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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 568–575
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Tentative investigation towards precision polishing of optical components with ultrasonically vibrating bound-abrasive pellets

Yaguo Li, Yongbo Wu, Jian Wang, Wei Yang, Yinbiao Guo, and Qiao Xu  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 568-575 (2012)
http://dx.doi.org/10.1364/OE.20.000568


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Abstract

Ultrasonic vibration has been employed to improve the quality of machined surface in the grinding of brittle materials. In this report, we transplant the philosophy of ultrasonic vibration assisted grinding to chemo-mechanical bound-abrasive-pellet polishing in anticipation of the improvement in either surface roughness or material removal rate. The preliminary experimental results show that the ultrasonic vibration assisted chemo-mechanical pellet polishing can yield desired results that material removal rate can be significantly raised while surface roughness is not degraded. The experimental results also indicate different mechanisms between ultrasonic-vibration-assisted chemo-mechanical pellet polishing and conventional chemo-mechanical bound-abrasive polishing.

© 2011 OSA

1. Introduction

Optical glass can find a wide spectrum of applications in scientific research and industrial fields, including luminescence, semiconductor industry, optical communication, laser systems, astronomical telescopes, etc. The optical glass is usually processed consecutively following the steps: shaping, coarse grinding, fine grinding, polishing and figuring if necessary. In the above-mentioned processes, grinding can remove material fast, although can induce cracks or fractures in the top surface of machined workpiece due to the fact that glass is removed owing to brittle fracture in classical grinding (excluding ductile grinding). Because the material is removed plastically/elastically in polishing and the residual stress can be released by virtue of polishing, polishing is indispensable to eliminate the residual cracks by grinding to guarantee manufactured optics usable. However, the material removal rate (MRR) in typical polishing processes is so exceedingly low that it takes several hours to polish out an optic to specular surface. In general, polishing process is accomplished by freshly feeding polishing slurry to polishing lap. The slurry consists of polishing powder (usually ceria, silica, or zicornia, etc.) mixed with water and/or other chemicals. Pitch or polyurethane is employed as polishing materials. Conventional pitch/pad polishing is time-consuming because typical removal rate is as low as 1μm/h [1

1. P. P. Hed, “Calculations of material removal, removal rate and Preston coefficient in continuous lapping/polishing machines,” Lawrence Livermore National Laboratory Report, UCRL-ID-115321 (1993).

5

5. Y. Li, J. Hou, Q. Xu, J. Wang, W. Yang, and Y. Guo, “The characteristics of optics polished with a polyurethane pad,” Opt. Express 16(14), 10285–10293 (2008). [CrossRef] [PubMed]

], as opposed to tens to hundreds of microns per hour in grinding process. In order to reduce the time of polishing, considerable emphasis is placed on two aspects: one is to thin the thickness of the residual layer by grinding, which should be removed in polishing process; the other refers to raise the material removal rate of polishing process. Ductile mode machining (including diamond and alumina polishing of glass) [6

6. D. Golini and S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt. 30(19), 2761–2777 (1991). [CrossRef] [PubMed]

8

8. B. K. A. Ngoi and P. S. Sreejith, “Ductile regime finish machining – a review,” Int. J. Adv. Manuf. Technol. 16(8), 547–550 (2000). [CrossRef]

], electrolytic in-process dressing (ELID) grinding [9

9. H. Ohmori and T. Nakagawa, “Analysis of mirror surface generation of hard and brittle materials by ELID (Electronic In-Process Dressing) grinding with superfine grain metallic bond wheels,” Ann. CIRP 44(1), 287–290 (1995). [CrossRef]

11

11. A. S. Kumar, H. S. Lim, M. Rahman, and K. Fathima, “A study on the grinding of glass using electrolytic in-process dressing,” J. Electron. Mater. 31(10), 1039–1046 (2002). [CrossRef]

] and vibration-assisted machining [12

12. W. Qu, K. Wang, M. H. Miller, Y. Huang, and A. Chandra, “Using vibration-assisted grinding to reduce subsurface damage,” Precis. Eng. 24(4), 329–337 (2000). [CrossRef]

