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Abstract
Benefiting from high specific stiffness and high reflectance, aluminum optics with a complex surface profile are widely used in aerospace optical systems which have strict requirements for volume of the systems. Contact figuring polishing process provides highly deterministic technology for the fabrication of high precision aluminum optics. However, due to the high chemical activity of aluminum, the inevitable contamination layer will generate on the surface and bring difficulties for the subsequent processes, which greatly limit the fabrication precision. Ion beam figuring (IBF) is an effectively technology that can remove the contamination layer and improve surface quality. But, the surface profile may deteriorate during IBF. In this study, through experimental method, the nonuniformity of the contamination layer is found to be the inducer for deterioration and deviation of surface profile during IBF. The mapping between the characteristics of contamination layer and dwell time of contact polishing is studied. The thickness of the contamination layer will firstly increase with dwell time and stabilize to 120 nm when the dwell time exceeds a specific value. The variation of the IBF removal function with removal depth is also revealed through experimental and theoretical methods. Due to the dynamic variation of the composition in the contamination layer during IBF, the removal function increases with the removal depth and stabilizes when the depth exceeds 60 nm (the contamination layer is fully removed). Consequently, we propose two processing strategies to improve the aluminum optics fabrication process. Comparative experiments are performed on two off-axis aspherical surfaces. The results indicate that the surface profile can be stably maintained and improved during IBF processing based on the proposed strategies. Our research will significantly improve the fabrication precision of aluminum optics and promote the application of aluminum optics to the visible and even ultraviolet band.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Aluminum optics with complex surface profile have a broad prospect in the applications of aerospace optical systems [1–4]. The application light band of aluminum optics is moving from mid-infrared and far-infrared to visible spectrum, which put forward higher requirements on machining accuracy [5,6]. Single point diamond turning (SPDT) is widely used in ultra-precision fabrication of aluminum optics because of the advantages of high efficiency and ability to manufacture complex surface [7–9]. Belonging to maternal processing, SPDT lathes are unable to fabricate aluminum optics with precision higher than machine tools. Nowadays, the machining precision of SPDT lathes is improving but still unable to acquire aluminum optics for visible light applications. Thus, more subsequent processes are needed to improve the surface profile. Contact figuring polishing (FP) processes such as Magnetorheological finishing (MRF) or bonnet polishing (BP) are highly stable and commonly used method for aluminum optics manufacture. FP breaks through the restriction of maternal processing and can significantly improve fabrication precision [10,11]. Assisted by high performance CNC system, FP can acquire complex surface profile with high precision. Remarkable works have been done to improve the fabrication accuracy, such as compensation of removal function [12,13], optimization of tool path [14–16], and improvement of tools [17,18]. By optimizing the process, freeform aluminum mirrors for visible light applications, which possess the form accuracy of 0.025μm RMS, have been fabricated. However, because of high chemical activity of aluminum, an inherent and inevitable contamination layer will generate, which severely deteriorates surface quality and reduces reflectivity [19,20].
Smoothing polishing (SP) is usually used as subsequent procedure after FP and the final procedure for aluminum optics manufacture [21,22]. SP can effectively remove contamination layer and improve surface quality. But, the removal of contamination layer by SP is a time-costing task [23]. During long-time SP for complex aluminum surface, problems such as misfit, uneven pressure distribution occur easily, which will cause the misconvergence of surface profile [24,25]. Therefore, the final precision will not exceed the machining precision of FP. In order to meet the fabrication requirement, the most used processing strategy is to improve the precision of the previous process (FP) to provide machining allowance for SP. Thus, the machining precision and efficiency are difficult to be further improved. Many significant works are conducted on optimization of SP process, such as optimization of work parameters [26,27], improvement of pad tools [28,29], etc. However, most researches only focus on single issues which can’t effectively improve the polishing process of multi-factor coupling. Thus, some researchers look for other methods to remove contamination layer. Zhao et al. have effectively removed contamination layer by using femtosecond laser [30]. Though achieving good results, this method is too expensive to be widely promoted. Also, previous works only try to maintain the machining precision of FP, which cannot further improve the precision of the aluminum optics.
