processing system. (d) Schematic drawing of the nozzle-type EEM system used in this study. (e) Double rotating wheel-type elastic launching processing device.Compared with other ultrasmooth polishing technologies, EEM technology has unique advantages in terms of material removal principles. The principle of material removal at the atomic level will eventually be attributed to the cross integration of many frontier disciplines such as elasticity and molecular dynamics. According to the present research, the processing mathematical model based on elastic mechanics and molecular dynamics with few variables still needs to be established; the prediction model of surface roughness and material removal efficiency of EEM technology needs to be improved, and the theory and process route of off-axis aspheric optical manufacturing in EEM need to be further explored. It can be predicted that the intelligent control equipment integrated with mechanics, sensing and automation, and the precision manufacturing of ultrasmooth complex surface optical parts are the future development direction of EEM technology.


### 3.4. Plasma-Assisted Polishing

In 2010, Yamamura et al. [90, 91] of Osaka University first proposed plasma-assisted polishing (PAP) for the surface finishing of superhard materials. The technical principle is shown in Figure 18. The technique uses a helium-based water vapor plasma to irradiate the surface of the workpiece so that the active reaction atom in the ion reacts with the surface atom of the workpiece and produces the volatile substance to remove the material. The experimental results show that the wear rate of the surface modified by water vapor plasma is 20 times higher than that of the surface without plasma irradiation. It is proved that plasma-assisted polishing with CeO2 abrasives can improve the surface roughness of the workpiece without subsurface damage, and a nonscratch and ultrasmooth surface with surface roughness better than RMS 0.3 nm was obtained. The following year, through further research, the team got a scratch-free atomic level flat surface with a surface roughness of RMS 0.1 nm.Figure 18
Plasma-assisted polishing principle [89].Since PAP technology has only risen in recent years, its research progress is mainly completed by the Yamamura et al. [89, 92–103]. After ten years of research, the team has made many achievements in applying PAP technology. In 2012, the team observed the material oxide layer after plasma irradiation with cross-sectional transmission electron microscopy. The observation results verified the strong oxidizability of OH radical in water vapor plasma. After soft abrasive polishing, the oxide layer was completely removed, and the crystal structure of 4H-SiC was clear and orderly without subsurface damage [93]. In the same year, using the experimental device shown in Figure 19, the morphology of the 4H-SiC surface after plasma-assisted polishing was analyzed, and the residual strain of the PAP machined surface was evaluated. The results showed that the lattice constant was close to the ideal value, which once again proved that PAP technology did not introduce crystal subsurface damage [92]. In subsequent research, the team conducted a detailed study on the material removal mechanism of SiC and the subsurface atomic structure of SiC after PAP, clarified the atomic scale flattening mechanism of 4H-SiC (001) after PAP, optimized the oxidation process and polishing process, and improved the material removal rate in the processing process [94–97].Figure 19
Schematic of experimental device [92].Yamamura et al. subsequently carried out plasma-assisted polishing research on hard and brittle materials such as diamond, sapphire, and gallium nitride. By combining helium-based water vapor plasma radiation with silica grinding and polishing, the removal rate of the C-surface of sapphire was greatly improved. Through research on the sapphire removal mechanism, a material removal model based on plasma-assisted polishing is proposed, as shown in Figure20. Based on this study, the team analyzed the mechanism of the generated pits during GaN surface polishing, combined plasma modification with soft abrasive polishing, effectively softened the GaN surface by CF4 plasma irradiation, and then removed the modified layer (GaF3) by CeO2 abrasive polishing. Finally, the ordered stepped structure surface without scratches and pits was obtained [100]. On this basis, to further improve the processing efficiency and economy of the process, Deng et al. proposed an electrochemical etching-enhanced CMP process, which significantly improved the material removal efficiency of the GaN surface [101]. For the single crystal diamond (SCD), an efficient nonabrasive plasma-irradiated SCD polishing technique was proposed [102]. The surface quality of Sq 0.13 nm was obtained, and the polishing rate was up to 2.1 μm/h, and there was no residual stress on the machined surface, which realized the nondamages and high-efficiency polishing of SCD [103].Figure 20
Proposed model of removal for sapphire in PAP [99].In recent years, with the wide application of free-form optical parts such as off-axis aspheric in national defense, aviation, and aerospace, Arnold et al. [104] combined laser processing with plasma-assisted polishing, proposed an alternative manufacturing method of free-form shapes exhibiting steep local slopes, and obtained an ultrasmooth surface better than RMS 0.3 nm. This method can make plasma-assisted polishing process workpieces with different surface shapes, making PAP technology more competitive.As plasma-assisted polishing is a new technology, the current research mostly focuses on the optimization of process parameters and the improvement of machining efficiency. References [105, 106] studied the relationship between the workpiece surface roughness and different process parameters in detail and found that the material removal rate can be improved by adding oxygen. References [107, 108] developed an arc enhanced plasma processing method that can improve processing efficiency and a fine focused plasma jet polishing method, which can be used for local plasma efficient polishing of silicon-based materials such as crystalline silicon. Based on CCOS technology, Dang [109] used the Lucy–Richardson deconvolution algorithm to improve the processing accuracy and efficiency of atmospheric plasma through the dwell time solution. Since the plasma jet is not only the source of reactive materials but also the source of heat, the chemical reaction in the machining process depends on the resulting local surface temperature distribution. Arnold et al. [110] established a coupling model including the finite element temperature field analysis and the complex dwell time algorithm, which significantly improves the convergence rate of the etching process and the precision machining of the free-form surface with a residual error of less than 30 nm is effectively realized. Su et al. [111] further considered the nonlinear effect of the machining temperature field on the tool effect function and proposed a dwell time calculation method based on time-variant TIF to reduce the nonlinear effect of the temperature field on the machining process.At present, from the application practice of plasma-assisted polishing technology, the production process with high efficiency, high precision, low energy consumption, and intelligent commercial equipment has become the development trend of this technology. In terms of technical support, the exact function correspondence between the depth of each point on the removal contour and the processing time needs to be further explored based on higher processing and detection levels to realize the accurate prediction of the removal amount. In addition, the relationship between different curvature parts on a large-scale complex curved surface and the plasma jet machining effect needs to be deeply discussed in many aspects, such as the dwell time calculation method and machining environments.


### 3.5. Hydrodynamic Floating Polishing

To produce high-precision and defect-free large-scale semiconductor integrated circuits, in 1981, Japanese scholars Watanabe et al. [112] developed hydrodynamic floating polishing (HFP) based on the principle of hydrodynamics and successfully obtained a surface quality of Ra 1 nm by processing 3-inch monocrystalline silicon with the hydrodynamic floating device, as shown in Figure 21. This method attempts to use the hydrodynamic pressure generated by the fluid driven by the rotation of the polishing pad with a particular structure to form a small gap between the workpiece and the polishing pad. The specially structured flow channel design on the polishing pad continuously brings the abrasive particles into the machining gap. After the abrasive particles obtain enough energy, they continuously impact the microprotrusions on the workpiece surface at a high frequency to produce shear force and weaken the binding energy of the surface atoms. When the energy accumulation reaches a certain degree, the atoms in the convex parts of the workpiece surface will fall off to achieve the material removal at the atomic level and obtain an ultrasmooth surface.Figure 21
Hydrodynamic floating polishing principle.HFP adopts the immersion method, the friction heat generated and the wear of the polishing pad can be almost ignored, and the standard surface will not change, so the workpiece can be precision machined repeatedly. The advantages of HFP technology attract many scholars to study it.In the process of HFP, the particular structure on the surface of the polishing pad generates hydrodynamic pressure during its rotation. The vertical component of the dynamic pressure makes the abrasive particles suspended, and the horizontal component increases the kinetic energy for the abrasive particles. The purpose of polishing the workpiece is achieved through the shear effect of the abrasive particles on the workpiece surface. Therefore, the structure of the polishing pad will directly affect the polishing quality and material removal rate.By establishing the mathematical model of the HFP pad, Ding [113] calculated and simulated the ability of wedge-shaped, L-shaped, and structured flow channels to produce hydrodynamic pressure. It is concluded that the upward floating capability of the parabolic polishing pad is the strongest. By building a fractal test platform for the flow field characteristics of HFP, the dynamic flow field of HFP was photographed at high speed, and the Matlab results were analyzed and calculated based on fractal and multifractal theory. The results show that under the condition of meeting the buoyancy requirements, the lower the rotating speed of the polishing pad, the more uniform the distribution of abrasive particles, and the better the continuity of polishing fluids and polishing effects.Li and Zhang [115] also established the flow field constraint mathematical model for the three typical structured flow channels of polishing pads, such as wedge-shaped, L-shaped, and parabolic, analyzed the ability of producing the liquid hydrodynamic pressure under different structural parameters, and obtained the relationship curve between the buoyancy and film thickness and the relationship curve between the buoyancy and various structural parameters. Meanwhile, the flow field pressure and velocity distribution of the three structured flow channel environments are simulated by Fluent, which further proves that the parabolic structured flow channel has the strongest buoyancy ability, followed by the wedge structured flow channel.Inspired by BFP and EEM, Dong-hui et al. [116, 117] combined them with hydrodynamic polishing, proposed a novel HFP technology, and creatively designed a polishing pad with a wedge-shaped area, constrained boundary, and liquid storage tank structure. After simulating the effect of the rotating speed and the suspension distance of the polishing pad on the hydrodynamic stress field by computational fluid dynamics (CFD), it is found that the novel polishing pad can achieve a stable dynamic stress field in the workpiece area, and the higher rotating speed and the shorter suspension distance can both raise the magnitudes of the hydrodynamic stress. Based on this technology, Yin [114, 118] used a genetic algorithm to optimize the process parameters of HFP and proposed HFP with a constrained boundary. The developed HFP machine tool (Figure 22) is used to polish the copper single crystal substrate, and the surface roughness can reach 3.42 nm. Zheng et al. [119, 120] subsequently optimized the structure of the HFP tool pad on this basis. The average and uniformity of the dynamic pressure generated by the polishing pad were improved by 30% after optimization. In the latest research results, by studying the division of structural units and their fluid hydrodynamic pressure, the analytical models of hydrodynamic bearing capacity and polishing fluid viscosity, polishing tool speed, polishing gap, and polishing pad structural parameters are derived, which lays a foundation for subsequent research on HFP technology.Figure 22
Hydrodynamic floating polishing machine [114]. (a) HFP polishing experiment. (b) HFP tool pad structure. (c) Nephogram of dynamic pressure of HFP tool pad.Through the literature research and comparison, at present, HFP technology mainly focuses on the optimization design of polishing pad structure and process parameters. Since the material removal process involves the interdisciplinary integration of physics, chemistry, acoustics, hydrodynamics, etc., there is still no accurate model to explain the polishing process. In its development direction, there has been a trend of integration with CMP and MRF. Peng et al. [121] proposed a new approach combining the technologies of magnetorheological finishing (MRF) and hydrodynamic effect polishing (HEP) in 2018. On the one hand, MRF can effectively improve the low efficiency of hydrodynamic pressure machining; on the other hand, HEP can obtain an ultrasmooth surface with good machining morphology. To improve the polishing efficiency, Zhong-yu et al. [122] combined hydrodynamic technology with CMP and treated the workpiece surface with a chemical erosion process before HFP. The results show that chemical erosion can effectively remove the surface deformation layer, the new polishing process can significantly reduce the surface roughness, and the minimum surface roughness is only Ra 0.81 nm. Meanwhile, the relationship between the abrasive particle kinetic energy and the copper atom binding energy is established, which provides a basis for understanding the two typical abrasive particle planarization mechanisms of removal and filling. Figure 23 shows the preparation of the ultrasmooth surface of copper. In addition, according to the current research, the removal effect of the fluid carrier on materials cannot be ignored because the fluid carrier appears in various polishing methods as a cutting fluid or working medium. It can be predicted that the research on composite polishing methods and processes combined with dynamic fluid pressure is still the direction being explored.Figure 23
Schematic diagram of preparation of the ultrasmooth surface of Cu [122].


## 3.1. Ion Beam Polishing

Ion beam polishing (IBP) is a process of deterministic shape modification polishing through surface shape error corrections, which is developed based on atomic sputtering theory. Its principle is shown in Figure8. In the vacuum environment, the ion source controlled by the numerical control system emits ions with a specific energy to bombard the polished surface. These ions continuously collide with the shallow atoms of the polished surface for the energy exchange. When the polished surface atoms obtain the energy to get rid of the lattice binding, the physical sputtering effect occurs to realize the atomic level machining of the workpiece.Figure 8
Ion beam polishing principle.In 1967, Narodny and Tarasevich used an argon ion beam to process a parabolic mirror with a diameter of 100 mm F/6D to form the prototype of IBP [32]. Bruce et al. [33] further studied IBP and realized structural defect treatment and surface cleaning on alkali halide single crystal materials. This work lays a foundation for the systematic study of IBP technology theory. In 1988, based on previous studies, Wilson et al. [34] systematically proposed the theory and critical methods of IBP technology for the first time and converged the fused quartz optical plane with a surface accuracy of RMS 259.45 nm to RMS 26.58 nm, which laid a foundation for the commercial application of IBP technology. In the late 1980s, Kodak company of the United States developed the world’s first IBP machine for machining large-diameter (2500 mm) off-axis aspheric surfaces. This is also the first time that an IBP machine has been reported for a large-diameter off-axis aspheric surface, which is of great significance for applying IBP technology in the field of optical machining. With the development of IBP technology, as a powerful tool for material surface polishing, the technology has been constantly improving and perfecting. Researchers in various countries have conducted a large amount of in-depth research in this field.


### 3.1.1. Study on the Mechanism of Material Removal

As a noncontact machining method, IBP is different from the traditional polishing process and cannot be modeled by the Preston equation. The emergence of Sigmund’s linear cascade collision theory makes up for this deficiency. Sigmund’s theory points out that the energy scattering of incident ions in the element follows a Gaussian distribution, puts forward a quantitative description of the ion sputtering process, and widely applies it to the calculation of the sputtering yield, which is very important for the establishment of an IBP removal function model [35, 36]. Based on Sigmund’s sputtering theory, Liao [37] studied the effect of the incident angle on the removal rate, revealed the nonlinear relationship between the removal rate and the incident angle, and established a mathematical model of the removal function. Zhang [38] further improved the model of the removal function by the current density distribution parameter. In addition, Zhang [39] studied the microscopic behavior of material removal and optimized the function removal model based on Sigmund’s sputtering theory and BH theory. At present, the research on the evolution of the surface microstructure under ion beam is still in the primary stage, and there is still a lack of theoretical analysis and systematic verification. The quantitative analysis of the surface microstructure change needs to be further studied.


### 3.1.2. Study on the Effects of Process Parameters on Polishing Quality

References [40–46] systematically studied the effect of various process parameters on the polishing process in IBP and determined that the ion beam energy, beam voltage, and incident angle are the main factors affecting the removal function. The research shows that the relationship between the incident angle and the sputtering yield is nonlinear under different energies. Therefore, how to optimize the incident angle and improve the machining efficiency is the difficulty of the current research. With the development of artificial intelligence in recent years, neural networks have been widely used in engineering because of their substantial advantages in dealing with complex nonlinear problems. References [47, 48] established the relationship between the ion beam energy, incident angle, and sputtering yield using a neural network, solved the problem of ignoring the effect of the incident angle on the removal function when solving the dwell time function in the traditional process, and provided theoretical guidance for realizing the angle control of the removal function. However, this research only focuses on the angle and sputtering yield under single energy. When the energy changes, massive calculations need to be performed to modify the neural network. Therefore, how to correlate the energy and other parameters needs further research. Based on these previous studies, the literature [49, 50] selects the ion beam energy, incident angle, and sputtering yield as the sample data for the training and testing of the neural network and selects the Gaussian function as the radial basis function of the RBF neural network to establish a three-layer RBF neural network. By solving the dwell time, the feasibility of solving the dwell time by the LSQR algorithm is verified, and the edge effect of the dwell time solution is eliminated by edge continuation.