,13

13. D. E. Brehl and T. A. Dow, “Review of vibration-assisted machining,” Precis. Eng. 32(3), 153–172 (2008). [CrossRef]

] were proposed with the aim of thinning residual defective layer as well as ameliorating surface quality. On the other hand, polyurethane pad polishing [5

5. Y. Li, J. Hou, Q. Xu, J. Wang, W. Yang, and Y. Guo, “The characteristics of optics polished with a polyurethane pad,” Opt. Express 16(14), 10285–10293 (2008). [CrossRef] [PubMed]

], bound-abrasive polishers [14

14. B. E. Gillman and S. D. Jacobs, “Bound-abrasive polishers for optical glass,” Appl. Opt. 37(16), 3498–3505 (1998). [CrossRef] [PubMed]

16

16. Y. D. Filatov, O. Y. Filatov, G. Monteil, U. Heisel, and M. Storchak, “Bound-abrasive grinding and polishing of surfaces of optical materials,” Opt. Eng. 50(6), 063401 (2011). [CrossRef]

], improved slurries and innovatory polishing agents [17

17. A. A. Tesar, B. A. Fuchs, and P. P. Hed, “Examination of the polished surface character of fused silica,” Appl. Opt. 31(34), 7164–7172 (1992). [CrossRef] [PubMed]

19

19. J. Matsuzawa, A. Sugimoto, M. Yoshida, K. Hirai, T. Ashizawa, and Y. Ootsuki, “Method for producing cerium oxide, cerium oxide abrasive, method for polishing substrate using the same and method for manufacturing semiconductor device,” US Patent No. US6615499 B1, (Sep. 9, 2003).

] have been applied to the polishing of optical glass successfully for the purpose of either enhancing the MRR or improving manufactured surface conditions of optical components. In most cases, polishing is implemented with free/loose abrasive slurries. Notwithstanding widespread use, loose abrasive polishing has many disadvantages associated with it, for instance, the difficulties in maintaining the uniform distribution of particles at the interface between polishing laps and components and disposing of waste slurries. Consequently, bound abrasive polishing technique as a probable substitute for loose abrasive polishing has appealed to many researchers [14

14. B. E. Gillman and S. D. Jacobs, “Bound-abrasive polishers for optical glass,” Appl. Opt. 37(16), 3498–3505 (1998). [CrossRef] [PubMed]

16

16. Y. D. Filatov, O. Y. Filatov, G. Monteil, U. Heisel, and M. Storchak, “Bound-abrasive grinding and polishing of surfaces of optical materials,” Opt. Eng. 50(6), 063401 (2011). [CrossRef]

, 20

20. L. Zhou, T. Shiina, Z. Qiu, J. Shimizu, T. Yamamoto, and T. Tashiro, “Research on chemo-mechanical grinding of large size quartz glass substrate,” Precis. Eng. 33(4), 499–504 (2009). [CrossRef]

]. Following this roadmap, we recently developed another bound-abrasive polisher for optical glass, the effectiveness of which has been verified [20

20. L. Zhou, T. Shiina, Z. Qiu, J. Shimizu, T. Yamamoto, and T. Tashiro, “Research on chemo-mechanical grinding of large size quartz glass substrate,” Precis. Eng. 33(4), 499–504 (2009). [CrossRef]

]. As it is well known, machining performance, at least material removal rate, can be improved by introducing ultrasonic vibration into manufacturing processes [21

21. I. D. Marinesu, M. Hitchiner, E. Uhlmann, W. B. Rowe, and I. Inasaki, Handbook of Machining with Grinding Wheels (CRC Press, 2007), Chap. 20.

23

23. N. Suzuki, S. Masuda, M. Haritani, and E. Shamoto, “Ultraprecision micromachining of brittle materials by applying ultrasonic elliptical vibration cutting,” in Proceedings of IEEE Conference on Micro-Nano Mechatronics and Human Science (Institute of Electrical and Electronics Engineers, 2004), 133–138.