Recently, electron and ion beam treatment are considered highly promising for surface modification, surface cleaning [31–33]. Ion beam figuring (IBF) is one of the advanced surface treatment methods, which shows efficient surface cleaning ability [34–36]. According to former works done by our research group, Ar+ ion beam bombardment can effectively improve surface quality and remove contamination layer [20]. The impurities will dynamically segregate to the surface and be preferentially sputtered from the surface. On the premise of removing contamination layer, IBF can be used as a subsequent figuring process after FP to further improve the surface profile. With highest machining precision, IBF will significantly improve the processing accuracy of aluminum optics [37–39]. However, during IBF, obvious deviation and misconvergence of surface profile are observed. Unlike homogeneous materials such as fused silica, the composition and characteristics of contamination layer varies dynamically during IBF, which will greatly affect the sputtering yield and machining precision. However, there is no relevant literature on such issues.
In this work, IBF is introduced in aluminum optics fabrication process to remove contamination layer and further improve precision of aluminum optics. IBF experiments are conducted on section 2 to address the surface profile variation process during IBF. In section 3, the characteristics of contamination layer and variation of removal function are firstly revealed through experimental and theoretical methods. In section 4, the processing strategy of IBF is optimized based on the previous study to acquire further convergence of surface profile. Finally, comparison experiments are conducted to verify the analysis in section 5. The results of this study will be beneficial for application of IBF in the field of aluminum optics manufacture and significantly improve the machining precision of aluminum optics.
2. IBF experiment
2.1. Experiment details
IBF experiments are conducted on two aluminums 6061 optic surfaces, which are off-axis aspherical surface with rectangular shape. The four corners of the surfaces are rounded. The samples are pre-processed by SPDT (Precitech Nanoform 350) and further polished by FP to improve surface shape accuracy. After FP, the reflectivity and surface quality are reduced. All IBF experiments are conducted on our self-developed IBF system (KDIBF650L-VT) under the bombardment of Ar+ ions at normal incidence with the work pressure of 2.5×10-3 Pa. KDIBF650L-VT is a five-axis IBF system, which can realize the processing of complex surface. Stable ion beam provides stable material removal. The parameters are shown in Table 1.
Table 1. Parameters of IBF process
A uniform raster scan is conducted as tool path to maintain surface profile. The scan speed is chosen to be 800 mm/min. For 1#, one processing cycle costs nearly 2 hours. For 2#, one processing cycle costs nearly 5hours. A 4D interferometer (PhaseCamTM 4020) with a compensator (CGH) is applied to measure the surface residual error. CGH can generate the ideal wave front required by any aspheric surface to be measured to compensate its phase and can accurately adjust the relative position to align to the measured surface.
2.2. Experiment results
First, a sample of aluminum material, which is pre-processed by SPDT and further polished by FP with uniform raster scan speed of 100 mm/min, is used to acquire IBF removal function for contamination layer. The IBF parameter in Table 1 is used. The volume removal rate is 12.3×10−3mm3/min. Three IBF iterations are costed for each sample. The contamination layer is fully removed and surface restores to its brightness state. Based on the acquired removal function and CCOS principle, the removal depth for 3 iterations is around 60 nm and the surface profile will remain unchanged. Figure 1 shows the IBF results for 1# and 2#. The initial FP surface profile of 1# is 392.285 nm PV and 42.185 nm RMS. After IBF, it deteriorates to 705.189 nm PV and 76.692nmRMS, which is inconsistent with prediction. Meanwhile, the surface profile before and after IBF shows obvious deviation, which means that the uniform material removal is not always guaranteed during processing. The same phenomenon is also observed on 2#. For sample 2#, the initial FP surface profile is 342.094 nm PV and 41.062 nm RMS. After IBF, it deteriorates to 938.309 nm PV and 135.037 nm RMS.
Fig. 1. Experimental results of IBF of sample 1# (a) surface profile after FP, (b) surface profile after IBF, and sample 2# (c) surface profile after FP, (d) surface profile after IBF.