### 3.1.3. IBP Combined with Chemical Etching

With the development of IBP technology, the content of the technology is also enriched. Generally, the physical sputtering technology is used in IBP. Still, if the physical sputtering polishing is continued in the processing of superhard materials (e.g., diamond, CBN, and SiC), the material removal rate will be significantly reduced. After the exploration of researchers from various countries, a chemical etching polishing method using oxygen ions was developed [51]. Hirata et al. [52] found that when the surface of a diamond film was processed by an ion beam, the removal efficiency of the oxygen ion was higher than that of the argon ion. Bovard et al. [53] used an oxygen-ion beam to reduce the surface roughness of diamond with a diameter of 5 cm to RMS 5.5 nm, which proved the feasibility of ion beam etching for polishing diamond films. Mahmud et al. [54] used ion beam processing technology to smooth the surface of a synthetic single crystal diamond chip (100). When a 1.0 keV Ar+ ion beam was used for normal incidence, a super smooth surface with a surface roughness of RMS 0.10 nm and waviness of RMS 0.12 nm was obtained. To improve the processing speed, a 0.5 keV O2+/O+ beam was used to smooth the diamond surface at the normal incidence angle. When the dose of the 0.5 keV O2+/O+ beam was much lower than that of 1 keV Ar+, a super smooth surface with ultrasmooth RMS 0.1 nm was obtained. In recent years, Russian scholars Ieshkin et al. [55] used a gas-cluster ion beam to polish the surface of superhard materials and obtained the smooth surfaces with a surface roughness of RMS 1.09 nm and 1.62 nm on SiC and diamond, respectively, which proved that the surface irradiation with gas-cluster ions does not introduce defects into the crystalline structure of irradiated materials. Mi et al. [56] proposed a modeling method of treating a brittle substrate by ion beam etching. Based on the inverse cone model of the surface pit, the relationship between the taper χ of the model and the incident angle θ was analyzed for the first time. The etching rate of the sidewall relative to that on the planar top surface at different depths was calculated. The results are shown in Figure 9. The results show that a larger incident angle can improve the removal effect. To quantitatively describe the removal process, a 2D axisymmetric simulation method was used to reveal the cross-section profile evolution in time during IBE treatment with sample rotation. Through the polishing experiment of single-crystal diamond and the simulation of the polishing process, it is found that 95% of the dent depth is removed in 30 minutes, and the method is proved to be flexible and suitable for various materials.Figure 9
(a): Sidewall etch rate relative to the planar top surface etch rate. (b): Temporal evolution of the cross-section profile of a pit withh = 100 nm and χ = 0.4 [56].
(a)(b)From the current research situation, IBP technology has made some progress and research results in theory and practice. Some breakthroughs have been made in improving the IBP on the surface roughness of optical parts, the numerical simulation, the study of technological parameters, and the establishment of physical models of the temperature field and stress field. IBP equipment has been developed in many countries (the United States, Germany, China, etc; Figure10). IBF series machine tools developed by NTG company in Germany have surface accuracy up to 6.33 nm and surface roughness better than RMS 1 nm; IFS300 series machine tools developed by Chinese AFiSy company based on the CCOS technology can converge the quartz material with an initial surface roughness of RMS 38.60 nm to RMS 4.43 nm after one iterative processing; German SCIA company and American AJA company have developed their ion beam etching system and magnetron sputtering coating system, which has the world-leading level in ion beam sputtering film deposition, large-area ion beam etching, and high-precision ion beam processing. However, IBP technology is not fully mature. According to the discipline research status and future industrial development needs, it is necessary to study IBP in the following aspects further:①
The effect of ion beam post-treatment on the surface roughness of optical films needs to be further explored. Revealing the relationship between the surface roughness of optical films and the ion beam post-treatment process is of great practical significance for preparing high-quality optical films with ultrasmooth and low scattering loss.②
After obtaining the dwell time matrix of IBP, there are few reports on how to divide the trajectory segment and its feed speed solution algorithm more quickly, efficiently, and accurately, which is also one of the follow-up research directions.Figure 10
Ion beam polishing equipment. (a) NGT IBF-450. (b) SCIA mill 150. (c) AFiSy IFS300. (d) AJA SI500.
(a)(b)(c)(d)


## 3.1.1. Study on the Mechanism of Material Removal

As a noncontact machining method, IBP is different from the traditional polishing process and cannot be modeled by the Preston equation. The emergence of Sigmund’s linear cascade collision theory makes up for this deficiency. Sigmund’s theory points out that the energy scattering of incident ions in the element follows a Gaussian distribution, puts forward a quantitative description of the ion sputtering process, and widely applies it to the calculation of the sputtering yield, which is very important for the establishment of an IBP removal function model [35, 36]. Based on Sigmund’s sputtering theory, Liao [37] studied the effect of the incident angle on the removal rate, revealed the nonlinear relationship between the removal rate and the incident angle, and established a mathematical model of the removal function. Zhang [38] further improved the model of the removal function by the current density distribution parameter. In addition, Zhang [39] studied the microscopic behavior of material removal and optimized the function removal model based on Sigmund’s sputtering theory and BH theory. At present, the research on the evolution of the surface microstructure under ion beam is still in the primary stage, and there is still a lack of theoretical analysis and systematic verification. The quantitative analysis of the surface microstructure change needs to be further studied.


## 3.1.2. Study on the Effects of Process Parameters on Polishing Quality

References [40–46] systematically studied the effect of various process parameters on the polishing process in IBP and determined that the ion beam energy, beam voltage, and incident angle are the main factors affecting the removal function. The research shows that the relationship between the incident angle and the sputtering yield is nonlinear under different energies. Therefore, how to optimize the incident angle and improve the machining efficiency is the difficulty of the current research. With the development of artificial intelligence in recent years, neural networks have been widely used in engineering because of their substantial advantages in dealing with complex nonlinear problems. References [47, 48] established the relationship between the ion beam energy, incident angle, and sputtering yield using a neural network, solved the problem of ignoring the effect of the incident angle on the removal function when solving the dwell time function in the traditional process, and provided theoretical guidance for realizing the angle control of the removal function. However, this research only focuses on the angle and sputtering yield under single energy. When the energy changes, massive calculations need to be performed to modify the neural network. Therefore, how to correlate the energy and other parameters needs further research. Based on these previous studies, the literature [49, 50] selects the ion beam energy, incident angle, and sputtering yield as the sample data for the training and testing of the neural network and selects the Gaussian function as the radial basis function of the RBF neural network to establish a three-layer RBF neural network. By solving the dwell time, the feasibility of solving the dwell time by the LSQR algorithm is verified, and the edge effect of the dwell time solution is eliminated by edge continuation.


## 3.1.3. IBP Combined with Chemical Etching

With the development of IBP technology, the content of the technology is also enriched. Generally, the physical sputtering technology is used in IBP. Still, if the physical sputtering polishing is continued in the processing of superhard materials (e.g., diamond, CBN, and SiC), the material removal rate will be significantly reduced. After the exploration of researchers from various countries, a chemical etching polishing method using oxygen ions was developed [51]. Hirata et al. [52] found that when the surface of a diamond film was processed by an ion beam, the removal efficiency of the oxygen ion was higher than that of the argon ion. Bovard et al. [53] used an oxygen-ion beam to reduce the surface roughness of diamond with a diameter of 5 cm to RMS 5.5 nm, which proved the feasibility of ion beam etching for polishing diamond films. Mahmud et al. [54] used ion beam processing technology to smooth the surface of a synthetic single crystal diamond chip (100). When a 1.0 keV Ar+ ion beam was used for normal incidence, a super smooth surface with a surface roughness of RMS 0.10 nm and waviness of RMS 0.12 nm was obtained. To improve the processing speed, a 0.5 keV O2+/O+ beam was used to smooth the diamond surface at the normal incidence angle. When the dose of the 0.5 keV O2+/O+ beam was much lower than that of 1 keV Ar+, a super smooth surface with ultrasmooth RMS 0.1 nm was obtained. In recent years, Russian scholars Ieshkin et al. [55] used a gas-cluster ion beam to polish the surface of superhard materials and obtained the smooth surfaces with a surface roughness of RMS 1.09 nm and 1.62 nm on SiC and diamond, respectively, which proved that the surface irradiation with gas-cluster ions does not introduce defects into the crystalline structure of irradiated materials. Mi et al. [56] proposed a modeling method of treating a brittle substrate by ion beam etching. Based on the inverse cone model of the surface pit, the relationship between the taper χ of the model and the incident angle θ was analyzed for the first time. The etching rate of the sidewall relative to that on the planar top surface at different depths was calculated. The results are shown in Figure 9. The results show that a larger incident angle can improve the removal effect. To quantitatively describe the removal process, a 2D axisymmetric simulation method was used to reveal the cross-section profile evolution in time during IBE treatment with sample rotation. Through the polishing experiment of single-crystal diamond and the simulation of the polishing process, it is found that 95% of the dent depth is removed in 30 minutes, and the method is proved to be flexible and suitable for various materials.Figure 9
(a): Sidewall etch rate relative to the planar top surface etch rate. (b): Temporal evolution of the cross-section profile of a pit withh = 100 nm and χ = 0.4 [56].
(a)(b)From the current research situation, IBP technology has made some progress and research results in theory and practice. Some breakthroughs have been made in improving the IBP on the surface roughness of optical parts, the numerical simulation, the study of technological parameters, and the establishment of physical models of the temperature field and stress field. IBP equipment has been developed in many countries (the United States, Germany, China, etc; Figure10). IBF series machine tools developed by NTG company in Germany have surface accuracy up to 6.33 nm and surface roughness better than RMS 1 nm; IFS300 series machine tools developed by Chinese AFiSy company based on the CCOS technology can converge the quartz material with an initial surface roughness of RMS 38.60 nm to RMS 4.43 nm after one iterative processing; German SCIA company and American AJA company have developed their ion beam etching system and magnetron sputtering coating system, which has the world-leading level in ion beam sputtering film deposition, large-area ion beam etching, and high-precision ion beam processing. However, IBP technology is not fully mature. According to the discipline research status and future industrial development needs, it is necessary to study IBP in the following aspects further:①
The effect of ion beam post-treatment on the surface roughness of optical films needs to be further explored. Revealing the relationship between the surface roughness of optical films and the ion beam post-treatment process is of great practical significance for preparing high-quality optical films with ultrasmooth and low scattering loss.②
After obtaining the dwell time matrix of IBP, there are few reports on how to divide the trajectory segment and its feed speed solution algorithm more quickly, efficiently, and accurately, which is also one of the follow-up research directions.Figure 10
Ion beam polishing equipment. (a) NGT IBF-450. (b) SCIA mill 150. (c) AFiSy IFS300. (d) AJA SI500.
(a)(b)(c)(d)


## 3.2. Float Polishing

In 1977, Namba of Osaka University first proposed float polishing (FP) technology (Figure11) and obtained a surface quality with a surface accuracy of 31.64 nm and a surface roughness Rz less than 1 nm on single crystals sapphire (α-Al2O3). In 1987, Namba et al. carried out float polishing on various single-crystal materials and obtained an ultrasmooth surface with a surface roughness better than 0.2 nm RMS. In the same year, the team developed the first ultraprecision floating polishing machine. After polishing workpieces of various materials with a diameter of 180 mm, they obtained an ultrasmooth surface of varying degrees of RMS 0.1–0.2 nm [57–59].Figure 11
Float polishing principle.FP technology is an improved result of traditional mechanical polishing. In the machining process, the workpiece and the polishing pad rotate stably. The hydrodynamic pressure caused by the polishing fluid creates a layer of liquid film between the workpiece and the polishing pad, and the abrasives move in the liquid film. The atoms on the surface of the workpiece drop off under the impact of abrasive particles, and then the material is removed [60]. In its research and development, it has gone through two stages: the first stage focuses on the processing of optical parts, focusing on the effect of processing parameters on the polished surface quality. The second stage is represented by compound polishing, which combines FP with magnetic flow control technology and pneumatic pressure technology to realize flexible polishing of large-size workpieces.


### 3.2.1. Study on the Technological Properties of FP

As a typically hard and brittle material, optical parts often appear to subsurface damage such as plastic deformation, fracture, and crystal structure changes in the traditional machining process. These subsurface damages have a significant impact on the performance of optical parts. Therefore, reducing or removing subsurface damage is an essential goal of optical components or semiconductor manufacturing [61]. Reicher et al. [62] found that there was no sign of crack propagation on the polished workpiece surface in the process of FP, the surface defects disappeared with the removal of the material surface, and the subsurface damage of the workpiece was significantly reduced, which verified the technical feasibility of FP in removing the subsurface damage of the workpiece. In 1992, the Changchun Institute of Optics and Mechanics began to study FP technology and established a laboratory. Experiments such as wet polishing, abrasive paste polishing, and liquid FP were carried out on the FPJ-1 polishing machine. An ultrasmooth surface with a surface roughness of less than RMS 1 nm was successfully processed on K9 glass [63]. Based on slip-line theory, Xu et al. [64] analyzed the contact stress between the crystal and the workpiece. They explained the relationship between the material removal and the contact pressure from a mechanical perspective. In addition, aiming at the effect of process parameters on the polishing surface roughness, the team also established the process parameter database, designed the float three-polishing pad polishing machine, studied its polishing law, and provided the data reference for follow-up float polishing technology research [65]. Using this technology, Chi et al. [66, 67] carried out float polishing on a GCr15 bearing steel workpiece, and obtained a metal nanoultrasmooth surface.


### 3.2.2. Research on FP Compound Machining

As shown in Figure12, Shimada et al. [68, 69] innovatively introduced magnetic compound fluid into FP technology, using a magnetic fluid with a shear thickening effect as the polishing fluid, forming a liquid film between the polishing surface of the grinding head and the workpiece to isolate the grinding head from the workpiece. The grinding head floats above the surface of the workpiece and finally reaches a state of automatic balance. In the polishing area, the convex peak of the rough surface of the workpiece produces resistance to the fluid, which causes the solid particles to tightly wrap the abrasive particles, form particle clusters, and produce solid-like particles, thus shearing the convex peak and removing the material on the workpiece surface.Figure 12
Schematic diagram of float polishing using MCF [68].Aiming at the problem of low machining surface quality caused by unstable grinding of the existing suspension polishing device, Yuan et al. [70] proposed an anticollision suspension polishing method based on air pressure floating (Figure 13), which adjusts the axial pressure distribution of the polishing device through an adaptive anticollision device, thereby improving the surface polishing quality. However, many experiments have shown that the surface roughness is saturated with the increase of the polishing solution exposure time or polishing time. Once the saturation limit is reached, a further reduction in surface roughness without the modification of processing conditions and the size of the abrasive particles is not possible. Therefore, the literature [71, 72] proposed a combination of jet technology and float polishing (Figure 14). This method establishes the characteristic relationship between the velocity and the angle of attack when the abrasive particles collide with the workpiece surface and uses the DCFP distribution curve to obtain the most matching FJP distribution curve under the float polishing condition. This research is expected to control the surface roughness of large-scale aspheric optical devices below 0.1 nm RMS, making up for the deficiency of float polishing in processing optical parts with large or curved surfaces.Figure 13
Schematic diagram of anticollision suspension polishing device based on air pressure floating [70]. 1, U-shaped polishing pad; 2, compressed gas inlet; 3, anti-collision device; 4, orifice; 5, gap gas film; 6, driving shaft; 7, polishing pad; 8, polishing fluid; 9, suspended base plate.Figure 14
Proposed plan for a novel “hybrid” finishing process [71].From these studies, float polishing has been dramatically improved in processability and machine tool structure. Practice shows that this technology can be used to process fused quartz and similar optical materials and can obtain small subsurface damage and an atomic level super smooth surface with a roughness of 0.2 nm and flatness of up to 31.64 nm. However, the polishing pad of the polishing equipment is difficult to make, and the requirements for the operating environment and spindle accuracy are high. Therefore, the technology is mainly used for plane processing. With the increase in processing demand for special-shaped optical elements such as large-size off-axis aspheric surfaces, using float polishing technology to polish large-scale freeform surface optical parts poses a challenge to researchers. The literature [73] reduced the friction coefficient and wear rate by adding a mixture of graphene and ethanol, and the results showed that the smooth surface was easier to obtain lower friction coefficient and wear rate under water lubrication conditions. This provides a new idea for researchers to think about how to control the friction behavior of the workpiece surface after mixing the polishing liquid with the abrasive particles to achieve the microremoval of materials. In addition, in the processing of freeform surface optical parts, the small residual roughness is in the form of long surface spatial wavelength waviness, which can probably be reduced even further if the optimum polishing conditions can be achieved. To control the surface topography, the lap flatness and temperature control of the polishing machine are very essential. Thus, it is unrealistic to consider polishing very large or curved optical parts without precise temperature control of the working area and polishing fluid. The technology for these tasks remains to be developed.