]. Thus we transplanted the fundamental concept to bound abrasive polishing in the hope of achieving analogous results to those in ultrasonic vibration assisted grinding. Then ultrasonic vibration assisted chemo-mechanical bound-abrasive machining (CMM) was put forward in an attempt to further boost the material removal rate and to reduce the machining time to fabricate an optical component. It is referred to as chemo-mechanical machining because the glass material is removed due to the synergy of chemical and mechanical actions. The hardness of abrasive CeO2 in bound-abrasive polisher is comparable to fused silica [24

24. T. Izumitani, Optical Glass, (1984) (in Japanese) [Translated by the American Institute of Physics (New York, USA, 1986), Chap. 4].

,25

25. T. Kasai and N. Yasunaga, Precision Grinding for High Additional Value (Nikkan Kogyo Shimbun, Ltd., 2010), Chap. 1.1 (in Japanese).

]; therefore, it is unlikely to remove the fused silica material purely mechanically. The studies show that softer substance than ceria abrasive is produced on the top surface of fused silica substrate as a result of chemical reactions between ceria and silica [26

26. L. Zhou, H. Eda, J. Shimizu, S. Kamiya, H. Iwase, S. Kimura, and H. Sato, “Defect-free fabrication for single crystal silicon substrate by chemo-mechanical grinding,” Ann. CIRP 55(1), 313–316 (2006). [CrossRef]

]. The chemical effect makes all the difference for the bound-abrasive machining.

We evaluated the performance of ultrasonic vibration assisted CMM in terms of surface roughness and MRR in this article. We found that the MRR in ultrasonic vibration CMM can be increased considerably while the surface roughness almost remains the same as that in conventional CMM. In addition, an interesting phenomenon is that the MRR of CMM, in effect, decreases with machining time (i.e. surface conditions) but surface conditions have limited influence on the MRR in ultrasonic vibration assisted CMM. The experiments and corresponding results will be detailed in the following parts.

2. Experimental

The experimental setup is depicted in Fig. 1
Fig. 1 The sketch of ultrasonic vibration polishing machine. The polishing head is capable of moving back and forth in X direction. The downward load is exerted by the movement of the head along Z axis. Two identical polishing pellets were stuck to the PZT vibrator. During the polishing, the head was oscillating in the X axis and the lower spindle rotated independently.
. Bound-abrasive polishing pellets were glued to the end of a PZT metallic body, onto which the ultrasonic vibration will be superimposed. The pellets are composed of ceria, prevailing abrasives in glass polishing community. The ceria is bound with special epoxy mixed with chemical additives. In addition, the pellets are full of abundant pores with diameter of tens of microns. The possible effect of pores may be to accommodate the polishing swarf and to expedite the dissipation of the heat generated in polishing process, which is conducive to the generation of the surface with low surface roughness and high material removal rate. The external downward load was supplied by a pair of compression springs and was calibrated with a dynamometer (Kistler 9257A, Switzerland). The downward load is determined by the relative displacement of the polishing head. A circular fused silica sample was placed on the lower platform. The platform is able to rotate with its central axis. The rotation rate was set to be ~400rpm in our experiments. The polishing head oscillated along the X axis at 3mm/s during the machining process. The detailed experimental parameters are tabulated in Table 1

Table 1. Processing Parameters and Specs of Ultrasonic Vibration Used in the Experiments

table-icon
View This Table
.

Ultrasonic vibration of polishing head was tested with a laser Doppler vibrometer (Ono Sokki LV-1610, Japan) around natural frequency. The trajectory of the ultrasonic vibration of polishing head was captured with an oscilloscope (LeCroy WaveJet 314, USA) as shown in Fig. 2
Fig. 2 The path of the grinding head due to ultrasonic vibration (f=15.3kHz, Vp-p=150V, phase difference=135°).
. The amplitude of vibration is 1.4μm and 1.7μm in X and Z directions, respectively.