The color of aluminum surface gets grey after FP, which reduces the surface reflectivity and surface quality. In actual FP process, the dwell time across various areas are different, which causes that the degree of graying varies across different areas of the surface. Surface color is positively correlated with dwell time. The subtraction between the surface profiles before and after process can reflect the dwell time distribution as well as the processing volume. In Fig. 2, the processing volume of FP and IBF of each sample is presented. As shown in Fig. 2(a)(b), for 1#, the removal volume distribution of FP is roughly opposite to that of IBF. The same phenomenon is also observed on sample 2#. The experimental results indicate that the material on the area with longer FP dwell time (with darker color) is more difficult to be removed by IBF process.
IBF can effectively remove the contamination layer and reduce surface hardness according to our previous study, which can highly improve the machining efficiency and accuracy of follow-up process. The experimental results indicate that due to the non-uniform state of contamination layer after FP, there are restrictions for IBF process to maintain and improve surface profile accuracy. The variation of contamination layer state will cause the great change of removal efficiency of IBF.
3. Theoretical analysis
3.1. Thickness of the contamination layer
Machining results of IBF are directly affected by the state of contamination layer. Thus, the characteristics of contamination layer are needed to be study firstly. Six samples with size of ϕ25×8 mm are fabricated by FP with different processing parameters. The peak removal rate and volume removal rate of FP removal function are 2.796μm/min and 0.059mm3/min, respectively. Raster uniform scan is adopted as tool path for all samples. The processing parameters of FP are presented in Table 2. The difference of dwell time is represented by different scan velocities. The removal depth of each sample can be calculated, which is also presented in Table 2.
Table 2. Parameters of FP process
Figure 3 shows the processing results of FP experiments. The surface state varies greatly with different FP processing parameters. The degree of graying increases with FP removal depth. However, for sample #4, #5 and #6, the surface states are quite similar, which indicates that the surface state may stabilize when the removal depth exceeds a specific value. In order to verify the assumption, the Depth-Sensing Indentation (DSI) (CSM UNHT + MCT) tests are conducted to measure the thickness of the contamination layer. By conducting cyclic loading experiments on samples, the curve of hardness with pressing depth can be obtained. The abrasives will embed into the substrate during FP, forming contamination layer. Thus, the hardness of contamination layer is significantly higher than the substrate and highly related to the concentration of impurities according to the Orowan equation [40]. Therefore, the thickness of the contamination layer can be determined by obtaining the abrupt change of hardness in the depth direction. Figure 4 shows the DSI test results for each sample. With the removal depth of 29.5 nm, the hardness changes abruptly at the depth of around 36 nm, which means the thickness of contamination layer is around 36 nm. The thickness of contamination layer increases significantly with the removal depth of FP. However, when the removal depth exceeds 295 nm, the thickness of contamination layer remains unchanged, which is quite consist with the results in Fig. 3. The thickness of stabilized contamination layer is around 120 nm. During FP, the abrasives will remove the material as well as embed into the substrate. With processing time increasing, an equilibrium will be achieved in material removal and embedding processes. Thus, the thickness of contamination layer will stabilize.
Fig. 3. Experiment results of FP with different processing parameters: upper row, #1 #2 #3 (left to right); lower row, #4 #5 #6 (left to right).
3.2. Variation of the removal function
Unlike homogeneous material, during the IBF, the thickness, hardness and color of contamination layer varies, which indicates that the composition of contamination layer varies greatly. Based on Bradley and Harper theory, the composition of materials greatly affects the removal efficiency [41–43]. In order to maintain high precision machining process, the variation of removal function during IBF needs to be studied. In order to show the change of removal function caused by different concentration of impurities as much as possible, the contamination layer is generated by FP with uniform raster scan speed of 100 mm/min. As a result, a stabilized contamination layer with thickness of 120 nm is acquired. The work parameters of IBF are shown in Table 3. Seven spots with removal depth ranging from 22 nm to 63 nm are sputtered on the contamination layer.