## 3.2.1. Study on the Technological Properties of FP

As a typically hard and brittle material, optical parts often appear to subsurface damage such as plastic deformation, fracture, and crystal structure changes in the traditional machining process. These subsurface damages have a significant impact on the performance of optical parts. Therefore, reducing or removing subsurface damage is an essential goal of optical components or semiconductor manufacturing [61]. Reicher et al. [62] found that there was no sign of crack propagation on the polished workpiece surface in the process of FP, the surface defects disappeared with the removal of the material surface, and the subsurface damage of the workpiece was significantly reduced, which verified the technical feasibility of FP in removing the subsurface damage of the workpiece. In 1992, the Changchun Institute of Optics and Mechanics began to study FP technology and established a laboratory. Experiments such as wet polishing, abrasive paste polishing, and liquid FP were carried out on the FPJ-1 polishing machine. An ultrasmooth surface with a surface roughness of less than RMS 1 nm was successfully processed on K9 glass [63]. Based on slip-line theory, Xu et al. [64] analyzed the contact stress between the crystal and the workpiece. They explained the relationship between the material removal and the contact pressure from a mechanical perspective. In addition, aiming at the effect of process parameters on the polishing surface roughness, the team also established the process parameter database, designed the float three-polishing pad polishing machine, studied its polishing law, and provided the data reference for follow-up float polishing technology research [65]. Using this technology, Chi et al. [66, 67] carried out float polishing on a GCr15 bearing steel workpiece, and obtained a metal nanoultrasmooth surface.


## 3.2.2. Research on FP Compound Machining

As shown in Figure12, Shimada et al. [68, 69] innovatively introduced magnetic compound fluid into FP technology, using a magnetic fluid with a shear thickening effect as the polishing fluid, forming a liquid film between the polishing surface of the grinding head and the workpiece to isolate the grinding head from the workpiece. The grinding head floats above the surface of the workpiece and finally reaches a state of automatic balance. In the polishing area, the convex peak of the rough surface of the workpiece produces resistance to the fluid, which causes the solid particles to tightly wrap the abrasive particles, form particle clusters, and produce solid-like particles, thus shearing the convex peak and removing the material on the workpiece surface.Figure 12
Schematic diagram of float polishing using MCF [68].Aiming at the problem of low machining surface quality caused by unstable grinding of the existing suspension polishing device, Yuan et al. [70] proposed an anticollision suspension polishing method based on air pressure floating (Figure 13), which adjusts the axial pressure distribution of the polishing device through an adaptive anticollision device, thereby improving the surface polishing quality. However, many experiments have shown that the surface roughness is saturated with the increase of the polishing solution exposure time or polishing time. Once the saturation limit is reached, a further reduction in surface roughness without the modification of processing conditions and the size of the abrasive particles is not possible. Therefore, the literature [71, 72] proposed a combination of jet technology and float polishing (Figure 14). This method establishes the characteristic relationship between the velocity and the angle of attack when the abrasive particles collide with the workpiece surface and uses the DCFP distribution curve to obtain the most matching FJP distribution curve under the float polishing condition. This research is expected to control the surface roughness of large-scale aspheric optical devices below 0.1 nm RMS, making up for the deficiency of float polishing in processing optical parts with large or curved surfaces.Figure 13
Schematic diagram of anticollision suspension polishing device based on air pressure floating [70]. 1, U-shaped polishing pad; 2, compressed gas inlet; 3, anti-collision device; 4, orifice; 5, gap gas film; 6, driving shaft; 7, polishing pad; 8, polishing fluid; 9, suspended base plate.Figure 14
Proposed plan for a novel “hybrid” finishing process [71].From these studies, float polishing has been dramatically improved in processability and machine tool structure. Practice shows that this technology can be used to process fused quartz and similar optical materials and can obtain small subsurface damage and an atomic level super smooth surface with a roughness of 0.2 nm and flatness of up to 31.64 nm. However, the polishing pad of the polishing equipment is difficult to make, and the requirements for the operating environment and spindle accuracy are high. Therefore, the technology is mainly used for plane processing. With the increase in processing demand for special-shaped optical elements such as large-size off-axis aspheric surfaces, using float polishing technology to polish large-scale freeform surface optical parts poses a challenge to researchers. The literature [73] reduced the friction coefficient and wear rate by adding a mixture of graphene and ethanol, and the results showed that the smooth surface was easier to obtain lower friction coefficient and wear rate under water lubrication conditions. This provides a new idea for researchers to think about how to control the friction behavior of the workpiece surface after mixing the polishing liquid with the abrasive particles to achieve the microremoval of materials. In addition, in the processing of freeform surface optical parts, the small residual roughness is in the form of long surface spatial wavelength waviness, which can probably be reduced even further if the optimum polishing conditions can be achieved. To control the surface topography, the lap flatness and temperature control of the polishing machine are very essential. Thus, it is unrealistic to consider polishing very large or curved optical parts without precise temperature control of the working area and polishing fluid. The technology for these tasks remains to be developed.


## 3.3. Elastic Emission Machining

To obtain ultrasmooth surfaces without surface defects, Japanese researchers Mori et al. [74] proposed elastic emission machining (EEM) in 1977. As shown in Figure 15, based on the principle of hydrodynamic pressure, the technology relies on highly rotating polyurethane polishing balls to drive the nanopolishing particles to collide with the workpiece surface to realize the atomic material removal and obtain a high-quality surface without subsurface damage, lattice dislocation, and other defects [75, 76].Figure 15
Elastic emission machining principle.


### 3.3.1. Research on the Mechanism of Material Removal

The research on the material removal mechanism of EEM technology generally focuses on three aspects: chemical characteristics, fluid characteristics, and particle motion characteristics. Mori discussed the mechanism of the material removal from the perspective of the interaction between the material surface and the powder particle surface. Through experimental observations, the luminescence spectrum of the optical parts is consistent with that obtained by chemical processing. It is considered that the process of removing surface atoms by EEM is similar to chemical etching. Yamauchi et al. [78] of Osaka University further improved this theory and studied the surface effect in EEM by employing the first principles of molecular dynamics (MD). Through the solid-phase chemical interaction between the ultrafine powder and the workpiece surface, the removal of atoms can be achieved. On this basis, reference [77] further found the effect of the oxygen atom content of nanosilicon oxide polishing particles on material removal. As shown in Figure 16, the angle of the Si-O-Si bond increases with the decrease of oxygen atoms, and the bond energy gradually increases, making it easier to tear the first layer of atoms on the surface of the optical parts to achieve material removal, which confirms that the processing performance largely depends on the matching degree between the polishing particles and optical parts and that the polishing particle structure also has a significant effect on the material removal. In terms of fluid characteristics, reference [79] established a mathematical model of liquid film thickness in EEM based on electrohydrodynamic lubrication theory. By machining fused silica optical parts with colloidal silica particles, it was found that the removal function contours all have an inverse pattern of the fluid film thickness distribution. In the aspect of particle movement characteristics, Kanaoka et al. [80] analyzed the relationship between the force and removal efficiency of polished particles in detail. Xu [81] further studied the trajectory of polished particles based on solid-liquid two-phase flow theory and tested K9 glass under different conditions by using the EEM test-bed with pressure feedback and online adjustment. It is found that the polishing particles reaching the surface of the optical parts are mainly concentrated in the front part of the lowest point of the polishing tool.Figure 16
MD calculation results for different structures. (a) (OH)3Si-O-Si(OH)3. (b) (OH)3Si-O-Si(OH)2. (c) (OH)3Si-O-Si(OH)1 [77].


### 3.3.2. Processing Device

In the past ten years, great changes have taken place in the device structure and processing mode of EEM, as shown in Figure17. Mori et al. initially used the cross spring to regulate the EEM machining clearance (Figure 17(a)). When the machining clearance changes, the axial and transverse forces of the horizontal spring will change, and the length will be adjusted through the spring deformation to keep the clearance constant. This device has the advantage of a simple structure. Still, when the clearance accuracy requirements are very high, it is difficult to maintain an accurate and rapid response to the clearance using the stiffness and deformation of the spring itself. Therefore, subsequent researchers have performed much research work on the clearance adjustment. With the development of industrial robots, a polishing machine tool with constant clearance is developed using intelligent manipulators to simplify the polishing device. Zhang [82] uses a 6-Dof joint robot to control the polishing clearance, and the XY worktable provides feed in the processing process to realize workpiece processing (Figure 17(b)). Zhang et al. [83] designed a relatively complete EEM CNC system (Figure 17(c)), in which sensors are installed for online measurement of the total load in the contact area, and the contact state between the tool and the workpiece can be adjusted by the combined control with the machine tool feed system. Takei and Mimura [84] proposed the method of controlling the shape of a stationary spot profile by realizing a focusing-flow state between the nozzle outlet and the workpiece surface in EEM (Figure 17(d)). The team developed an EEM nozzle with less than 60 μm and obtained a fixed spot with a diameter of 100 μm. This technology successfully solved the problem of unsatisfactory machining of steep curved surfaces by rotating ball EEM. An ultrasmooth surface of RMS 0.16 nm was obtained on a slender glass column using EEM. Meanwhile, the applicability of EEM to extreme ultraviolet and soft X-ray optical devices with complex surfaces such as ellipsoid mirrors has also been proved [85, 86]. References [87, 88] designed a double rotating wheel elastic emission processing device (Figure 17(e)). Under the combined action of rotation and revolution of the polishing wheel, the ultrasmooth surface of quartz glass of RMS 0.0801 nm and monocrystalline silicon of RMS 0.151 nm was obtained.Figure 17
Development of processing device in EEM. (a) Cross spring-type EEM. (b) Robotic type EEM. (c) Structural schematic diagram of elastic constrained-free abrasive particle processing system. (d) Schematic drawing of the nozzle-type EEM system used in this study. (e) Double rotating wheel-type elastic launching processing device.Compared with other ultrasmooth polishing technologies, EEM technology has unique advantages in terms of material removal principles. The principle of material removal at the atomic level will eventually be attributed to the cross integration of many frontier disciplines such as elasticity and molecular dynamics. According to the present research, the processing mathematical model based on elastic mechanics and molecular dynamics with few variables still needs to be established; the prediction model of surface roughness and material removal efficiency of EEM technology needs to be improved, and the theory and process route of off-axis aspheric optical manufacturing in EEM need to be further explored. It can be predicted that the intelligent control equipment integrated with mechanics, sensing and automation, and the precision manufacturing of ultrasmooth complex surface optical parts are the future development direction of EEM technology.


## 3.3.1. Research on the Mechanism of Material Removal

The research on the material removal mechanism of EEM technology generally focuses on three aspects: chemical characteristics, fluid characteristics, and particle motion characteristics. Mori discussed the mechanism of the material removal from the perspective of the interaction between the material surface and the powder particle surface. Through experimental observations, the luminescence spectrum of the optical parts is consistent with that obtained by chemical processing. It is considered that the process of removing surface atoms by EEM is similar to chemical etching. Yamauchi et al. [78] of Osaka University further improved this theory and studied the surface effect in EEM by employing the first principles of molecular dynamics (MD). Through the solid-phase chemical interaction between the ultrafine powder and the workpiece surface, the removal of atoms can be achieved. On this basis, reference [77] further found the effect of the oxygen atom content of nanosilicon oxide polishing particles on material removal. As shown in Figure 16, the angle of the Si-O-Si bond increases with the decrease of oxygen atoms, and the bond energy gradually increases, making it easier to tear the first layer of atoms on the surface of the optical parts to achieve material removal, which confirms that the processing performance largely depends on the matching degree between the polishing particles and optical parts and that the polishing particle structure also has a significant effect on the material removal. In terms of fluid characteristics, reference [79] established a mathematical model of liquid film thickness in EEM based on electrohydrodynamic lubrication theory. By machining fused silica optical parts with colloidal silica particles, it was found that the removal function contours all have an inverse pattern of the fluid film thickness distribution. In the aspect of particle movement characteristics, Kanaoka et al. [80] analyzed the relationship between the force and removal efficiency of polished particles in detail. Xu [81] further studied the trajectory of polished particles based on solid-liquid two-phase flow theory and tested K9 glass under different conditions by using the EEM test-bed with pressure feedback and online adjustment. It is found that the polishing particles reaching the surface of the optical parts are mainly concentrated in the front part of the lowest point of the polishing tool.Figure 16
MD calculation results for different structures. (a) (OH)3Si-O-Si(OH)3. (b) (OH)3Si-O-Si(OH)2. (c) (OH)3Si-O-Si(OH)1 [77].


## 3.3.2. Processing Device

In the past ten years, great changes have taken place in the device structure and processing mode of EEM, as shown in Figure17. Mori et al. initially used the cross spring to regulate the EEM machining clearance (Figure 17(a)). When the machining clearance changes, the axial and transverse forces of the horizontal spring will change, and the length will be adjusted through the spring deformation to keep the clearance constant. This device has the advantage of a simple structure. Still, when the clearance accuracy requirements are very high, it is difficult to maintain an accurate and rapid response to the clearance using the stiffness and deformation of the spring itself. Therefore, subsequent researchers have performed much research work on the clearance adjustment. With the development of industrial robots, a polishing machine tool with constant clearance is developed using intelligent manipulators to simplify the polishing device. Zhang [82] uses a 6-Dof joint robot to control the polishing clearance, and the XY worktable provides feed in the processing process to realize workpiece processing (Figure 17(b)). Zhang et al. [83] designed a relatively complete EEM CNC system (Figure 17(c)), in which sensors are installed for online measurement of the total load in the contact area, and the contact state between the tool and the workpiece can be adjusted by the combined control with the machine tool feed system. Takei and Mimura [84] proposed the method of controlling the shape of a stationary spot profile by realizing a focusing-flow state between the nozzle outlet and the workpiece surface in EEM (Figure 17(d)). The team developed an EEM nozzle with less than 60 μm and obtained a fixed spot with a diameter of 100 μm. This technology successfully solved the problem of unsatisfactory machining of steep curved surfaces by rotating ball EEM. An ultrasmooth surface of RMS 0.16 nm was obtained on a slender glass column using EEM. Meanwhile, the applicability of EEM to extreme ultraviolet and soft X-ray optical devices with complex surfaces such as ellipsoid mirrors has also been proved [85, 86]. References [87, 88] designed a double rotating wheel elastic emission processing device (Figure 17(e)). Under the combined action of rotation and revolution of the polishing wheel, the ultrasmooth surface of quartz glass of RMS 0.0801 nm and monocrystalline silicon of RMS 0.151 nm was obtained.Figure 17
Development of processing device in EEM. (a) Cross spring-type EEM. (b) Robotic type EEM. (c) Structural schematic diagram of elastic constrained-free abrasive particle processing system. (d) Schematic drawing of the nozzle-type EEM system used in this study. (e) Double rotating wheel-type elastic launching processing device.Compared with other ultrasmooth polishing technologies, EEM technology has unique advantages in terms of material removal principles. The principle of material removal at the atomic level will eventually be attributed to the cross integration of many frontier disciplines such as elasticity and molecular dynamics. According to the present research, the processing mathematical model based on elastic mechanics and molecular dynamics with few variables still needs to be established; the prediction model of surface roughness and material removal efficiency of EEM technology needs to be improved, and the theory and process route of off-axis aspheric optical manufacturing in EEM need to be further explored. It can be predicted that the intelligent control equipment integrated with mechanics, sensing and automation, and the precision manufacturing of ultrasmooth complex surface optical parts are the future development direction of EEM technology.