The machined region was an annular zone ~15mm away from the center of the sample. Four measurements of surface roughness were made near the middle of the annulus at 3, 6, 9, 12 o’clock positions with an optical profilometer at 10 × magnification (Zygo Newview 600, USA). The reported surface roughness is the average of the four measurements. The material removal was evaluated with a contact stylus profiler (Tokyo Seimitsu Surfcom480A, Japan). The surface roughness and material removal were inspected every 10min after cleaning the surface with ethanol. During each run, the polishing swarf was not removed. Each sample was machined for 60min. All the experiments were conducted without introducing any fluids into the polishing process.

3. Results and discussion

3.1 Surface roughness and MRR

3.2 Surface morphology

The samples in our present experiments were not subjected to chemical etching to observe possible mechanical damage in conventional CMM and UV CMM, which will be investigated in the future. However, it should be pointed out that the Mohs hardness of ceria abrasive used to manufacture fused silica glass is ~6, comparable to fused silica and therefore it is unlikely to induce mechanical damage [24

24. T. Izumitani, Optical Glass, (1984) (in Japanese) [Translated by the American Institute of Physics (New York, USA, 1986), Chap. 4].

,25

25. T. Kasai and N. Yasunaga, Precision Grinding for High Additional Value (Nikkan Kogyo Shimbun, Ltd., 2010), Chap. 1.1 (in Japanese).

]. In addition, it is apparent from force measurements (measured with a dynamometer Kistler 9257A, Switzerland) that the normal force between the polishing head and samples is actually decreased after introducing ultrasonic vibration (Fig. 6
Fig. 6 Comparison of normal forces before and after introducing ultrasonic vibration. The normal force decreased by >10% after imposing ultrasonic vibration upon polishing head.
), which is well known in grinding community [13

13. D. E. Brehl and T. A. Dow, “Review of vibration-assisted machining,” Precis. Eng. 32(3), 153–172 (2008). [CrossRef]

]. Since the normal force is smaller in UV CMM than conventional CMM under similar experimental conditions, the possibility of mechanical damage occurrence in UV CMM is lowered according to fracture theory of brittle materials [27

27. B. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, 1993), Chap. 8.

]. Thus the periodic structure does not represent a transition from ductile to brittle mode and just results from the periodic motion of polishing head.

We also observed the morphology of the pellets before and after machining, respectively. It is found that most ceria abrasives are covered with chemical reaction products in conventional CMM. In contrast, the ceria abrasives can be quite readily identified in the pellet used for UV CMM. The products can prevent ceria from reacting with silica in solid state and slow down the material removal rate. It is also found that the polishing swarf during UV CMM was obviously much more than that in conventional CMM process, which suggests more intensive chemical reaction and severer wear of pellets in UV CMM. The above phenomena can, to some extent, account for the great MRR in UV CMM. The similarity and difference of CMM and UV CMM in machining mechanism is still under investigation.

4. Summary

The ultrasonic vibration assisted chemo-mechanical machining is manifested to be an effective method for polishing optical components after being ground. With the UV CMM, the material removal rate has been improved substantially while the surface roughness remains as conventional CMM. The material removal rate in UV CMM is as high as up to >5μm/h compared to 1~2μm/h in conventional CMM. The best results of surface roughness both in UV CMM and conventional CMM are <2nm (Ra). The surface roughness is probably further lowered and the material removal rate is increased by altering the processing parameters and conditions. The effects of processing parameters on the characteristics of UV CMM are under investigation.

Acknowledgments

The authors are grateful to reviewers for invaluable comments and advice on the manuscript. The supply of pellets used in the experiments by Tokyo Diamond Tools Mfg. Co., Ltd. is gratefully acknowledged. The discussions with Prof. Libo Zhou of Ibaraki University (Japan), Assist. Prof. Masakazu Fujimoto and Mr. Shoichi Sasaki of Akita Prefectural University are thankfully appreciated, too. Yaguo Li would like to express his sincere thanks to the Fine Optical Engineering Research Center for the assistance in meeting the publication costs of this article.

References and links

1.