Table 3. Parameters of IBF process
Figure 5 shows the removal function corresponding to specific removal depth. The removal functions are calculated based on the processing time and corresponding material removal. The height of Gaussian removal function increases with the removal depth. In Fig. 6, the variation of peak removal rate (PRR) and volume removal rate (VRR) with removal depth are demonstrated. The variation forms of the two removal rates are consistent. Firstly, the removal rate increases rapidly with removal depth. When the removal depth exceeds 50 nm, the increasing rate is moderated. The variations of PRR and VRR are 3% and 2%, respectively. When the removal depth reaches 63 nm, the total variations of PRR and VRR are 32% and 49%, which cause great deviation between actual material removal and the prediction.
Fig. 5. Removal function of different removal depth of (a) 22 nm, (b) 27 nm, (c) 35 nm, (d) 42 nm, (e) 49 nm, (f) 55 nm, (g) 63 nm.
Fig. 6. Corresponding removal rate variation with different removal depth, (a) Peak removal rate, (b) Volume removal rate.
When the removal depth is shallow, the sputtering of impurities causes great changes in surface composition which will greatly affect the removal rate. Based on our previous research, the impurities dynamically migrate to the surface and are sputtered preferentially. Even the removal depth doesn’t exceed the depth of contamination layer, the impurities can be fully eliminated. Sequentially, the composition of materials remains unchanged and the material removal per unit time becomes stable. With a specific IBF process parameters, define that contamination layer will be fully removed by depth of dc with process time of tc. When the removal depth exceeding dc, the PRR can be expressed as:
where t is the sputtering time, and PRRAl is the peak removal rate of substrate. According to the experimental results, the PRRAl is significantly larger than that of contamination layer. Thus, with the increase of t (sputtering depth), the increase of PRR slows down and finally reaches a steady value, which explains the moderated increasing rate in Fig. 6. The apparent turning point in Fig. 6 represents the fully removal of the contamination layer.In order to verify our analysis, another spot sputtering experiment is repeated on the same samples. Eight spots are sputtered with the removal depth ranging from 50nm-190 nm, which is higher than the depth required to completely remove the contamination layer. Figure 7 shows the removal function corresponding to specific removal depth and Fig. 8 shows the variations of PRR and VRR. There is a slight increase as the removal depth increasing. The total variations of PRR and VRR are 7% and 6%, respectively, which is obviously lower than the variation when the contamination layer is not fully removed. The experimental results match well with theoretical prediction.
Fig. 7. Removal function of different removal depth of (a) 50 nm, (b) 75 nm, (c) 100 nm, (d) 125 nm, (e) 150 nm, (f) 160 nm, (g) 175 nm, (h) 190 nm.
Fig. 8. Corresponding removal rate variation with different removal depth, (a) Peak removal rate, (b) Volume removal rate.
Summarizing from the theoretical analysis, the depth of the contamination layer increases with the dwell time. When the dwell time exceeds a specific value, the depth of the contamination layer stabilizes. In actual FP process, the non-uniform dwell time matrix will cause the non-uniform state of contamination layer. The dynamic variation of impurities during FP will cause the change of removal function. However, when the impurities are fully removed, the variation of removal function will slow down and finally the removal function will reach a steady value with the increasing of the removal depth.
4. Optimization of fabrication strategies
4.1. Introduction of FP process
The fabrication strategies of IBF need to be optimized based on the processing status of FP. The typical processing strategy of FP is shown in Fig. 9(a). Origin surface profile, known as surface residual error, is firstly measured by interferometer. The materials between target surface profile and origin surface profile are the total desire material removal [44,45],
where R(x,y) is the total desire material removal, T (x,y) is dwell time matrix, r(x,y) is the removal function. Based on the steady removal function of FP, the dwell time matrix can be calculated and used for creating NC program.The lowest point of the origin surface error exists on the target surface profile, which means that no material is removed on such point, as indicated in Fig. 9(a). Zero dwell time and infinite tool velocity occur, which is unrealizable in the actual process. Thus, a uniform extra material removal layer is added to the desire material removal to solve such problem, as shown in Fig. 9(b). Thus, the machining process can be revised as follow,
where Ractual(x,y) is the actual total material removal, Runiform(x,y) and Tuniform (x,y) are the uniform extra material removal and the dwell time matrix, respectively. The additional uniform removal layer will not cause the variation of surface profile. Therefore, the actual surface profile and desire surface profile have the identical form.Based on the analysis of the variation of removal function in section 3.2, two different IBF machining strategies for different processing target can be obtained.