## 3.4. Plasma-Assisted Polishing

In 2010, Yamamura et al. [90, 91] of Osaka University first proposed plasma-assisted polishing (PAP) for the surface finishing of superhard materials. The technical principle is shown in Figure 18. The technique uses a helium-based water vapor plasma to irradiate the surface of the workpiece so that the active reaction atom in the ion reacts with the surface atom of the workpiece and produces the volatile substance to remove the material. The experimental results show that the wear rate of the surface modified by water vapor plasma is 20 times higher than that of the surface without plasma irradiation. It is proved that plasma-assisted polishing with CeO2 abrasives can improve the surface roughness of the workpiece without subsurface damage, and a nonscratch and ultrasmooth surface with surface roughness better than RMS 0.3 nm was obtained. The following year, through further research, the team got a scratch-free atomic level flat surface with a surface roughness of RMS 0.1 nm.Figure 18
Plasma-assisted polishing principle [89].Since PAP technology has only risen in recent years, its research progress is mainly completed by the Yamamura et al. [89, 92–103]. After ten years of research, the team has made many achievements in applying PAP technology. In 2012, the team observed the material oxide layer after plasma irradiation with cross-sectional transmission electron microscopy. The observation results verified the strong oxidizability of OH radical in water vapor plasma. After soft abrasive polishing, the oxide layer was completely removed, and the crystal structure of 4H-SiC was clear and orderly without subsurface damage [93]. In the same year, using the experimental device shown in Figure 19, the morphology of the 4H-SiC surface after plasma-assisted polishing was analyzed, and the residual strain of the PAP machined surface was evaluated. The results showed that the lattice constant was close to the ideal value, which once again proved that PAP technology did not introduce crystal subsurface damage [92]. In subsequent research, the team conducted a detailed study on the material removal mechanism of SiC and the subsurface atomic structure of SiC after PAP, clarified the atomic scale flattening mechanism of 4H-SiC (001) after PAP, optimized the oxidation process and polishing process, and improved the material removal rate in the processing process [94–97].Figure 19
Schematic of experimental device [92].Yamamura et al. subsequently carried out plasma-assisted polishing research on hard and brittle materials such as diamond, sapphire, and gallium nitride. By combining helium-based water vapor plasma radiation with silica grinding and polishing, the removal rate of the C-surface of sapphire was greatly improved. Through research on the sapphire removal mechanism, a material removal model based on plasma-assisted polishing is proposed, as shown in Figure20. Based on this study, the team analyzed the mechanism of the generated pits during GaN surface polishing, combined plasma modification with soft abrasive polishing, effectively softened the GaN surface by CF4 plasma irradiation, and then removed the modified layer (GaF3) by CeO2 abrasive polishing. Finally, the ordered stepped structure surface without scratches and pits was obtained [100]. On this basis, to further improve the processing efficiency and economy of the process, Deng et al. proposed an electrochemical etching-enhanced CMP process, which significantly improved the material removal efficiency of the GaN surface [101]. For the single crystal diamond (SCD), an efficient nonabrasive plasma-irradiated SCD polishing technique was proposed [102]. The surface quality of Sq 0.13 nm was obtained, and the polishing rate was up to 2.1 μm/h, and there was no residual stress on the machined surface, which realized the nondamages and high-efficiency polishing of SCD [103].Figure 20
Proposed model of removal for sapphire in PAP [99].In recent years, with the wide application of free-form optical parts such as off-axis aspheric in national defense, aviation, and aerospace, Arnold et al. [104] combined laser processing with plasma-assisted polishing, proposed an alternative manufacturing method of free-form shapes exhibiting steep local slopes, and obtained an ultrasmooth surface better than RMS 0.3 nm. This method can make plasma-assisted polishing process workpieces with different surface shapes, making PAP technology more competitive.As plasma-assisted polishing is a new technology, the current research mostly focuses on the optimization of process parameters and the improvement of machining efficiency. References [105, 106] studied the relationship between the workpiece surface roughness and different process parameters in detail and found that the material removal rate can be improved by adding oxygen. References [107, 108] developed an arc enhanced plasma processing method that can improve processing efficiency and a fine focused plasma jet polishing method, which can be used for local plasma efficient polishing of silicon-based materials such as crystalline silicon. Based on CCOS technology, Dang [109] used the Lucy–Richardson deconvolution algorithm to improve the processing accuracy and efficiency of atmospheric plasma through the dwell time solution. Since the plasma jet is not only the source of reactive materials but also the source of heat, the chemical reaction in the machining process depends on the resulting local surface temperature distribution. Arnold et al. [110] established a coupling model including the finite element temperature field analysis and the complex dwell time algorithm, which significantly improves the convergence rate of the etching process and the precision machining of the free-form surface with a residual error of less than 30 nm is effectively realized. Su et al. [111] further considered the nonlinear effect of the machining temperature field on the tool effect function and proposed a dwell time calculation method based on time-variant TIF to reduce the nonlinear effect of the temperature field on the machining process.At present, from the application practice of plasma-assisted polishing technology, the production process with high efficiency, high precision, low energy consumption, and intelligent commercial equipment has become the development trend of this technology. In terms of technical support, the exact function correspondence between the depth of each point on the removal contour and the processing time needs to be further explored based on higher processing and detection levels to realize the accurate prediction of the removal amount. In addition, the relationship between different curvature parts on a large-scale complex curved surface and the plasma jet machining effect needs to be deeply discussed in many aspects, such as the dwell time calculation method and machining environments.


## 3.5. Hydrodynamic Floating Polishing

To produce high-precision and defect-free large-scale semiconductor integrated circuits, in 1981, Japanese scholars Watanabe et al. [112] developed hydrodynamic floating polishing (HFP) based on the principle of hydrodynamics and successfully obtained a surface quality of Ra 1 nm by processing 3-inch monocrystalline silicon with the hydrodynamic floating device, as shown in Figure 21. This method attempts to use the hydrodynamic pressure generated by the fluid driven by the rotation of the polishing pad with a particular structure to form a small gap between the workpiece and the polishing pad. The specially structured flow channel design on the polishing pad continuously brings the abrasive particles into the machining gap. After the abrasive particles obtain enough energy, they continuously impact the microprotrusions on the workpiece surface at a high frequency to produce shear force and weaken the binding energy of the surface atoms. When the energy accumulation reaches a certain degree, the atoms in the convex parts of the workpiece surface will fall off to achieve the material removal at the atomic level and obtain an ultrasmooth surface.Figure 21
Hydrodynamic floating polishing principle.HFP adopts the immersion method, the friction heat generated and the wear of the polishing pad can be almost ignored, and the standard surface will not change, so the workpiece can be precision machined repeatedly. The advantages of HFP technology attract many scholars to study it.In the process of HFP, the particular structure on the surface of the polishing pad generates hydrodynamic pressure during its rotation. The vertical component of the dynamic pressure makes the abrasive particles suspended, and the horizontal component increases the kinetic energy for the abrasive particles. The purpose of polishing the workpiece is achieved through the shear effect of the abrasive particles on the workpiece surface. Therefore, the structure of the polishing pad will directly affect the polishing quality and material removal rate.By establishing the mathematical model of the HFP pad, Ding [113] calculated and simulated the ability of wedge-shaped, L-shaped, and structured flow channels to produce hydrodynamic pressure. It is concluded that the upward floating capability of the parabolic polishing pad is the strongest. By building a fractal test platform for the flow field characteristics of HFP, the dynamic flow field of HFP was photographed at high speed, and the Matlab results were analyzed and calculated based on fractal and multifractal theory. The results show that under the condition of meeting the buoyancy requirements, the lower the rotating speed of the polishing pad, the more uniform the distribution of abrasive particles, and the better the continuity of polishing fluids and polishing effects.Li and Zhang [115] also established the flow field constraint mathematical model for the three typical structured flow channels of polishing pads, such as wedge-shaped, L-shaped, and parabolic, analyzed the ability of producing the liquid hydrodynamic pressure under different structural parameters, and obtained the relationship curve between the buoyancy and film thickness and the relationship curve between the buoyancy and various structural parameters. Meanwhile, the flow field pressure and velocity distribution of the three structured flow channel environments are simulated by Fluent, which further proves that the parabolic structured flow channel has the strongest buoyancy ability, followed by the wedge structured flow channel.Inspired by BFP and EEM, Dong-hui et al. [116, 117] combined them with hydrodynamic polishing, proposed a novel HFP technology, and creatively designed a polishing pad with a wedge-shaped area, constrained boundary, and liquid storage tank structure. After simulating the effect of the rotating speed and the suspension distance of the polishing pad on the hydrodynamic stress field by computational fluid dynamics (CFD), it is found that the novel polishing pad can achieve a stable dynamic stress field in the workpiece area, and the higher rotating speed and the shorter suspension distance can both raise the magnitudes of the hydrodynamic stress. Based on this technology, Yin [114, 118] used a genetic algorithm to optimize the process parameters of HFP and proposed HFP with a constrained boundary. The developed HFP machine tool (Figure 22) is used to polish the copper single crystal substrate, and the surface roughness can reach 3.42 nm. Zheng et al. [119, 120] subsequently optimized the structure of the HFP tool pad on this basis. The average and uniformity of the dynamic pressure generated by the polishing pad were improved by 30% after optimization. In the latest research results, by studying the division of structural units and their fluid hydrodynamic pressure, the analytical models of hydrodynamic bearing capacity and polishing fluid viscosity, polishing tool speed, polishing gap, and polishing pad structural parameters are derived, which lays a foundation for subsequent research on HFP technology.Figure 22
Hydrodynamic floating polishing machine [114]. (a) HFP polishing experiment. (b) HFP tool pad structure. (c) Nephogram of dynamic pressure of HFP tool pad.Through the literature research and comparison, at present, HFP technology mainly focuses on the optimization design of polishing pad structure and process parameters. Since the material removal process involves the interdisciplinary integration of physics, chemistry, acoustics, hydrodynamics, etc., there is still no accurate model to explain the polishing process. In its development direction, there has been a trend of integration with CMP and MRF. Peng et al. [121] proposed a new approach combining the technologies of magnetorheological finishing (MRF) and hydrodynamic effect polishing (HEP) in 2018. On the one hand, MRF can effectively improve the low efficiency of hydrodynamic pressure machining; on the other hand, HEP can obtain an ultrasmooth surface with good machining morphology. To improve the polishing efficiency, Zhong-yu et al. [122] combined hydrodynamic technology with CMP and treated the workpiece surface with a chemical erosion process before HFP. The results show that chemical erosion can effectively remove the surface deformation layer, the new polishing process can significantly reduce the surface roughness, and the minimum surface roughness is only Ra 0.81 nm. Meanwhile, the relationship between the abrasive particle kinetic energy and the copper atom binding energy is established, which provides a basis for understanding the two typical abrasive particle planarization mechanisms of removal and filling. Figure 23 shows the preparation of the ultrasmooth surface of copper. In addition, according to the current research, the removal effect of the fluid carrier on materials cannot be ignored because the fluid carrier appears in various polishing methods as a cutting fluid or working medium. It can be predicted that the research on composite polishing methods and processes combined with dynamic fluid pressure is still the direction being explored.Figure 23
Schematic diagram of preparation of the ultrasmooth surface of Cu [122].


## 4. Quasicontact Polishing

Quasicontact polishing refers to the formation of a hydrodynamic pressure film between the polishing pad and the workpiece due to the hydrodynamic pressure of the fluid in the machining process. The hydrodynamic pressure film makes the polishing pad and the workpiece have a specific clearance to prevent the polishing pad and the workpiece from contacting directly and from the quasicontact polishing.


### 4.1. Magnetorheological Finishing

The principle of magnetorheological finishing (MRF) is shown in Figure24. As a quasicontact polishing, magnetorheological finishing (MRF) is developed from the magnetic medium-assisted polishing, which can realize the flexible polishing of workpieces. In the process of polishing, the abrasive particles in the magnetorheological fluid adhere to the magnetic medium and form a chain-like structure under the action of magnetic fields, which will turn the polishing liquid into a viscoelastic Bingham medium and form a ribbon bulge. When the medium moves relative to the workpiece driven by the polishing pad, the shearing force is generated on the surface of the workpiece, and the material on the workpiece surface is removed by the combined action of the chemical and rheological forces.Figure 24
Magnetorheological finishing principle.MRF was first invented in 1974 by Kordonski and Golini in the laboratory of the Institute of Heat and Mass Transfer in Minsk, Belarus [123]. In 1978, Shlyago et al. [124] used magnetorheological fluid to finish glass, which is the beginning of MRF to finish optical components. In 1986, Kordonski and Golini [125] formally proposed applying magnetorheological fluid to the processing of optical parts and manufactured the first magnetorheological polishing prototype in 1990. Different from the wheel-type magnetorheological polishing machine, it uses an annular groove to store magnetorheological fluid. When the annular groove rotates, it drives the magnetorheological fluid. When passing through the magnetic field, the magnetorheological fluid hardens to realize the polishing of optical parts. From this polishing structure, it can be seen that the original MRF equipment does not have the basic idea of CCOS and can only polish the aspheric surface, which makes it difficult to trim the surface shape. In 1993, Kordonski et al. cooperated with the team led by Steve Jacobs of the University of Rochester to manufacture the engineering prototype of magnetorheological finishing. Its basic structure has not changed significantly compared with before. Through the prototype experiment, the optical polishing ability of the MRF with high efficiency, high precision, and low damage is verified, and the D-shaped material removal distribution is preliminarily obtained [126] (Figure 25), The real innovation began with the wheel-type structure proposed by the optical center (COM) of the University of Rochester in 1995 [127]. Its workpiece is located above the polishing wheel and the design significance is that the magnetorheological polishing technology can be indeed used for aspheric optical modification and polishing. With the help of the basic idea of CCOS, modern magnetorheological polishing technology has been established. In 1996, the COM designed a vertical wheel MRF polishing machine constructed by CNC systems. The device allows the software to sweep a rotating lens through the fluid about a virtual pivot point, enabling aspheres to be made in a deterministic manner, which indicates that MRF technology has truly entered the ranks of optical processing technology. In 1997, based on the research of MRF technology by COM, QED company was established, and the commercialization of MRF began [127]. Magnetorheological polishing technology has the excellent characteristics of high surface precision, minor surface roughness, easy control, and no new damage in the processing process, which attracts researchers to explore continuously, mainly focusing on the following aspects.Figure 25
Polishing spot observed when stationary glass workpiece is held in rotating RMF trough for 5 s [126].