P. P. Hed, “Calculations of material removal, removal rate and Preston coefficient in continuous lapping/polishing machines,” Lawrence Livermore National Laboratory Report, UCRL-ID-115321 (1993).

2.

A. Tesar and B. A. Fuchs, “Removal rates of fused silica with cerium oxide/pitch polishing,” Proc. SPIE 1531, 80–90 (1992). [CrossRef]

3.

M. J. Cumbo, “Chemo-mechanical Interactions in optical polishing,” Ph.D. Dissertation, Univ. of Rochester, (Rochester, NY, 1993).

4.

R. R. Berggren and R. A. Schmell, “Pad polishing for rapid production of large flats,” Proc. SPIE 3134, 252–257 (1997). [CrossRef]

5.

Y. Li, J. Hou, Q. Xu, J. Wang, W. Yang, and Y. Guo, “The characteristics of optics polished with a polyurethane pad,” Opt. Express 16(14), 10285–10293 (2008). [CrossRef] [PubMed]

6.

D. Golini and S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt. 30(19), 2761–2777 (1991). [CrossRef] [PubMed]

7.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113(2), 184–189 (1991). [CrossRef]

8.

B. K. A. Ngoi and P. S. Sreejith, “Ductile regime finish machining – a review,” Int. J. Adv. Manuf. Technol. 16(8), 547–550 (2000). [CrossRef]

9.

H. Ohmori and T. Nakagawa, “Analysis of mirror surface generation of hard and brittle materials by ELID (Electronic In-Process Dressing) grinding with superfine grain metallic bond wheels,” Ann. CIRP 44(1), 287–290 (1995). [CrossRef]

10.

W. Lin, H. Ohmori, Y. Yamagata, and S. Moriyasu, “Improvement in the ground surface roughness of fused silica X-ray mirror with ELID-grinding,” Key Eng. Mater. 238–239, 143–146 (2003). [CrossRef]

11.

A. S. Kumar, H. S. Lim, M. Rahman, and K. Fathima, “A study on the grinding of glass using electrolytic in-process dressing,” J. Electron. Mater. 31(10), 1039–1046 (2002). [CrossRef]

12.

W. Qu, K. Wang, M. H. Miller, Y. Huang, and A. Chandra, “Using vibration-assisted grinding to reduce subsurface damage,” Precis. Eng. 24(4), 329–337 (2000). [CrossRef]

13.

D. E. Brehl and T. A. Dow, “Review of vibration-assisted machining,” Precis. Eng. 32(3), 153–172 (2008). [CrossRef]

14.

B. E. Gillman and S. D. Jacobs, “Bound-abrasive polishers for optical glass,” Appl. Opt. 37(16), 3498–3505 (1998). [CrossRef] [PubMed]

15.

V. V. Rogov, Y. Filatov, W. Kottler, and V. P. Sobol, “New technology of precision polishing of glass optics,” Opt. Eng. 40(8), 1641–1645 (2001). [CrossRef]

16.

Y. D. Filatov, O. Y. Filatov, G. Monteil, U. Heisel, and M. Storchak, “Bound-abrasive grinding and polishing of surfaces of optical materials,” Opt. Eng. 50(6), 063401 (2011). [CrossRef]

17.

A. A. Tesar, B. A. Fuchs, and P. P. Hed, “Examination of the polished surface character of fused silica,” Appl. Opt. 31(34), 7164–7172 (1992). [CrossRef] [PubMed]

18.

A. Tesar, B. Fuchs, and P. Hed, “Improvement in polishing of fused-silica parts,” Appl. Opt. 30(31), 4459 (1991). [CrossRef] [PubMed]

19.

J. Matsuzawa, A. Sugimoto, M. Yoshida, K. Hirai, T. Ashizawa, and Y. Ootsuki, “Method for producing cerium oxide, cerium oxide abrasive, method for polishing substrate using the same and method for manufacturing semiconductor device,” US Patent No. US6615499 B1, (Sep. 9, 2003).

20.

L. Zhou, T. Shiina, Z. Qiu, J. Shimizu, T. Yamamoto, and T. Tashiro, “Research on chemo-mechanical grinding of large size quartz glass substrate,” Precis. Eng. 33(4), 499–504 (2009). [CrossRef]

21.