4.2. Strategy for surface profile maintenance (SPM)
Though possessing the highest machining precision, IBF has relatively low machining efficiency. When the machining precision of FP satisfied the processing target, in order to improving the processing efficiency of the whole processing flow, the IBF can be used as a surface modified method to remove the contamination layer while maintaining the surface profile. For surface profile maintaining, the state of contamination layer is required to be homogeneous. Based on the above theoretical analysis in section 3.1, the contamination layer will stabilize when the dwell time exceeds a specific value. By adjusting the uniform extra material removal Runiform(x,y) >295 nm, dwell time at any point on the entire surface can exceed such value. Thus, the homogeneous contamination layer can be generated, as shown in Fig. 10(a). Then, a uniform raster scan with speed of Vscan is conducted as tool path of IBF, seeing Fig. 10(b). The surface profile can be maintained because of the uniformity of contamination layer.
In previous aluminum optics processing strategy, the subsequent technique, such as smoothing polishing, usually deteriorates the surface profile. Comparing with previous strategies, the new strategy can reach the fullest potentials for FP and further improve the final machining precision and efficiency.
4.3. Strategy for surface profile improvement (SPI)
In order to pursue higher surface profile convergence ratio and machining efficiency, the actual machining process requires fewer iterations. In this case, the extra material removal is relatively small. Thus, the thickness of contamination layer varies greatly across the whole surface. According to the theoretical analysis in section 3.1, the thickness of the contamination layer increases with the dwell time. The residual surface error after FP has the identical form as contamination layer distribution, as shown in Fig. 11(a). Then, IBF can further improve the surface profile precision. The effects of IBF process are shown in two aspects: (a) more material will be removed from the high point of the surface residual error, which improves the final surface profile precision, (b) the high point of the surface residual error also has a thicker contamination layer. More material will be removed from the thicker contamination layer, which homogenizes the surface state.
The IBF process can be expressed by Eq. (2). However, considering the particularity of the process, there are several restrictions for IBF. Firstly, the removal function varies across the whole process, which is related to the processing time of FP. To prevent the misconvergence of the surface profile, the removal function of critical point is chosen, at which the FP processing time is the shortest (the contamination layer is thinnest). Secondly, the uniform extra material removal layer also needs to be added and optimized according to the thickness of contamination layer in critical point to meet the dynamic performance requirements of machine tools and the target for effective removal of the contamination layer. Thus, the IBF process can be expressed as follow:
where Rcp(x,y) is the uniform extra removal layer and rcp(x,y) is the removal function of critical point. For simplicity, the thickness of contamination layer in critical point is chosen to be Rcp(x,y), which can be determined by dwell time of previous FP.5. Experimental verification
5.1. Technique description
During the first processing stage, the FP is employed to rapidly correct low-frequency errors and SPDT marks with high convergence and high materials removal rate. Subsequently, IBF is used to eliminate the contamination layers and maintain or improve the surface profile. The processing parameters adopted in the IBF experiment are beam energy Eion=700 eV, beam current J=15 mA, beam diameter d=30 mm. For two fabrication strategies, the restrictions for specific processing technic in the experiments are described in Table 4.
Table 4. Specific restrictions for processing technic of two strategies
5.2. Experiment results
To demonstrate the feasibility and the advantages of the proposed strategy, the experiments are performed on the same two off-axis aspherical surfaces. For the strategy of SPI, the surface profile processed by FP restores to 413.44 nm PV and 40.963 nm RMS, as shown in Fig. 12 (a), which is quite close to the result in Fig. 1(a). After IBF, the surface profile improves to 303.693 nm PV and 35.474 nm RMS, which verifies the feasibility of SPI. However, little local bulge can still be observed on the surface in Fig. 12(b), which doesn’t agree with the simulation results in Fig. 12(c). It indicates that there is still room for optimization of IBF restrictions. For the strategy of SPM, the surface profile firstly restores by FP to 376.034 nm PV and 40.279 nm RMS. With the uniform scan of IBF, the surface profile is maintained, as shown in Fig. 12(f). It is worth mentioning that the residual surface errors in Fig. 12(e)(f) have the similar distribution, which verifies the conformal ability of SPM.