#### 4.1.1. Study of the Material Removal Model

A stable removal function is a basis for machining a good surface shape accuracy and plays a vital role in the deterministic polishing process. The Preston equation is the most commonly used material removal model in MRF. The equation is a semiempirical and phenomenological model proposed by Burke and Warnock based on Preston’s first mechanical model. Zhang et al. [128] established a mathematical model of the removal function based on the Preston equation for the first time, expressed as R = KPV, where K is the Preston coefficient under specific process parameters; P is the pressure of the polishing fluid on the workpiece, which is the sum of the hydrodynamic pressure Pd and magnetization pressure Pm; V is the relative velocity between the magnetorheological fluid and the workpiece surface. It is concluded that the material removal rate is directly proportional to the pressure parameters. Peng et al. [129, 130] enriched the material removal function model based on this conclusion and established the hydrodynamic pressure model in the MRF area using the Bingham medium Reynolds equation of grease-lubricated bearings. The hydrodynamic pressure was obtained by solving the Reynolds equation according to the difference between discrete and over-relaxation iterative methods. According to short bearing lubrication theory, a three-dimensional material removal model was established. The average value of the quasiPreston coefficient under this process parameter was calculated, which provided a theoretical basis for CNC MRF technology and magnetorheological finishing of optical parts with complex surfaces. Yuan [131] analyzed the removal function model of convex spheres and the stability of the removal function through spot tests in the research of MRF technology for steep conformal optical domes and designed a six-axis linkage MRF machine tool suitable for high steepness conformal optical parts and capable of predicting various errors. Based on these previous studies, Li [132] established the mathematical model of the material removal rate, modified the solution equation of pressure P, and derived the calculation formula of relative velocity V. Aiming at the problems of cumbersome iterative calculation, poor convergence, and low efficiency of the traditional dwell time algorithm, the dwell time algorithm of matrix theory was proposed. The single and multifactor optimization of polishing process parameters was realized based on grey theory. The best combination scheme of process parameters considering the surface quality and removal rate was successfully obtained. Su [133] proposed using the Bingham-like constitutive equation as the constitutive equation of magnetorheological fluid and established a three-dimensional hydrodynamic model of the polishing area. On this basis, Xu [134] established the magnetorheological fluid dynamics model of small tool head for small parts. The deterministic machining of the workpiece was achieved through the dwell time algorithm in the form of a matrix.It can be seen from the above research that in recent years, the removal model mechanism of MRF has begun to turn to the study of the removal behavior on the molecular dynamics scale. This is because the problem of underpolishing or overpolishing of edges often occurs in the finishing stage of optical parts, which will lead to the aberration correction defect of optical mirrors. It is difficult to explain the material removal behavior based on the macroPreston equation model, so scholars began to put forward the micromodel from the physical law, that is, the forces and motions of the particles and the matrix are analyzed separately from the perspective of molecular dynamics, and the macroscopic physical quantities are obtained by statistical averaging.At present, the research on the removal dynamics of MRF is mainly manifested in two aspects. One is the computational fluid dynamics method. The basic idea is to use the discretization method to solve the fluid mass, momentum, energy equations, and other equations in a fixed geometric space [135].For macroscale problems, the magnetic fluid is usually regarded as a non-Newtonian fluid, ignoring the microscopic physical phenomena between particles. For microscale problems, the flow of magnetic fluid is usually regarded as a fluid-solid coupling problem. In practical applications, to improve the computing power, a multiscale model is generally established by combining the atomic scale and continuous scale, and the physical parameters obtained from the microscale are transferred to the macroscale through an equivalent method, and the macroscale simulation also provides the corresponding boundary conditions for the microscale simulation [136].Based on the above ideas, literature [137] established a hydrodynamic analysis method for the MRF process suitable for first-order discontinuous surface shape, which provides a key theoretical basis for deterministic analysis of first-order discontinuous surface material removal processes. Another study of the removal dynamics of MRF is the particle dynamics method. In this method, the matrix is regarded as a continuous medium, and the micromechanical model under the working mode of MRF is directly applied. The motion of particles is still solved by Newton’s motion equations, and finally, the macrophysical quantities are statistically averaged. The method model is simple and intuitive and is the most commonly used numerical simulation method [138].


#### 4.1.2. Research on the Dwell Time Algorithm

As one of the core technologies of MRF, the accurate control of the dwell time is an essential basis for realizing deterministic polishing. The removal amount of the MRF is the convolution of the dwell time function and the removal function. In general, the dwell time algorithm is discussed by convolution and convolution inversion methods; that is, the removal amount and removal function are transformed by discrete Fourier transform. The result of their division after transformation is the discrete Fourier change of the dwell time. Then, the inverse discrete Fourier transform is carried out to obtain the dwell time of each point on the workpiece surface. Satake et al. [139] found that excessive material removal often occurs when using the fast Fourier transform alone. To solve this problem, the team first uses the removed shape calculated by the FFT method as a constraint and then uses the constraint condition method to solve the dwell time. The experiment shows that this is a feasible method to improve machining accuracy. To further enhance the adaptability and stability of the algorithm and solve the problems of cumbersome iterative calculation, poor convergence, and low efficiency, references [140–144] studied a new dwell time algorithm from the perspective of the matrix. Subsequently, a matrix-based dwell time algorithm for aspheric surfaces is proposed. Its basic idea is to transform the mathematical model of machining from the convolution process of the removal function and the dwell time to the product process of the removal matrix and the dwell time vector, so as to change the calculation of dwell time into the solution process of linear equations. In solving the matrix equation, Tikhonov regularization is used to eliminate the ill-posedness of the matrix equation and obtain a stable solution. Compared with the results of the iterative algorithm and Fourier transform method, the solution accuracy of this method is improved by more than 30%. Li et al. [144, 145] studied a non-negative least-squares method of CGMRES combined with the adaptive Tikhonov regulation and obtained a more accurate optical surface by developing a general surface error graph extension. Subsequently, based on the non-negative algorithm, a positive dwell time algorithm was established. Simulation results show the effectiveness of the positive dwell time algorithm for the minimum equal extra material removal. Zhang et al. [146] took the dynamic performance of the machine tool as the constraint based on the least-squares method and used the two-metric projection Newton iteration algorithm to solve the large-scale dwell time model, which greatly improved the calculation efficiency. The experiments and simulations show that the proposed algorithm will give a very high convergence accuracy for optical finishing with machine tools with different dynamic performances.


#### 4.1.3. Progress of Processing Methods

(1) Cluster MRF. In 2008, Yan et al. [147] first proposed the grinding and polishing technology of microgrinding heads with the cluster magnetorheological effect. The basic principle of this technology is that several permanent magnets are regularly arranged on a nonmagnetic polishing pad to form a new polishing pad with cluster MRF effects. The magnetic particles in the magnetorheological fluid form a convex micromagnetic cluster at each magnetic pole. With the relative movement of the workpiece, the micromagnetic cluster shears the workpiece surface to remove the material on the workpiece surface. The basic principle of the polishing is shown in Figure 26. Subsequently, the team carried out a series of studies on cluster MRF technology. Wu [148] studied the trajectory of abrasive particles at any point on the polishing pad relative to the workpiece under the two processing modes of fixed and indefinite eccentricity. It is found that the anisotropic arrangement of magnetic poles is better than the isotropic arrangement of magnetic poles. This discovery has enlightening significance for the design of magnetic field arrangements.Figure 26
Cluster MRF principle.Aiming at some problems existing in the permanent magnet, such as the magnetic field strength of the permanent magnet being small, the magnetic field strength not being adjusted, and the magnetic sensitive medium easily adhering to the surface of the polishing pad, Tong [149] proposed the electromagnet excitation scheme and simulated the cluster effect of the electromagnet poles by using Ansoft software and carried out the optimal design. Bai et al. [150] studied the polishing force (tangential force Ft and normal force Fn) in the cluster MRF process by building a three-dimensional force measuring platform for cluster magnetorheological plane polishing. It is found that the magnitude of cluster MRF force and Ft/Fn value are directly proportional to the material hardness, which is conducive to improving the ultrasmooth and flattening polishing of hard and brittle materials. In addition, Yan et al. also made various innovations in cluster MRF technology. For example, Li et al. [151] combined cluster magnetorheological technology with polyurethane pads and realized the high-efficiency processing of hard and brittle materials based on the advantages of the two processing methods. Guo et al. [152–154] studied the mechanism of dynamic magnetic field cluster magnetorheological finishing and adopted the dynamic change of magnetic field gradient to improve the material removal efficiency. Figure 27 shows the comparison of the surface morphology under static and dynamic magnetic fields.Figure 27
Surface morphology under different magnetic fields [152]. (a) Static magnetic field (68 nm). (b) Dynamic magnetic field (16.2 nm).
(a)(b)Liao et al. [155, 156] combined the extrusion strengthening effect of the magnetorheological fluid with the principle of cluster MRF, proposed the cluster magnetorheological variable gap hydrodynamic pressure polishing process, and established the material removal model of cluster magnetorheological variable gap hydrodynamic pressure polishing based on the Preston equation. Figure 28 shows the comparison of the surface morphology between the conventional cluster MRF and cluster magnetorheological variable gap hydrodynamic pressure flattening. In the latest research, an ultrasmooth surface with a surface roughness of Ra 0.45 nm was obtained, and the material removal rate reached 3.28 nm/min.Figure 28
Surface morphology of sapphire wafer processed by different methods [155]. (a) Conventional cluster magnetorheological finishing. (b) Cluster magnetorheological variable gap dynamic pressure flattening.
(a)(b)(2) Belt-MRF. It is found that the material removal rate is obviously insufficient when machining large-diameter optical parts by MRF technology. In 2014, Ren et al. [157, 158] proposed Belt-MRF for the first time and manufactured the prototype with the structure diagram, as shown in Figure 29(a). Through simulations and tests, it is found that Belt-MRF polishing can significantly improve the material removal rate, which provides a new idea for the processing of large-aperture optical parts. Figure 29(b) shows the removal function comparison between the Belt-MRF and the existing wheel-type MRF. Since the shape of the material removal function of the Belt-MRF is long and the unstable belt drive system has severe effects on the material removal rate and surface accuracy of the Belt-MRF, it is of great significance to study the distribution of the removal function of the Belt-MRF and the stable operation of the belt drive system. Based on Ren’s research, Wang et al. [159] proposed the theory of virtual ribbon bulge and the transmission mode of a synchronous belt with an air-floating layer to realize the stable operation and high-precision transmission of the system.Figure 29
(a) Belt-MRF principle; (b) the removal function comparison between belt-MRF and the existing wheel-type MRF [157, 158].
(a)(b)(3) Ultrasonic-Magnetorheological Compound Finishing. In 2007, Wang et al. [160] proposed a kind of ultrasonic-magnetorheological compound finishing technology and carried out the experiment in detail (Figure 30), which laid the foundation for further research on this technology. Hu [161] used ultrasonic-magnetorheological compound finishing to study the polishing process of ZrO2, which opened up a new idea for the development of MRF technology, Meanwhile, the processing method of combining magnetorheological and ultrasonic vibration also brings a new challenge to the research of magnetorheological compound processing technology. In the ultrasonic-magnetorheological compound finishing, although the material removal efficiency has been improved, the surface roughness has not changed much, so it is necessary to explore the technology further to improve the surface quality.Figure 30
Ultrasonic-magnetorheological compound finishing [160].Magnetorheological polishing is a combination of fluid mechanics, electromagnetism, rheology, chemistry, and other disciplines. It is an expansion of traditional machining and is of great significance to the development of modern manufacturing technology. With the development of precision and ultraprecision machining technology, there are still some problems to be further studied, such as establishing a real-time material removal model based on online measurement feedback and the preparation technology of MRF fluids with excellent cutting characteristics. From the perspective of future development, it will be a meaningful research direction to explore a composite magnetorheological polishing technology that can not only improve the material removal efficiency but also improve the surface quality and has a wide range of workpiece processing adaptability.


### 4.2. Chemical Mechanical Planarization/Polishing

In 1965, reference [162] first proposed chemical mechanical planarization (CMP) technology, which uses the principle of soft grinding to realize the high-quality polishing of hard materials [163]. In 1983, IBM company began developing CMP technology and introduced CMP technology into the integrated circuit manufacturing industry. It is first used for the planarization of the intermetallic insulating medium (IMD) layer in the post-treatment process and then for the planarization of shallow trench isolation (STI) and copper (Cu). The entire CMP process can be completed in just 30 seconds. In 1988, IBM applied CMP technology to the manufacture of 4 Mb DRAM. In 1991, IBM successfully applied CMP technology to the production of 64 Mb DRAM to meet the global planarization requirement with feature sizes below 0.35 μm. CMP is the only surface finishing technology that can effectively provide global planarization, which plays an important role in the ultraprecision surface finishing of integrated circuits such as semiconductor chips, computer hard disk, etc. Subsequently, many universities and companies began to research CMP technology [164–168].


#### 4.2.1. Research on Material Removal Model

The principle of CMP can be simplified as shown in Figure31. In the process of machining, there is a certain pressure on the workpiece surface that performs mechanical grinding and chemical etching on the workpiece surface. The material removal mechanism in the CMP process is very complex and involves chemistry, fluid mechanics, tribology, etc. At present, there are three main modeling methods for CMP research.Figure 31
Chemical mechanical planarization principle.The first is the phenomenological model based on the results of the polishing process, that is, the pure mechanical action model represented by the Preston equation. This model analyzes the material removal process from the perspective of mechanical removal of abrasive particles and idealizes the polishing process, so it does not fully reveal the wear mechanism.The second is the mechanical-fluid film model. In the polishing process, in addition to the mechanical force, the hydrodynamic pressure produced by the fluid film also affects the distribution of the removal stress and the material removal rate [169]. Based on contact mechanics and hydrodynamics theory, McGrath et al. [170] proposed a material removal model based on lubrication and wear, and Kim et al. [171] perfected and enriched this theory. The hydrodynamic pressure distributions on the workpiece surface under different load pressures, flow rates, and slurry viscosities were studied experimentally, and a relatively complete mechanical-fluid film interaction model was established.The third model is the mechanical-chemical interaction model. The chemical composition and pH value of the polishing fluid are the main factors that affect the chemical interaction of CMP, and there is no effective mathematical model to analyze the material removal rate quantitatively. Zhao et al. [172] argue that chemical reactions turn the strong bonds between atoms/molecules on a material’s machined surface into weak bonds to remove the material at the atomic level. Based on elastic-plastic contact theory, chemical dynamics, and molecular dynamics, the material removal rate equation was built. The model reveals some characteristics of the CMP process, that is, the material removal rate is related to the concentration of abrasive in the polishing fluid and greatly affected by the applied load, and it is most affected by the surface hardness and abrasive particle size of the workpiece. However, the model’s accuracy is not high since the actual contact area and the molecular bond energy are difficult to accurately determine. In follow-up studies, most researchers focus on the relationship between the chemical composition of the polishing fluid and the polishing process [173, 174]. Different from other polishing technologies, CMP technology is developed from engineering practice, and its invention, development, and application are accomplished in industry rather than academia, so systematic research, especially theoretical research, needs to be further improved.