I. D. Marinesu, M. Hitchiner, E. Uhlmann, W. B. Rowe, and I. Inasaki, Handbook of Machining with Grinding Wheels (CRC Press, 2007), Chap. 20.

22.

C. Brecher, R. Schug, A. Weber, C. Wenzel, and S. Hannig, “New systematic and time-saving procedure to design cup grinding wheels for the application of ultrasonic-assisted grinding,” Int. J. Adv. Manuf. Technol. 47(1–4), 153–159 (2010). [CrossRef]

23.

N. Suzuki, S. Masuda, M. Haritani, and E. Shamoto, “Ultraprecision micromachining of brittle materials by applying ultrasonic elliptical vibration cutting,” in Proceedings of IEEE Conference on Micro-Nano Mechatronics and Human Science (Institute of Electrical and Electronics Engineers, 2004), 133–138.

24.

T. Izumitani, Optical Glass, (1984) (in Japanese) [Translated by the American Institute of Physics (New York, USA, 1986), Chap. 4].

25.

T. Kasai and N. Yasunaga, Precision Grinding for High Additional Value (Nikkan Kogyo Shimbun, Ltd., 2010), Chap. 1.1 (in Japanese).

26.

L. Zhou, H. Eda, J. Shimizu, S. Kamiya, H. Iwase, S. Kimura, and H. Sato, “Defect-free fabrication for single crystal silicon substrate by chemo-mechanical grinding,” Ann. CIRP 55(1), 313–316 (2006). [CrossRef]

27.

B. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, 1993), Chap. 8.

OCIS Codes
(160.6030) Materials : Silica
(220.4610) Optical design and fabrication : Optical fabrication
(220.5450) Optical design and fabrication : Polishing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: September 22, 2011
Revised Manuscript: November 10, 2011
Manuscript Accepted: November 24, 2011
Published: December 22, 2011

Citation
Yaguo Li, Yongbo Wu, Jian Wang, Wei Yang, Yinbiao Guo, and Qiao Xu, "Tentative investigation towards precision polishing of optical components with ultrasonically vibrating bound-abrasive pellets," Opt. Express 20, 568-575 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-568