Fig. 12. Experimental results of combined fabrication technique with strategy of SPI (a) surface profile after FP, (b) surface profile after IBF, (c) simulation results of residual error, (d) simulation results of dwell time, and SPM (e) surface profile after FP, (f) surface profile after IBF.
The proposed strategies can significantly maintain and improve the surface profile precision, which will reach the fullest potentials for FP and also extend application of IBF in the aluminum optics fabrication filed.
6. Conclusion
The contamination layer generated by FP on aluminum optics will cause severely deterioration of reflectivity and surface qualities. IBF can effectively remove the contamination layer and restore the surface qualities. But, the surface profile may deteriorate during IBF due to the nonuniformity of the contamination layer.
- (1) The properties of contamination layer are firstly studied in this research. Contamination layer will generate because of the embedment of abrasives, which will cause the increase of surface hardness. DSI results reveal that the thickness of the contamination layer increases with processing dwell time. But, when the dwell time exceeds a specific value, the contamination layer stabilizes with thickness of 120 nm.
- (2) The concentration of the impurities dynamically varies with the removal depth during IBF, which will cause the variation of the removal function. According to the experimental results, the removal function increases with the removal depth. When the removal depth doesn’t exceed the depth of contamination layer, the total variations of the peak removal rate and volume removal rate are 32% and 49%, respectively. When the impurities are fully removed, the variation of removal function slows down and finally reaches a steady value with the increasing of the removal depth.
- (3) Consequently, two fabrication strategies, SPM and SPI, are proposed to improve the aluminum optics fabrication process. The same two off-axis aspherical surfaces are taken as demonstration of the feasibility and the advantage of the fabrication strategies. With the removal of the contamination layer, one surface profile is maintained to 357.62 nm PV and 40.339 nm RMS and another is improved to 303.694 nm PV and 35.474 nm RMS.
Funding
Major Programs of the National Natural Science Foundation of China (51991371); National Natural Science Foundation of China (51835013); Postgraduate Scientific Innovation Fund of Hunan Province.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. Y. Wang, Z. Li, X. Liu, and F. Fang, “Freeform-objective Chernin multipass cell: application of a freeform surface on assembly simplification,” Appl. Opt. 56(30), 8541–8546 (2017). [CrossRef]
2. Z. Li, X. Liu, F. Fang, and X. Zhang, “Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment,” Opt. Express 26(6), 7625–7637 (2018). [CrossRef]
3. G.P.H Gubbels, B.W.H van Venrooy, A. J. Bosch, and R. Senden, “Rapidly solidified aluminum for optical applications,” Proc. of SPIE. 7018, 70183A (2008). [CrossRef]
4. J. Bauer, F. Frost, and T. Arnold, “Reactive ion beam figuring of optical aluminum surfaces,” J. Phys. D: Appl. Phys. 50(8), 085101 (2017). [CrossRef]
5. C.C. Wang, S.C. Lin, and H. Hong, “A material removal model for polishing glass-ceramic and aluminum magnesium storage disk,” Int J Mach Tool Manu. 42(8), 979–984 (2002). [CrossRef]
6. Y. Ahn, J.Y. Yoon, C.W. Baek, and Y.K. Kim, “Chemical mechanical polishing by colloidal silica-based slurry for micro-scratch reduction,” Wear 257(7-8), 785–789 (2004). [CrossRef]