#### 4.2.2. Process Research

Since IBM developed CMP planarization technology in the 1980s, the process research on CMP initially focused on the field of silicon wafers. The improvement of the CMP process by researchers has dramatically improved the flatness and surface quality of parts. It has undergone great development in mechanism research and production applications and is widely used in MEMS, integrated circuits, and other fields [175–177]. CMP has been widely used in the finishing of optical components, such as sapphire crystals and lithium niobate crystals, and has achieved many research results.Sapphire crystal has the characteristics of high hardness, wear resistance, corrosion resistance, and high transmittance and has good optical, chemical, and mechanical properties. Therefore, sapphire crystal is often used as window materials for satellite space technology, military infrared devices, and high-intensity lasers, and it is also used in large-scale integrated circuits and some superconducting nanostructure films. Practical applications require surface roughnessRa < 0.3 nm [178, 179]. Wang et al. [180] studied the CMP process parameters of sapphire substrates and established a perfect CMP model, which lays a foundation for the following research on the material removal model of sapphire. Zhang et al. [181] used silicon oxide as abrasives to polish the sapphire substrate and improved the material removal efficiency by controlling the temperature, pH value, abrasive particle size, and concentration. To further enhance the polishing quality and material removal rate and perfect the flattening process of sapphire surfaces, Li [182] studied the regularity of material removal and surface roughness of sapphire substrate by orthogonal test and then adjusted the parameters. The alkaline polishing fluid for sapphire substrate was prepared by a single factor test. The material removal rate was 26 nm/min, and the surface roughness was better than Ra 1 nm. Vovk et al. [183] studied the chemical mechanical polishing of sapphire by silica colloid and proposed the reaction mechanism between Al2O3 and SiO2. The research results show that sapphire samples with different crystallographic orientations have anisotropic material removal rates. This anisotropy can be explained by the difference in the formation rate of intermediate products of chemical reactions between aluminum and silicon oxides on different planes. Hu [184] studied the high-efficiency and low damage processing of sapphire based on previous work, built a double-sided CMP test platform, analyzed the subsurface damage mechanism during sapphire processing, and established a prediction model of polishing subsurface damage depth. The results show that the subsurface damage depth increases with the increase of polishing pressure and polishing pad speed and decreases with the extension of polishing time, and the impact of polishing time is the greatest. Shi et al. [185] successfully designed an in-situ study of CMP behaviors on sapphire (0001) by simulating the chemical product removal process using AFM-tapping mode for the first time, which provides a new method for studying CMP behavior on different materials and fills the gap in knowledge of CMP’s basic mechanism. Figure 32 shows CMP and atomic force microscopy (AFM)-tapping mode principles.Figure 32
CMP and atomic force microscopy (AFM)-tapping mode principles diagram [185].Although CMP technology is one of the most effective processing methods for optical crystals to have an ultrasmooth surface, the operation is relatively simple, and the cost is relatively low in the process of obtaining the ultrasmooth surface, the current theoretical development is still imperfect, and the research on the microtheory of material removal has not formed a unified theory. The effect of the coupling between the factors on the performance of each component of the polishing system is not clear. Therefore, in-depth study of the fluid dynamics in the CMP process, analysis of the influence of abrasive particle movement trajectories on polishing quality, explanation of the removal mechanism of surface materials from a microscopic point of view (atomic and molecular interaction), and establishing the contact model between the polishing pad, abrasive particles, and the surface of the workpiece are all topics that need to be further explored in the future.


## 4.1. Magnetorheological Finishing

The principle of magnetorheological finishing (MRF) is shown in Figure24. As a quasicontact polishing, magnetorheological finishing (MRF) is developed from the magnetic medium-assisted polishing, which can realize the flexible polishing of workpieces. In the process of polishing, the abrasive particles in the magnetorheological fluid adhere to the magnetic medium and form a chain-like structure under the action of magnetic fields, which will turn the polishing liquid into a viscoelastic Bingham medium and form a ribbon bulge. When the medium moves relative to the workpiece driven by the polishing pad, the shearing force is generated on the surface of the workpiece, and the material on the workpiece surface is removed by the combined action of the chemical and rheological forces.Figure 24
Magnetorheological finishing principle.MRF was first invented in 1974 by Kordonski and Golini in the laboratory of the Institute of Heat and Mass Transfer in Minsk, Belarus [123]. In 1978, Shlyago et al. [124] used magnetorheological fluid to finish glass, which is the beginning of MRF to finish optical components. In 1986, Kordonski and Golini [125] formally proposed applying magnetorheological fluid to the processing of optical parts and manufactured the first magnetorheological polishing prototype in 1990. Different from the wheel-type magnetorheological polishing machine, it uses an annular groove to store magnetorheological fluid. When the annular groove rotates, it drives the magnetorheological fluid. When passing through the magnetic field, the magnetorheological fluid hardens to realize the polishing of optical parts. From this polishing structure, it can be seen that the original MRF equipment does not have the basic idea of CCOS and can only polish the aspheric surface, which makes it difficult to trim the surface shape. In 1993, Kordonski et al. cooperated with the team led by Steve Jacobs of the University of Rochester to manufacture the engineering prototype of magnetorheological finishing. Its basic structure has not changed significantly compared with before. Through the prototype experiment, the optical polishing ability of the MRF with high efficiency, high precision, and low damage is verified, and the D-shaped material removal distribution is preliminarily obtained [126] (Figure 25), The real innovation began with the wheel-type structure proposed by the optical center (COM) of the University of Rochester in 1995 [127]. Its workpiece is located above the polishing wheel and the design significance is that the magnetorheological polishing technology can be indeed used for aspheric optical modification and polishing. With the help of the basic idea of CCOS, modern magnetorheological polishing technology has been established. In 1996, the COM designed a vertical wheel MRF polishing machine constructed by CNC systems. The device allows the software to sweep a rotating lens through the fluid about a virtual pivot point, enabling aspheres to be made in a deterministic manner, which indicates that MRF technology has truly entered the ranks of optical processing technology. In 1997, based on the research of MRF technology by COM, QED company was established, and the commercialization of MRF began [127]. Magnetorheological polishing technology has the excellent characteristics of high surface precision, minor surface roughness, easy control, and no new damage in the processing process, which attracts researchers to explore continuously, mainly focusing on the following aspects.Figure 25
Polishing spot observed when stationary glass workpiece is held in rotating RMF trough for 5 s [126].


### 4.1.1. Study of the Material Removal Model

A stable removal function is a basis for machining a good surface shape accuracy and plays a vital role in the deterministic polishing process. The Preston equation is the most commonly used material removal model in MRF. The equation is a semiempirical and phenomenological model proposed by Burke and Warnock based on Preston’s first mechanical model. Zhang et al. [128] established a mathematical model of the removal function based on the Preston equation for the first time, expressed as R = KPV, where K is the Preston coefficient under specific process parameters; P is the pressure of the polishing fluid on the workpiece, which is the sum of the hydrodynamic pressure Pd and magnetization pressure Pm; V is the relative velocity between the magnetorheological fluid and the workpiece surface. It is concluded that the material removal rate is directly proportional to the pressure parameters. Peng et al. [129, 130] enriched the material removal function model based on this conclusion and established the hydrodynamic pressure model in the MRF area using the Bingham medium Reynolds equation of grease-lubricated bearings. The hydrodynamic pressure was obtained by solving the Reynolds equation according to the difference between discrete and over-relaxation iterative methods. According to short bearing lubrication theory, a three-dimensional material removal model was established. The average value of the quasiPreston coefficient under this process parameter was calculated, which provided a theoretical basis for CNC MRF technology and magnetorheological finishing of optical parts with complex surfaces. Yuan [131] analyzed the removal function model of convex spheres and the stability of the removal function through spot tests in the research of MRF technology for steep conformal optical domes and designed a six-axis linkage MRF machine tool suitable for high steepness conformal optical parts and capable of predicting various errors. Based on these previous studies, Li [132] established the mathematical model of the material removal rate, modified the solution equation of pressure P, and derived the calculation formula of relative velocity V. Aiming at the problems of cumbersome iterative calculation, poor convergence, and low efficiency of the traditional dwell time algorithm, the dwell time algorithm of matrix theory was proposed. The single and multifactor optimization of polishing process parameters was realized based on grey theory. The best combination scheme of process parameters considering the surface quality and removal rate was successfully obtained. Su [133] proposed using the Bingham-like constitutive equation as the constitutive equation of magnetorheological fluid and established a three-dimensional hydrodynamic model of the polishing area. On this basis, Xu [134] established the magnetorheological fluid dynamics model of small tool head for small parts. The deterministic machining of the workpiece was achieved through the dwell time algorithm in the form of a matrix.It can be seen from the above research that in recent years, the removal model mechanism of MRF has begun to turn to the study of the removal behavior on the molecular dynamics scale. This is because the problem of underpolishing or overpolishing of edges often occurs in the finishing stage of optical parts, which will lead to the aberration correction defect of optical mirrors. It is difficult to explain the material removal behavior based on the macroPreston equation model, so scholars began to put forward the micromodel from the physical law, that is, the forces and motions of the particles and the matrix are analyzed separately from the perspective of molecular dynamics, and the macroscopic physical quantities are obtained by statistical averaging.At present, the research on the removal dynamics of MRF is mainly manifested in two aspects. One is the computational fluid dynamics method. The basic idea is to use the discretization method to solve the fluid mass, momentum, energy equations, and other equations in a fixed geometric space [135].For macroscale problems, the magnetic fluid is usually regarded as a non-Newtonian fluid, ignoring the microscopic physical phenomena between particles. For microscale problems, the flow of magnetic fluid is usually regarded as a fluid-solid coupling problem. In practical applications, to improve the computing power, a multiscale model is generally established by combining the atomic scale and continuous scale, and the physical parameters obtained from the microscale are transferred to the macroscale through an equivalent method, and the macroscale simulation also provides the corresponding boundary conditions for the microscale simulation [136].Based on the above ideas, literature [137] established a hydrodynamic analysis method for the MRF process suitable for first-order discontinuous surface shape, which provides a key theoretical basis for deterministic analysis of first-order discontinuous surface material removal processes. Another study of the removal dynamics of MRF is the particle dynamics method. In this method, the matrix is regarded as a continuous medium, and the micromechanical model under the working mode of MRF is directly applied. The motion of particles is still solved by Newton’s motion equations, and finally, the macrophysical quantities are statistically averaged. The method model is simple and intuitive and is the most commonly used numerical simulation method [138].


### 4.1.2. Research on the Dwell Time Algorithm

As one of the core technologies of MRF, the accurate control of the dwell time is an essential basis for realizing deterministic polishing. The removal amount of the MRF is the convolution of the dwell time function and the removal function. In general, the dwell time algorithm is discussed by convolution and convolution inversion methods; that is, the removal amount and removal function are transformed by discrete Fourier transform. The result of their division after transformation is the discrete Fourier change of the dwell time. Then, the inverse discrete Fourier transform is carried out to obtain the dwell time of each point on the workpiece surface. Satake et al. [139] found that excessive material removal often occurs when using the fast Fourier transform alone. To solve this problem, the team first uses the removed shape calculated by the FFT method as a constraint and then uses the constraint condition method to solve the dwell time. The experiment shows that this is a feasible method to improve machining accuracy. To further enhance the adaptability and stability of the algorithm and solve the problems of cumbersome iterative calculation, poor convergence, and low efficiency, references [140–144] studied a new dwell time algorithm from the perspective of the matrix. Subsequently, a matrix-based dwell time algorithm for aspheric surfaces is proposed. Its basic idea is to transform the mathematical model of machining from the convolution process of the removal function and the dwell time to the product process of the removal matrix and the dwell time vector, so as to change the calculation of dwell time into the solution process of linear equations. In solving the matrix equation, Tikhonov regularization is used to eliminate the ill-posedness of the matrix equation and obtain a stable solution. Compared with the results of the iterative algorithm and Fourier transform method, the solution accuracy of this method is improved by more than 30%. Li et al. [144, 145] studied a non-negative least-squares method of CGMRES combined with the adaptive Tikhonov regulation and obtained a more accurate optical surface by developing a general surface error graph extension. Subsequently, based on the non-negative algorithm, a positive dwell time algorithm was established. Simulation results show the effectiveness of the positive dwell time algorithm for the minimum equal extra material removal. Zhang et al. [146] took the dynamic performance of the machine tool as the constraint based on the least-squares method and used the two-metric projection Newton iteration algorithm to solve the large-scale dwell time model, which greatly improved the calculation efficiency. The experiments and simulations show that the proposed algorithm will give a very high convergence accuracy for optical finishing with machine tools with different dynamic performances.


### 4.1.3. Progress of Processing Methods

(1) Cluster MRF. In 2008, Yan et al. [147] first proposed the grinding and polishing technology of microgrinding heads with the cluster magnetorheological effect. The basic principle of this technology is that several permanent magnets are regularly arranged on a nonmagnetic polishing pad to form a new polishing pad with cluster MRF effects. The magnetic particles in the magnetorheological fluid form a convex micromagnetic cluster at each magnetic pole. With the relative movement of the workpiece, the micromagnetic cluster shears the workpiece surface to remove the material on the workpiece surface. The basic principle of the polishing is shown in Figure 26. Subsequently, the team carried out a series of studies on cluster MRF technology. Wu [148] studied the trajectory of abrasive particles at any point on the polishing pad relative to the workpiece under the two processing modes of fixed and indefinite eccentricity. It is found that the anisotropic arrangement of magnetic poles is better than the isotropic arrangement of magnetic poles. This discovery has enlightening significance for the design of magnetic field arrangements.Figure 26
Cluster MRF principle.Aiming at some problems existing in the permanent magnet, such as the magnetic field strength of the permanent magnet being small, the magnetic field strength not being adjusted, and the magnetic sensitive medium easily adhering to the surface of the polishing pad, Tong [149] proposed the electromagnet excitation scheme and simulated the cluster effect of the electromagnet poles by using Ansoft software and carried out the optimal design. Bai et al. [150] studied the polishing force (tangential force Ft and normal force Fn) in the cluster MRF process by building a three-dimensional force measuring platform for cluster magnetorheological plane polishing. It is found that the magnitude of cluster MRF force and Ft/Fn value are directly proportional to the material hardness, which is conducive to improving the ultrasmooth and flattening polishing of hard and brittle materials. In addition, Yan et al. also made various innovations in cluster MRF technology. For example, Li et al. [151] combined cluster magnetorheological technology with polyurethane pads and realized the high-efficiency processing of hard and brittle materials based on the advantages of the two processing methods. Guo et al. [152–154] studied the mechanism of dynamic magnetic field cluster magnetorheological finishing and adopted the dynamic change of magnetic field gradient to improve the material removal efficiency. Figure 27 shows the comparison of the surface morphology under static and dynamic magnetic fields.Figure 27
Surface morphology under different magnetic fields [152]. (a) Static magnetic field (68 nm). (b) Dynamic magnetic field (16.2 nm).
(a)(b)Liao et al. [155, 156] combined the extrusion strengthening effect of the magnetorheological fluid with the principle of cluster MRF, proposed the cluster magnetorheological variable gap hydrodynamic pressure polishing process, and established the material removal model of cluster magnetorheological variable gap hydrodynamic pressure polishing based on the Preston equation. Figure 28 shows the comparison of the surface morphology between the conventional cluster MRF and cluster magnetorheological variable gap hydrodynamic pressure flattening. In the latest research, an ultrasmooth surface with a surface roughness of Ra 0.45 nm was obtained, and the material removal rate reached 3.28 nm/min.Figure 28
Surface morphology of sapphire wafer processed by different methods [155]. (a) Conventional cluster magnetorheological finishing. (b) Cluster magnetorheological variable gap dynamic pressure flattening.
(a)(b)(2) Belt-MRF. It is found that the material removal rate is obviously insufficient when machining large-diameter optical parts by MRF technology. In 2014, Ren et al. [157, 158] proposed Belt-MRF for the first time and manufactured the prototype with the structure diagram, as shown in Figure 29(a). Through simulations and tests, it is found that Belt-MRF polishing can significantly improve the material removal rate, which provides a new idea for the processing of large-aperture optical parts. Figure 29(b) shows the removal function comparison between the Belt-MRF and the existing wheel-type MRF. Since the shape of the material removal function of the Belt-MRF is long and the unstable belt drive system has severe effects on the material removal rate and surface accuracy of the Belt-MRF, it is of great significance to study the distribution of the removal function of the Belt-MRF and the stable operation of the belt drive system. Based on Ren’s research, Wang et al. [159] proposed the theory of virtual ribbon bulge and the transmission mode of a synchronous belt with an air-floating layer to realize the stable operation and high-precision transmission of the system.Figure 29
(a) Belt-MRF principle; (b) the removal function comparison between belt-MRF and the existing wheel-type MRF [157, 158].
(a)(b)(3) Ultrasonic-Magnetorheological Compound Finishing. In 2007, Wang et al. [160] proposed a kind of ultrasonic-magnetorheological compound finishing technology and carried out the experiment in detail (Figure 30), which laid the foundation for further research on this technology. Hu [161] used ultrasonic-magnetorheological compound finishing to study the polishing process of ZrO2, which opened up a new idea for the development of MRF technology, Meanwhile, the processing method of combining magnetorheological and ultrasonic vibration also brings a new challenge to the research of magnetorheological compound processing technology. In the ultrasonic-magnetorheological compound finishing, although the material removal efficiency has been improved, the surface roughness has not changed much, so it is necessary to explore the technology further to improve the surface quality.Figure 30
Ultrasonic-magnetorheological compound finishing [160].Magnetorheological polishing is a combination of fluid mechanics, electromagnetism, rheology, chemistry, and other disciplines. It is an expansion of traditional machining and is of great significance to the development of modern manufacturing technology. With the development of precision and ultraprecision machining technology, there are still some problems to be further studied, such as establishing a real-time material removal model based on online measurement feedback and the preparation technology of MRF fluids with excellent cutting characteristics. From the perspective of future development, it will be a meaningful research direction to explore a composite magnetorheological polishing technology that can not only improve the material removal efficiency but also improve the surface quality and has a wide range of workpiece processing adaptability.