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References

  1. P. P. Hed, “Calculations of material removal, removal rate and Preston coefficient in continuous lapping/polishing machines,” Lawrence Livermore National Laboratory Report, UCRL-ID-115321 (1993).
  2. A. Tesar and B. A. Fuchs, “Removal rates of fused silica with cerium oxide/pitch polishing,” Proc. SPIE1531, 80–90 (1992). [CrossRef]
  3. M. J. Cumbo, “Chemo-mechanical Interactions in optical polishing,” Ph.D. Dissertation, Univ. of Rochester, (Rochester, NY, 1993).
  4. R. R. Berggren and R. A. Schmell, “Pad polishing for rapid production of large flats,” Proc. SPIE3134, 252–257 (1997). [CrossRef]
  5. Y. Li, J. Hou, Q. Xu, J. Wang, W. Yang, and Y. Guo, “The characteristics of optics polished with a polyurethane pad,” Opt. Express16(14), 10285–10293 (2008). [CrossRef] [PubMed]
  6. D. Golini and S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt.30(19), 2761–2777 (1991). [CrossRef] [PubMed]
  7. T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind.113(2), 184–189 (1991). [CrossRef]
  8. B. K. A. Ngoi and P. S. Sreejith, “Ductile regime finish machining – a review,” Int. J. Adv. Manuf. Technol.16(8), 547–550 (2000). [CrossRef]
  9. H. Ohmori and T. Nakagawa, “Analysis of mirror surface generation of hard and brittle materials by ELID (Electronic In-Process Dressing) grinding with superfine grain metallic bond wheels,” Ann. CIRP44(1), 287–290 (1995). [CrossRef]
  10. W. Lin, H. Ohmori, Y. Yamagata, and S. Moriyasu, “Improvement in the ground surface roughness of fused silica X-ray mirror with ELID-grinding,” Key Eng. Mater.238–239, 143–146 (2003). [CrossRef]
  11. A. S. Kumar, H. S. Lim, M. Rahman, and K. Fathima, “A study on the grinding of glass using electrolytic in-process dressing,” J. Electron. Mater.31(10), 1039–1046 (2002). [CrossRef]
  12. W. Qu, K. Wang, M. H. Miller, Y. Huang, and A. Chandra, “Using vibration-assisted grinding to reduce subsurface damage,” Precis. Eng.24(4), 329–337 (2000). [CrossRef]
  13. D. E. Brehl and T. A. Dow, “Review of vibration-assisted machining,” Precis. Eng.32(3), 153–172 (2008). [CrossRef]
  14. B. E. Gillman and S. D. Jacobs, “Bound-abrasive polishers for optical glass,” Appl. Opt.37(16), 3498–3505 (1998). [CrossRef] [PubMed]
  15. V. V. Rogov, Y. Filatov, W. Kottler, and V. P. Sobol, “New technology of precision polishing of glass optics,” Opt. Eng.40(8), 1641–1645 (2001). [CrossRef]
  16. Y. D. Filatov, O. Y. Filatov, G. Monteil, U. Heisel, and M. Storchak, “Bound-abrasive grinding and polishing of surfaces of optical materials,” Opt. Eng.50(6), 063401 (2011). [CrossRef]
  17. A. A. Tesar, B. A. Fuchs, and P. P. Hed, “Examination of the polished surface character of fused silica,” Appl. Opt.31(34), 7164–7172 (1992). [CrossRef] [PubMed]
  18. A. Tesar, B. Fuchs, and P. Hed, “Improvement in polishing of fused-silica parts,” Appl. Opt.30(31), 4459 (1991). [CrossRef] [PubMed]
  19. J. Matsuzawa, A. Sugimoto, M. Yoshida, K. Hirai, T. Ashizawa, and Y. Ootsuki, “Method for producing cerium oxide, cerium oxide abrasive, method for polishing substrate using the same and method for manufacturing semiconductor device,” US Patent No. US6615499 B1, (Sep. 9, 2003).
  20. L. Zhou, T. Shiina, Z. Qiu, J. Shimizu, T. Yamamoto, and T. Tashiro, “Research on chemo-mechanical grinding of large size quartz glass substrate,” Precis. Eng.33(4), 499–504 (2009). [CrossRef]
  21. I. D. Marinesu, M. Hitchiner, E. Uhlmann, W. B. Rowe, and I. Inasaki, Handbook of Machining with Grinding Wheels (CRC Press, 2007), Chap. 20.
  22. C. Brecher, R. Schug, A. Weber, C. Wenzel, and S. Hannig, “New systematic and time-saving procedure to design cup grinding wheels for the application of ultrasonic-assisted grinding,” Int. J. Adv. Manuf. Technol.47(1–4), 153–159 (2010). [CrossRef]
  23. N. Suzuki, S. Masuda, M. Haritani, and E. Shamoto, “Ultraprecision micromachining of brittle materials by applying ultrasonic elliptical vibration cutting,” in Proceedings of IEEE Conference on Micro-Nano Mechatronics and Human Science (Institute of Electrical and Electronics Engineers, 2004), 133–138.
  24. T. Izumitani, Optical Glass, (1984) (in Japanese) [Translated by the American Institute of Physics (New York, USA, 1986), Chap. 4].
  25. T. Kasai and N. Yasunaga, Precision Grinding for High Additional Value (Nikkan Kogyo Shimbun, Ltd., 2010), Chap. 1.1 (in Japanese).
  26. L. Zhou, H. Eda, J. Shimizu, S. Kamiya, H. Iwase, S. Kimura, and H. Sato, “Defect-free fabrication for single crystal silicon substrate by chemo-mechanical grinding,” Ann. CIRP55(1), 313–316 (2006). [CrossRef]
  27. B. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, 1993), Chap. 8.

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