7. H. Y. Wu, W. B. Lee, C. F. Cheung, S. To, and Y. P. Chen, “Computer simulation of single-point diamond turning using finite element method,” J. Mater. Process. Technol. 167(2-3), 549–554 (2005). [CrossRef]
8. Z. Zhu, S. To, W.L. Zhu, P. Huang, and X. Zhou, “Cutting forces in fast-/slow tool servo diamond turning of micro-structured surfaces,” Int J Adv Manuf Technol 136, 62–75 (2019). [CrossRef]
9. H. Gong, F. ZH. Fang, and X. T. Hu, “Accurate spiral tool path generation of ultraprecision three-axis turning for non- zero rake angle using symbolic computation,” Int. J. Adv. Manuf Technol. 58(9-12), 841–847 (2012). [CrossRef]
10. P. Dumas, D. Golini, and M. Tricard, “Improvement of figure and finish of diamond turned surfaces with magneto-rheological finishing,” Proc. SPIE. 5786, 296–304 (2005). [CrossRef]
11. H. Hu, Y. F. Dai, and X. Q. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18(22), 22973–22981 (2010). [CrossRef]
12. H. Hu, Y. F. Dai, X. Q. Peng, and J. M. Wang, “Research on reducing the edge effect in magnetorheological finishing,” Appl. Opt. 50(9), 1220–1226 (2011). [CrossRef]
13. H. Yang, Q. Zhang, Z. Zhu, W. Fan, and W. Huang, “Dynamic approximation method for removal function size in magnetorheological finishing,” Opt. Eng. 58(9), 095103 (2019). [CrossRef]
14. C. Song, Y. F. Dai, and X. Q. Peng, “Model and algorithm based on accurate realization of dwell time in magnetorheological finishing,” Appl. Opt. 49(19), 3676–3683 (2010). [CrossRef]
15. Y. F. Dai, H. Hu, X. Q. Peng, J. M. Wang, and F. Shi, “Research on error control and compensation in magnetorheological finishing,” Appl. Opt. 50(19), 3321–3329 (2011). [CrossRef]
16. M. Singh and A. K. Singh, “Magnetorheological finishing of grooved drum surface and its performance analysis in winding process,” Int. J. Adv. Manuf. Tech. 106(7-8), 2921–2937 (2020). [CrossRef]
17. F. Guan, H. Hu, S. Y. Li, Z. Y. Liu, X. Q. Peng, and F. Shi, “A novel Lap-MRF method for large aperture mirrors,” Int. J. Adv. Manuf. Tech. 95(1), 1–13 (2018). [CrossRef]
18. F. Guan, H. Hu, S. Y. Li, X. Q. Peng, and F. Shi, “Analysis of material removal rate and stability in lap-magnetorheological finishing,” Opt. Eng. 57(05), 1 (2018). [CrossRef]
19. T. Zhao, H. Hu, X. Q. Peng, C. Y. Du, C. L. Guan, and J. H. Yong, “Study on the surface crystallization mechanism and inhibition method in the CMP process of aluminum alloy mirrors,” Appl. Opt. 58(22), 6091–6097 (2019). [CrossRef]
20. C. Y. Du, Y. F. Dai, C. L. Guan, and H. Hu, “Rapid fabrication technique for aluminum optics by inducing a MRF contamination layer modification with Ar+ ion beam sputtering,” Opt. Express 29(6), 8951–8966 (2021). [CrossRef]
21. M. T. Tuell, J. H. Burge, and B. Anderson, “Aspheric optics: smoothing the ripples with semi-flexible tools,” Opt. Eng. 41(7), 1473–1474 (2002). [CrossRef]
22. D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions™ process,” Proc. SPIE. 6671, 66711H (2007). [CrossRef]
23. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortes, and C. Robledo-Sanchez, “Edge effects with the preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004). [CrossRef]
24. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef]
25. S. Urara, E. Toshiyuki, M. Teppei, O. Takuya, N. Hidenori, and F. Katsuhiro, “Stabilization of Removal Rate in Small Tool Polishing of Glass Lenses,” Int. J. Automat. Tech. 13(2), 221–229 (2019). [CrossRef]
26. X. Q. Nie, S. Y. Li, H. Hu, and Q. Li, “Control of mid-spatial frequency errors considering the pad groove feature in smoothing polishing process,” Appl. Opt. 53(28), 6332–6339 (2014). [CrossRef]