## 4.1.1. Study of the Material Removal Model

A stable removal function is a basis for machining a good surface shape accuracy and plays a vital role in the deterministic polishing process. The Preston equation is the most commonly used material removal model in MRF. The equation is a semiempirical and phenomenological model proposed by Burke and Warnock based on Preston’s first mechanical model. Zhang et al. [128] established a mathematical model of the removal function based on the Preston equation for the first time, expressed as R = KPV, where K is the Preston coefficient under specific process parameters; P is the pressure of the polishing fluid on the workpiece, which is the sum of the hydrodynamic pressure Pd and magnetization pressure Pm; V is the relative velocity between the magnetorheological fluid and the workpiece surface. It is concluded that the material removal rate is directly proportional to the pressure parameters. Peng et al. [129, 130] enriched the material removal function model based on this conclusion and established the hydrodynamic pressure model in the MRF area using the Bingham medium Reynolds equation of grease-lubricated bearings. The hydrodynamic pressure was obtained by solving the Reynolds equation according to the difference between discrete and over-relaxation iterative methods. According to short bearing lubrication theory, a three-dimensional material removal model was established. The average value of the quasiPreston coefficient under this process parameter was calculated, which provided a theoretical basis for CNC MRF technology and magnetorheological finishing of optical parts with complex surfaces. Yuan [131] analyzed the removal function model of convex spheres and the stability of the removal function through spot tests in the research of MRF technology for steep conformal optical domes and designed a six-axis linkage MRF machine tool suitable for high steepness conformal optical parts and capable of predicting various errors. Based on these previous studies, Li [132] established the mathematical model of the material removal rate, modified the solution equation of pressure P, and derived the calculation formula of relative velocity V. Aiming at the problems of cumbersome iterative calculation, poor convergence, and low efficiency of the traditional dwell time algorithm, the dwell time algorithm of matrix theory was proposed. The single and multifactor optimization of polishing process parameters was realized based on grey theory. The best combination scheme of process parameters considering the surface quality and removal rate was successfully obtained. Su [133] proposed using the Bingham-like constitutive equation as the constitutive equation of magnetorheological fluid and established a three-dimensional hydrodynamic model of the polishing area. On this basis, Xu [134] established the magnetorheological fluid dynamics model of small tool head for small parts. The deterministic machining of the workpiece was achieved through the dwell time algorithm in the form of a matrix.It can be seen from the above research that in recent years, the removal model mechanism of MRF has begun to turn to the study of the removal behavior on the molecular dynamics scale. This is because the problem of underpolishing or overpolishing of edges often occurs in the finishing stage of optical parts, which will lead to the aberration correction defect of optical mirrors. It is difficult to explain the material removal behavior based on the macroPreston equation model, so scholars began to put forward the micromodel from the physical law, that is, the forces and motions of the particles and the matrix are analyzed separately from the perspective of molecular dynamics, and the macroscopic physical quantities are obtained by statistical averaging.At present, the research on the removal dynamics of MRF is mainly manifested in two aspects. One is the computational fluid dynamics method. The basic idea is to use the discretization method to solve the fluid mass, momentum, energy equations, and other equations in a fixed geometric space [135].For macroscale problems, the magnetic fluid is usually regarded as a non-Newtonian fluid, ignoring the microscopic physical phenomena between particles. For microscale problems, the flow of magnetic fluid is usually regarded as a fluid-solid coupling problem. In practical applications, to improve the computing power, a multiscale model is generally established by combining the atomic scale and continuous scale, and the physical parameters obtained from the microscale are transferred to the macroscale through an equivalent method, and the macroscale simulation also provides the corresponding boundary conditions for the microscale simulation [136].Based on the above ideas, literature [137] established a hydrodynamic analysis method for the MRF process suitable for first-order discontinuous surface shape, which provides a key theoretical basis for deterministic analysis of first-order discontinuous surface material removal processes. Another study of the removal dynamics of MRF is the particle dynamics method. In this method, the matrix is regarded as a continuous medium, and the micromechanical model under the working mode of MRF is directly applied. The motion of particles is still solved by Newton’s motion equations, and finally, the macrophysical quantities are statistically averaged. The method model is simple and intuitive and is the most commonly used numerical simulation method [138].


## 4.1.2. Research on the Dwell Time Algorithm

As one of the core technologies of MRF, the accurate control of the dwell time is an essential basis for realizing deterministic polishing. The removal amount of the MRF is the convolution of the dwell time function and the removal function. In general, the dwell time algorithm is discussed by convolution and convolution inversion methods; that is, the removal amount and removal function are transformed by discrete Fourier transform. The result of their division after transformation is the discrete Fourier change of the dwell time. Then, the inverse discrete Fourier transform is carried out to obtain the dwell time of each point on the workpiece surface. Satake et al. [139] found that excessive material removal often occurs when using the fast Fourier transform alone. To solve this problem, the team first uses the removed shape calculated by the FFT method as a constraint and then uses the constraint condition method to solve the dwell time. The experiment shows that this is a feasible method to improve machining accuracy. To further enhance the adaptability and stability of the algorithm and solve the problems of cumbersome iterative calculation, poor convergence, and low efficiency, references [140–144] studied a new dwell time algorithm from the perspective of the matrix. Subsequently, a matrix-based dwell time algorithm for aspheric surfaces is proposed. Its basic idea is to transform the mathematical model of machining from the convolution process of the removal function and the dwell time to the product process of the removal matrix and the dwell time vector, so as to change the calculation of dwell time into the solution process of linear equations. In solving the matrix equation, Tikhonov regularization is used to eliminate the ill-posedness of the matrix equation and obtain a stable solution. Compared with the results of the iterative algorithm and Fourier transform method, the solution accuracy of this method is improved by more than 30%. Li et al. [144, 145] studied a non-negative least-squares method of CGMRES combined with the adaptive Tikhonov regulation and obtained a more accurate optical surface by developing a general surface error graph extension. Subsequently, based on the non-negative algorithm, a positive dwell time algorithm was established. Simulation results show the effectiveness of the positive dwell time algorithm for the minimum equal extra material removal. Zhang et al. [146] took the dynamic performance of the machine tool as the constraint based on the least-squares method and used the two-metric projection Newton iteration algorithm to solve the large-scale dwell time model, which greatly improved the calculation efficiency. The experiments and simulations show that the proposed algorithm will give a very high convergence accuracy for optical finishing with machine tools with different dynamic performances.


## 4.1.3. Progress of Processing Methods

(1) Cluster MRF. In 2008, Yan et al. [147] first proposed the grinding and polishing technology of microgrinding heads with the cluster magnetorheological effect. The basic principle of this technology is that several permanent magnets are regularly arranged on a nonmagnetic polishing pad to form a new polishing pad with cluster MRF effects. The magnetic particles in the magnetorheological fluid form a convex micromagnetic cluster at each magnetic pole. With the relative movement of the workpiece, the micromagnetic cluster shears the workpiece surface to remove the material on the workpiece surface. The basic principle of the polishing is shown in Figure 26. Subsequently, the team carried out a series of studies on cluster MRF technology. Wu [148] studied the trajectory of abrasive particles at any point on the polishing pad relative to the workpiece under the two processing modes of fixed and indefinite eccentricity. It is found that the anisotropic arrangement of magnetic poles is better than the isotropic arrangement of magnetic poles. This discovery has enlightening significance for the design of magnetic field arrangements.Figure 26
Cluster MRF principle.Aiming at some problems existing in the permanent magnet, such as the magnetic field strength of the permanent magnet being small, the magnetic field strength not being adjusted, and the magnetic sensitive medium easily adhering to the surface of the polishing pad, Tong [149] proposed the electromagnet excitation scheme and simulated the cluster effect of the electromagnet poles by using Ansoft software and carried out the optimal design. Bai et al. [150] studied the polishing force (tangential force Ft and normal force Fn) in the cluster MRF process by building a three-dimensional force measuring platform for cluster magnetorheological plane polishing. It is found that the magnitude of cluster MRF force and Ft/Fn value are directly proportional to the material hardness, which is conducive to improving the ultrasmooth and flattening polishing of hard and brittle materials. In addition, Yan et al. also made various innovations in cluster MRF technology. For example, Li et al. [151] combined cluster magnetorheological technology with polyurethane pads and realized the high-efficiency processing of hard and brittle materials based on the advantages of the two processing methods. Guo et al. [152–154] studied the mechanism of dynamic magnetic field cluster magnetorheological finishing and adopted the dynamic change of magnetic field gradient to improve the material removal efficiency. Figure 27 shows the comparison of the surface morphology under static and dynamic magnetic fields.Figure 27
Surface morphology under different magnetic fields [152]. (a) Static magnetic field (68 nm). (b) Dynamic magnetic field (16.2 nm).
(a)(b)Liao et al. [155, 156] combined the extrusion strengthening effect of the magnetorheological fluid with the principle of cluster MRF, proposed the cluster magnetorheological variable gap hydrodynamic pressure polishing process, and established the material removal model of cluster magnetorheological variable gap hydrodynamic pressure polishing based on the Preston equation. Figure 28 shows the comparison of the surface morphology between the conventional cluster MRF and cluster magnetorheological variable gap hydrodynamic pressure flattening. In the latest research, an ultrasmooth surface with a surface roughness of Ra 0.45 nm was obtained, and the material removal rate reached 3.28 nm/min.Figure 28
Surface morphology of sapphire wafer processed by different methods [155]. (a) Conventional cluster magnetorheological finishing. (b) Cluster magnetorheological variable gap dynamic pressure flattening.
(a)(b)(2) Belt-MRF. It is found that the material removal rate is obviously insufficient when machining large-diameter optical parts by MRF technology. In 2014, Ren et al. [157, 158] proposed Belt-MRF for the first time and manufactured the prototype with the structure diagram, as shown in Figure 29(a). Through simulations and tests, it is found that Belt-MRF polishing can significantly improve the material removal rate, which provides a new idea for the processing of large-aperture optical parts. Figure 29(b) shows the removal function comparison between the Belt-MRF and the existing wheel-type MRF. Since the shape of the material removal function of the Belt-MRF is long and the unstable belt drive system has severe effects on the material removal rate and surface accuracy of the Belt-MRF, it is of great significance to study the distribution of the removal function of the Belt-MRF and the stable operation of the belt drive system. Based on Ren’s research, Wang et al. [159] proposed the theory of virtual ribbon bulge and the transmission mode of a synchronous belt with an air-floating layer to realize the stable operation and high-precision transmission of the system.Figure 29
(a) Belt-MRF principle; (b) the removal function comparison between belt-MRF and the existing wheel-type MRF [157, 158].
(a)(b)(3) Ultrasonic-Magnetorheological Compound Finishing. In 2007, Wang et al. [160] proposed a kind of ultrasonic-magnetorheological compound finishing technology and carried out the experiment in detail (Figure 30), which laid the foundation for further research on this technology. Hu [161] used ultrasonic-magnetorheological compound finishing to study the polishing process of ZrO2, which opened up a new idea for the development of MRF technology, Meanwhile, the processing method of combining magnetorheological and ultrasonic vibration also brings a new challenge to the research of magnetorheological compound processing technology. In the ultrasonic-magnetorheological compound finishing, although the material removal efficiency has been improved, the surface roughness has not changed much, so it is necessary to explore the technology further to improve the surface quality.Figure 30
Ultrasonic-magnetorheological compound finishing [160].Magnetorheological polishing is a combination of fluid mechanics, electromagnetism, rheology, chemistry, and other disciplines. It is an expansion of traditional machining and is of great significance to the development of modern manufacturing technology. With the development of precision and ultraprecision machining technology, there are still some problems to be further studied, such as establishing a real-time material removal model based on online measurement feedback and the preparation technology of MRF fluids with excellent cutting characteristics. From the perspective of future development, it will be a meaningful research direction to explore a composite magnetorheological polishing technology that can not only improve the material removal efficiency but also improve the surface quality and has a wide range of workpiece processing adaptability.


## 4.2. Chemical Mechanical Planarization/Polishing

In 1965, reference [162] first proposed chemical mechanical planarization (CMP) technology, which uses the principle of soft grinding to realize the high-quality polishing of hard materials [163]. In 1983, IBM company began developing CMP technology and introduced CMP technology into the integrated circuit manufacturing industry. It is first used for the planarization of the intermetallic insulating medium (IMD) layer in the post-treatment process and then for the planarization of shallow trench isolation (STI) and copper (Cu). The entire CMP process can be completed in just 30 seconds. In 1988, IBM applied CMP technology to the manufacture of 4 Mb DRAM. In 1991, IBM successfully applied CMP technology to the production of 64 Mb DRAM to meet the global planarization requirement with feature sizes below 0.35 μm. CMP is the only surface finishing technology that can effectively provide global planarization, which plays an important role in the ultraprecision surface finishing of integrated circuits such as semiconductor chips, computer hard disk, etc. Subsequently, many universities and companies began to research CMP technology [164–168].


### 4.2.1. Research on Material Removal Model

The principle of CMP can be simplified as shown in Figure31. In the process of machining, there is a certain pressure on the workpiece surface that performs mechanical grinding and chemical etching on the workpiece surface. The material removal mechanism in the CMP process is very complex and involves chemistry, fluid mechanics, tribology, etc. At present, there are three main modeling methods for CMP research.Figure 31
Chemical mechanical planarization principle.The first is the phenomenological model based on the results of the polishing process, that is, the pure mechanical action model represented by the Preston equation. This model analyzes the material removal process from the perspective of mechanical removal of abrasive particles and idealizes the polishing process, so it does not fully reveal the wear mechanism.The second is the mechanical-fluid film model. In the polishing process, in addition to the mechanical force, the hydrodynamic pressure produced by the fluid film also affects the distribution of the removal stress and the material removal rate [169]. Based on contact mechanics and hydrodynamics theory, McGrath et al. [170] proposed a material removal model based on lubrication and wear, and Kim et al. [171] perfected and enriched this theory. The hydrodynamic pressure distributions on the workpiece surface under different load pressures, flow rates, and slurry viscosities were studied experimentally, and a relatively complete mechanical-fluid film interaction model was established.The third model is the mechanical-chemical interaction model. The chemical composition and pH value of the polishing fluid are the main factors that affect the chemical interaction of CMP, and there is no effective mathematical model to analyze the material removal rate quantitatively. Zhao et al. [172] argue that chemical reactions turn the strong bonds between atoms/molecules on a material’s machined surface into weak bonds to remove the material at the atomic level. Based on elastic-plastic contact theory, chemical dynamics, and molecular dynamics, the material removal rate equation was built. The model reveals some characteristics of the CMP process, that is, the material removal rate is related to the concentration of abrasive in the polishing fluid and greatly affected by the applied load, and it is most affected by the surface hardness and abrasive particle size of the workpiece. However, the model’s accuracy is not high since the actual contact area and the molecular bond energy are difficult to accurately determine. In follow-up studies, most researchers focus on the relationship between the chemical composition of the polishing fluid and the polishing process [173, 174]. Different from other polishing technologies, CMP technology is developed from engineering practice, and its invention, development, and application are accomplished in industry rather than academia, so systematic research, especially theoretical research, needs to be further improved.


### 4.2.2. Process Research

Since IBM developed CMP planarization technology in the 1980s, the process research on CMP initially focused on the field of silicon wafers. The improvement of the CMP process by researchers has dramatically improved the flatness and surface quality of parts. It has undergone great development in mechanism research and production applications and is widely used in MEMS, integrated circuits, and other fields [175–177]. CMP has been widely used in the finishing of optical components, such as sapphire crystals and lithium niobate crystals, and has achieved many research results.Sapphire crystal has the characteristics of high hardness, wear resistance, corrosion resistance, and high transmittance and has good optical, chemical, and mechanical properties. Therefore, sapphire crystal is often used as window materials for satellite space technology, military infrared devices, and high-intensity lasers, and it is also used in large-scale integrated circuits and some superconducting nanostructure films. Practical applications require surface roughnessRa < 0.3 nm [178, 179]. Wang et al. [180] studied the CMP process parameters of sapphire substrates and established a perfect CMP model, which lays a foundation for the following research on the material removal model of sapphire. Zhang et al. [181] used silicon oxide as abrasives to polish the sapphire substrate and improved the material removal efficiency by controlling the temperature, pH value, abrasive particle size, and concentration. To further enhance the polishing quality and material removal rate and perfect the flattening process of sapphire surfaces, Li [182] studied the regularity of material removal and surface roughness of sapphire substrate by orthogonal test and then adjusted the parameters. The alkaline polishing fluid for sapphire substrate was prepared by a single factor test. The material removal rate was 26 nm/min, and the surface roughness was better than Ra 1 nm. Vovk et al. [183] studied the chemical mechanical polishing of sapphire by silica colloid and proposed the reaction mechanism between Al2O3 and SiO2. The research results show that sapphire samples with different crystallographic orientations have anisotropic material removal rates. This anisotropy can be explained by the difference in the formation rate of intermediate products of chemical reactions between aluminum and silicon oxides on different planes. Hu [184] studied the high-efficiency and low damage processing of sapphire based on previous work, built a double-sided CMP test platform, analyzed the subsurface damage mechanism during sapphire processing, and established a prediction model of polishing subsurface damage depth. The results show that the subsurface damage depth increases with the increase of polishing pressure and polishing pad speed and decreases with the extension of polishing time, and the impact of polishing time is the greatest. Shi et al. [185] successfully designed an in-situ study of CMP behaviors on sapphire (0001) by simulating the chemical product removal process using AFM-tapping mode for the first time, which provides a new method for studying CMP behavior on different materials and fills the gap in knowledge of CMP’s basic mechanism. Figure 32 shows CMP and atomic force microscopy (AFM)-tapping mode principles.Figure 32
CMP and atomic force microscopy (AFM)-tapping mode principles diagram [185].Although CMP technology is one of the most effective processing methods for optical crystals to have an ultrasmooth surface, the operation is relatively simple, and the cost is relatively low in the process of obtaining the ultrasmooth surface, the current theoretical development is still imperfect, and the research on the microtheory of material removal has not formed a unified theory. The effect of the coupling between the factors on the performance of each component of the polishing system is not clear. Therefore, in-depth study of the fluid dynamics in the CMP process, analysis of the influence of abrasive particle movement trajectories on polishing quality, explanation of the removal mechanism of surface materials from a microscopic point of view (atomic and molecular interaction), and establishing the contact model between the polishing pad, abrasive particles, and the surface of the workpiece are all topics that need to be further explored in the future.


## 4.2.1. Research on Material Removal Model

The principle of CMP can be simplified as shown in Figure31. In the process of machining, there is a certain pressure on the workpiece surface that performs mechanical grinding and chemical etching on the workpiece surface. The material removal mechanism in the CMP process is very complex and involves chemistry, fluid mechanics, tribology, etc. At present, there are three main modeling methods for CMP research.Figure 31
Chemical mechanical planarization principle.The first is the phenomenological model based on the results of the polishing process, that is, the pure mechanical action model represented by the Preston equation. This model analyzes the material removal process from the perspective of mechanical removal of abrasive particles and idealizes the polishing process, so it does not fully reveal the wear mechanism.The second is the mechanical-fluid film model. In the polishing process, in addition to the mechanical force, the hydrodynamic pressure produced by the fluid film also affects the distribution of the removal stress and the material removal rate [169]. Based on contact mechanics and hydrodynamics theory, McGrath et al. [170] proposed a material removal model based on lubrication and wear, and Kim et al. [171] perfected and enriched this theory. The hydrodynamic pressure distributions on the workpiece surface under different load pressures, flow rates, and slurry viscosities were studied experimentally, and a relatively complete mechanical-fluid film interaction model was established.The third model is the mechanical-chemical interaction model. The chemical composition and pH value of the polishing fluid are the main factors that affect the chemical interaction of CMP, and there is no effective mathematical model to analyze the material removal rate quantitatively. Zhao et al. [172] argue that chemical reactions turn the strong bonds between atoms/molecules on a material’s machined surface into weak bonds to remove the material at the atomic level. Based on elastic-plastic contact theory, chemical dynamics, and molecular dynamics, the material removal rate equation was built. The model reveals some characteristics of the CMP process, that is, the material removal rate is related to the concentration of abrasive in the polishing fluid and greatly affected by the applied load, and it is most affected by the surface hardness and abrasive particle size of the workpiece. However, the model’s accuracy is not high since the actual contact area and the molecular bond energy are difficult to accurately determine. In follow-up studies, most researchers focus on the relationship between the chemical composition of the polishing fluid and the polishing process [173, 174]. Different from other polishing technologies, CMP technology is developed from engineering practice, and its invention, development, and application are accomplished in industry rather than academia, so systematic research, especially theoretical research, needs to be further improved.


## 4.2.2. Process Research

Since IBM developed CMP planarization technology in the 1980s, the process research on CMP initially focused on the field of silicon wafers. The improvement of the CMP process by researchers has dramatically improved the flatness and surface quality of parts. It has undergone great development in mechanism research and production applications and is widely used in MEMS, integrated circuits, and other fields [175–177]. CMP has been widely used in the finishing of optical components, such as sapphire crystals and lithium niobate crystals, and has achieved many research results.Sapphire crystal has the characteristics of high hardness, wear resistance, corrosion resistance, and high transmittance and has good optical, chemical, and mechanical properties. Therefore, sapphire crystal is often used as window materials for satellite space technology, military infrared devices, and high-intensity lasers, and it is also used in large-scale integrated circuits and some superconducting nanostructure films. Practical applications require surface roughnessRa < 0.3 nm [178, 179]. Wang et al. [180] studied the CMP process parameters of sapphire substrates and established a perfect CMP model, which lays a foundation for the following research on the material removal model of sapphire. Zhang et al. [181] used silicon oxide as abrasives to polish the sapphire substrate and improved the material removal efficiency by controlling the temperature, pH value, abrasive particle size, and concentration. To further enhance the polishing quality and material removal rate and perfect the flattening process of sapphire surfaces, Li [182] studied the regularity of material removal and surface roughness of sapphire substrate by orthogonal test and then adjusted the parameters. The alkaline polishing fluid for sapphire substrate was prepared by a single factor test. The material removal rate was 26 nm/min, and the surface roughness was better than Ra 1 nm. Vovk et al. [183] studied the chemical mechanical polishing of sapphire by silica colloid and proposed the reaction mechanism between Al2O3 and SiO2. The research results show that sapphire samples with different crystallographic orientations have anisotropic material removal rates. This anisotropy can be explained by the difference in the formation rate of intermediate products of chemical reactions between aluminum and silicon oxides on different planes. Hu [184] studied the high-efficiency and low damage processing of sapphire based on previous work, built a double-sided CMP test platform, analyzed the subsurface damage mechanism during sapphire processing, and established a prediction model of polishing subsurface damage depth. The results show that the subsurface damage depth increases with the increase of polishing pressure and polishing pad speed and decreases with the extension of polishing time, and the impact of polishing time is the greatest. Shi et al. [185] successfully designed an in-situ study of CMP behaviors on sapphire (0001) by simulating the chemical product removal process using AFM-tapping mode for the first time, which provides a new method for studying CMP behavior on different materials and fills the gap in knowledge of CMP’s basic mechanism. Figure 32 shows CMP and atomic force microscopy (AFM)-tapping mode principles.Figure 32
CMP and atomic force microscopy (AFM)-tapping mode principles diagram [185].Although CMP technology is one of the most effective processing methods for optical crystals to have an ultrasmooth surface, the operation is relatively simple, and the cost is relatively low in the process of obtaining the ultrasmooth surface, the current theoretical development is still imperfect, and the research on the microtheory of material removal has not formed a unified theory. The effect of the coupling between the factors on the performance of each component of the polishing system is not clear. Therefore, in-depth study of the fluid dynamics in the CMP process, analysis of the influence of abrasive particle movement trajectories on polishing quality, explanation of the removal mechanism of surface materials from a microscopic point of view (atomic and molecular interaction), and establishing the contact model between the polishing pad, abrasive particles, and the surface of the workpiece are all topics that need to be further explored in the future.


## 5. Conclusion

The development and application of modern optical systems put forward higher requirements for the manufacturing of optical parts. With the continuous improvement of equipment performance, the requirements of these optical systems for the surface accuracy and surface quality of optical parts are almost close to the physical limit, which poses a higher challenge to the optical manufacturing technology, making it become the development frontier of the nanomanufacturing technology. For example, in the field of lithography objective lenses, to improve the lithography resolution, in addition to the reduction of the exposure wavelength, the numerical apertureNA of the optical system is also increasing [186]. From the perspective of optical manufacturing, the reduction of exposure wavelength and the increase of numerical aperture will greatly increase the difficulty of optical manufacturing. From the standpoint of processing, the removal resolution of surface materials must reach the atomic and molecular level, and its design and manufacturing technology have entered the field of nanomanufacturing, reaching the limit of the top-down processing principle, which poses a challenge to the manufacturing of ultrahigh precision optical parts for optical manufacturing. Similarly, in high-tech fields such as space large aperture optical manufacturing and strong light optical manufacturing, high-precision and low damage processing challenges are put forward for optical parts. It is necessary to innovate new principles, new processing methods, new materials, and new technologies of optical micromachining. From the perspective of development prospects, the key technologies of optical surface nanofabrication include the following aspects.


### 5.1. Stable and Controllable Technology for Nanoscale Material Removal

In the establishment of the material removal model, most researchers hope that a theoretical model can explain the material removal mechanism of the polishing process, but most of the material removal mechanisms of the polishing process are not single as the result of the joint action of multiple factors. Different material removal mechanisms may play a leading role in different processing stages. Therefore, the removal model considering the combined effect of various factors still needs to be further explored. For some high-precision optical parts, the method with controllable removal of atoms and molecules can achieve the nano or even subnano precision. From the perspective of manufacturing, the material removal method should not only have the atomic and molecular level controllable resolution to achieve the machining accuracy but also have high removal efficiency to achieve manufacturing goals.


### 5.2. Controllable Compensation Modification Technology for Complex Freeform Surface

The convolution of the removal function and dwell time is usually used in the material removal of computer-controlled modification of the optical surface. In practical applications, due to the constraints of surface geometry and processing technology, the surface shape function and the removal function in the polishing process will produce corresponding nonlinear changes in the two-dimensional convolution equation, which will be difficult to meet the requirements of nano or subnano surface. Therefore, establishing a controllable and flexible dynamic removal function, constructing a material removal model that can truly reflect the machining process, improving the calculation accuracy of the dwell time, and realizing the controllable compensation modification of complex freeform surface should be the directions to be explored in future [187].


### 5.3. Controllable Flexible Motion Design considering Machine Tool Dynamics

Optical parts with complex freeform surfaces cannot be represented by elementary analytic surfaces, and the complexity of their geometric characteristics and the motion of machine tools make the tool path planning and machining accuracy difficult to guarantee. Therefore, it is essential to optimize the tool path planning algorithm and improve the machining efficiency and quality for practical engineering applications. For example, in time-related processes, such as bonnet polishing and jet polishing, surface quality and accurate machining depend heavily on the careful planning of tool feeds. The traditional NC feed speed command is usually generated by the dwell time diagram obtained by deconvolution or numerical iteration. These methods are time consuming and numerically unstable, and most of them do not consider the dynamic characteristics of machine tools, so machining error defects often occur. In addition, the optimization standards of tool paths are different. Generally, it can be considered from the processing time, processing accuracy, material removal rate, residual height, path continuity, tool axis swing amplitude, etc. Most of the existing tool path optimization algorithms are single-objective optimization, and there are few algorithms to weigh and consider each optimization objective. Some new algorithms are difficult to implement and cannot be applied to engineering practice. Therefore, in the tool path planning of machining optical parts with complex freeform surfaces, the analytical algorithm not only considers the kinematic and dynamic characteristics of machine tools but also realizes multiobjective optimization, which is still a subject worthy of further research.


## 5.1. Stable and Controllable Technology for Nanoscale Material Removal

In the establishment of the material removal model, most researchers hope that a theoretical model can explain the material removal mechanism of the polishing process, but most of the material removal mechanisms of the polishing process are not single as the result of the joint action of multiple factors. Different material removal mechanisms may play a leading role in different processing stages. Therefore, the removal model considering the combined effect of various factors still needs to be further explored. For some high-precision optical parts, the method with controllable removal of atoms and molecules can achieve the nano or even subnano precision. From the perspective of manufacturing, the material removal method should not only have the atomic and molecular level controllable resolution to achieve the machining accuracy but also have high removal efficiency to achieve manufacturing goals.


## 5.2. Controllable Compensation Modification Technology for Complex Freeform Surface

The convolution of the removal function and dwell time is usually used in the material removal of computer-controlled modification of the optical surface. In practical applications, due to the constraints of surface geometry and processing technology, the surface shape function and the removal function in the polishing process will produce corresponding nonlinear changes in the two-dimensional convolution equation, which will be difficult to meet the requirements of nano or subnano surface. Therefore, establishing a controllable and flexible dynamic removal function, constructing a material removal model that can truly reflect the machining process, improving the calculation accuracy of the dwell time, and realizing the controllable compensation modification of complex freeform surface should be the directions to be explored in future [187].


## 5.3. Controllable Flexible Motion Design considering Machine Tool Dynamics

Optical parts with complex freeform surfaces cannot be represented by elementary analytic surfaces, and the complexity of their geometric characteristics and the motion of machine tools make the tool path planning and machining accuracy difficult to guarantee. Therefore, it is essential to optimize the tool path planning algorithm and improve the machining efficiency and quality for practical engineering applications. For example, in time-related processes, such as bonnet polishing and jet polishing, surface quality and accurate machining depend heavily on the careful planning of tool feeds. The traditional NC feed speed command is usually generated by the dwell time diagram obtained by deconvolution or numerical iteration. These methods are time consuming and numerically unstable, and most of them do not consider the dynamic characteristics of machine tools, so machining error defects often occur. In addition, the optimization standards of tool paths are different. Generally, it can be considered from the processing time, processing accuracy, material removal rate, residual height, path continuity, tool axis swing amplitude, etc. Most of the existing tool path optimization algorithms are single-objective optimization, and there are few algorithms to weigh and consider each optimization objective. Some new algorithms are difficult to implement and cannot be applied to engineering practice. Therefore, in the tool path planning of machining optical parts with complex freeform surfaces, the analytical algorithm not only considers the kinematic and dynamic characteristics of machine tools but also realizes multiobjective optimization, which is still a subject worthy of further research.



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*Source: 8723269-2022-05-12.xml*