27. X. Q. Nie, S. Y. Li, F. Shi, and H. Hu, “Generalized numerical pressure distribution model for smoothing polishing of irregular mid-spatial frequency errors,” Appl. Opt. 53(6), 1020–1027 (2014). [CrossRef]
28. B. Pak, D. Lee, S. Jeong, H. Kim, and H. Jeong, “Finite Element Analysis on Dynamic Viscoelasticity of CMP Polishing Pad,” J. Korean. Soc. Precis. Eng. 36(2), 177–181 (2019). [CrossRef]
29. H. Lee and S. Lee, “Investigation of pad wear in CMP with swing-arm conditioning and uniformity of material removal,” Precis. Eng. 49, 85–91 (2017). [CrossRef]
30. T. Zhao, H. Hu, X. Q. Peng, C. L. Guan, Y. F. Dai, J. H. Yong, and Z. H. Gan, “Novel high-precision processing method for aluminum mirror assisted with femtosecond laser,” Appl. Opt. 59(26), 1–7 (2020). [CrossRef]
31. S. S. Chen, S. Y. Li, X. Q. Peng, H. Hu, and G. P. Tie, “Research of polishing process to control the iron contamination on the magnetorheological finished KDP crystal surface,” Appl. Opt. 54(6), 1478–1484 (2015). [CrossRef]
32. F. R. Li, X. H. Xie, G. P. Tie, H. Hu, and L. Zhou, “Research on temperature field of KDP crystal under ion beam cleaning,” Appl. Opt. 55(18), 4888–4894 (2016). [CrossRef]
33. Z. Yuan, Y. F. Dai, L. Zhou, and S. R. Feng, “Cleaning of iron powders embedded into the surface of KDP crystal by ion beam figuring,” J. Synth. Cryst. 42(4), 582–586 (2013).
34. Y. F. Dai, W. L. Liao, L. Zhou, S. S. Chen, and X. X. Xie, “Ion beam figuring of high-slope surfaces based on figure error compensation algorithm,” Appl. Opt. 49(34), 6630–6636 (2010). [CrossRef]
35. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17(1), 10–21 (1995). [CrossRef]
36. M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. Sect. B. 267(8-9), 1390–1393 (2009). [CrossRef]
37. T. Wang, L. Huang, Y. Zhu, M. Vescovi, and M. Idir, “Development of a Position-Velocity-Time modulated two dimensional ion beam figuring system for synchrotron X-ray mirrors fabrication,” Appl. Opt. 59(11), 3306–3314 (2020). [CrossRef]
38. A. Chernyshev, N. Chkhalo, I. Malyshev, M. Mikhailenko, and M. Toropov, “Matrix based algorithm for ion-beam figuring of optical elements,” Precis. Eng. 69(16), 29–35 (2021). [CrossRef]
39. Z. B. Fan, Y. F. Dai, C. L. Guan, and G. P. Tie, “Thermal control for ion beam figuring of thin-layer unimorph deformable mirror,” Opt. Eng. 58(1), 015102 (2019). [CrossRef]
40. B. A. Szajewski, J. C. Crone, and J. Knap, “Analytic model for the Orowan dislocation-precipitate bypass mechanism,” Materialia 11, 100671 (2020). [CrossRef]
41. R. M. Bradley, “Surface instability of binary compounds caused by sputter yield amplification,” Appl. Phys. Rev. 111(11), 114305 (2012). [CrossRef]
42. P. D. Shipman and R.M. Bradley, “Theory of nanoscale pattern formation induced by normal-incidence ion bombardment of binary compounds,” Phys. Rev. B 84(8), 085420 (2011). [CrossRef]
43. R. M. Bradley and P. D. Shipman, “A surface layer of altered composition can play a key role in nanoscale pattern formation induced by ion bombardment,” Appl. Phys. Sci. 258(9), 4161–4170 (2012). [CrossRef]
44. W. L. Liao, Y. F. Dai, X. H. Xie, and L Zhou, “Combined figuring technology for high-precision optical surfaces using a deterministic ion beam material adding and removal method,” Opt. Eng. 52(1), 010503 (2013). [CrossRef]
45. Y. Lu, X. H. Xie, L. Zhou, Z. C. Dai, and G. Y. Chen, “Improve optics fabrication efficiency by using a radio frequency ion beam figuring tool,” Appl. Opt. 56(2), 260–266 (2017). [CrossRef]
