Abstract

During the thinning process of plate-shaped optical parts (PSOP), the release of internal stress would cause the deformation of ultra-thin PSOP, which deteriorates the processed surface figure. The stress-release-induced deformation is hard to be predicted and controlled due to the difficulty in measuring the tiny internal stress in ultra-thin PSOP. In this paper, an analytical model is established to depict the variation of internal stress and deformation during the thinning process. It can be used to calculate the initial internal stress distribution along the thickness according to the deformation and the residual thickness of the sample. Meanwhile, the model can predict the residual stress distribution and deformation in the whole thinning process. The prediction results obtained from the proposed model agree well with the experimental results, and the prediction error is less than 13%. The presented model has great significance for the analysis of the tiny internal stress and then guide the process of making ultra-thin PSOP.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  2. T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
    [Crossref]
  3. D. W. Kim, H. M. Martin, and J. H. Burge, “Calibration and optimization of computer-controlled optical surfacing for large optics,” in Optical Manufacturing and Testing IX (International Society for Optics and Photonics, 2011), Vol. 8126, p. 812615.
  4. D. C. Harris, “History of magnetorheological finishing,” in Window and Dome Technologies and Materials XII (International Society for Optics and Photonics, 2011), Vol. 8016, p. 80160N.
  5. F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
    [Crossref]
  6. H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
    [Crossref]
  7. H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
    [Crossref]
  8. T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
    [Crossref]
  9. T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (1)

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

2016 (2)

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

K. Ramesh and V. Ramakrishnan, “Digital photoelasticity of glass: A comprehensive review,” Opt. Lasers Eng. 87, 59–74 (2016).
[Crossref]

2015 (1)

H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
[Crossref]

2014 (2)

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

2013 (1)

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

2012 (2)

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing: An established alternative for commercial applications,” Opt. Photonik 7(2), 56–58 (2012).
[Crossref]

2010 (1)

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

2008 (1)

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

1998 (1)

T. Kuttner and R. P. Wahi, “Modelling of internal stress distribution and deformation behaviour in the precipitation hardened superalloy SC16,” Mater. Sci. Eng., A 242(1-2), 259–267 (1998).
[Crossref]

1969 (1)

O. S. Narayanaswamy and R. Gardon, “Calculation of residual stresses in glass,” J. Am. Ceram. Soc. 52(10), 554–558 (1969).
[Crossref]

1965 (1)

E. H. Lee, T. G. Rogers, and T. C. Woo, “Residual stresses in a glass plate cooled symmetrically from both surfaces,” J. Am. Ceram. Soc. 48(9), 480–487 (1965).
[Crossref]

1920 (1)

L. H. Adams and E. D. Williamson, “The annealing of glass,” J. Franklin Inst. 190(6), 835–870 (1920).
[Crossref]

Adams, L. H.

L. H. Adams and E. D. Williamson, “The annealing of glass,” J. Franklin Inst. 190(6), 835–870 (1920).
[Crossref]

Aida, H.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Akilian, M.

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

Allahkarami, M.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Arnold, T.

H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
[Crossref]

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Baert, K.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Benedetti, M.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Boehm, G.

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Böhm, G.

H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
[Crossref]

Burge, J. H.

D. W. Kim, H. M. Martin, and J. H. Burge, “Calibration and optimization of computer-controlled optical surfacing for large optics,” in Optical Manufacturing and Testing IX (International Society for Optics and Photonics, 2011), Vol. 8126, p. 812615.

Chen, X.

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Dai, Z.

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

De Moor, P.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

De Munck, K.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Desjardin, R.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Doi, T.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Dylla-Spears, R.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Eichentopf, I.

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Fan, Z.

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

Feit, M.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Fontanari, V.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Forest, C. R.

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

Gardon, R.

O. S. Narayanaswamy and R. Gardon, “Calculation of residual stresses in glass,” J. Am. Ceram. Soc. 52(10), 554–558 (1969).
[Crossref]

Geraghty, P.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Hanan, J. C.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Harris, D. C.

D. C. Harris, “History of magnetorheological finishing,” in Window and Dome Technologies and Materials XII (International Society for Optics and Photonics, 2011), Vol. 8016, p. 80160N.

He, P.

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

Hibbard, R. L.

R. L. Hibbard, Design of Precision Mounts for Optimizing the Conversion Efficiency of KDP Crystals for the National Ignition Facility (Lawrence Livermore National Lab., CA (United States), 1998).

Janietz, M.

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Katakura, H.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Kim, D. W.

D. W. Kim, H. M. Martin, and J. H. Burge, “Calibration and optimization of computer-controlled optical surfacing for large optics,” in Optical Manufacturing and Testing IX (International Society for Optics and Photonics, 2011), Vol. 8126, p. 812615.

Kim, S.-W.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Kiontke, S.

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing: An established alternative for commercial applications,” Opt. Photonik 7(2), 56–58 (2012).
[Crossref]

Knüttel, A.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Kobayashi, T.

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Koyama, K.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Kuttner, T.

T. Kuttner and R. P. Wahi, “Modelling of internal stress distribution and deformation behaviour in the precipitation hardened superalloy SC16,” Mater. Sci. Eng., A 242(1-2), 259–267 (1998).
[Crossref]

Lamure, A.

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

Lee, E. H.

E. H. Lee, T. G. Rogers, and T. C. Woo, “Residual stresses in a glass plate cooled symmetrically from both surfaces,” J. Am. Ceram. Soc. 48(9), 480–487 (1965).
[Crossref]

Li, J.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

Li, M.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

Liao, D.

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Lin, K.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

Makimoto, N.

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Martin, H. M.

D. W. Kim, H. M. Martin, and J. H. Burge, “Calibration and optimization of computer-controlled optical surfacing for large optics,” in Optical Manufacturing and Testing IX (International Society for Optics and Photonics, 2011), Vol. 8126, p. 812615.

Mason, D.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Meister, J.

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Miller, P.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Narayanaswamy, O. S.

O. S. Narayanaswamy and R. Gardon, “Calculation of residual stresses in glass,” J. Am. Ceram. Soc. 52(10), 554–558 (1969).
[Crossref]

Nogami, H.

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Paetzelt, H.

H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
[Crossref]

Ramakrishnan, V.

K. Ramesh and V. Ramakrishnan, “Digital photoelasticity of glass: A comprehensive review,” Opt. Lasers Eng. 87, 59–74 (2016).
[Crossref]

Ramesh, K.

K. Ramesh and V. Ramakrishnan, “Digital photoelasticity of glass: A comprehensive review,” Opt. Lasers Eng. 87, 59–74 (2016).
[Crossref]

Rogers, T. G.

E. H. Lee, T. G. Rogers, and T. C. Woo, “Residual stresses in a glass plate cooled symmetrically from both surfaces,” J. Am. Ceram. Soc. 48(9), 480–487 (1965).
[Crossref]

Sawada, R.

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Schajer, G. S.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Schattenburg, M. L.

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

Schindler, A.

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Shen, L.

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

Shen, N.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Steele, R.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Suratwala, T.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Swinnen, B.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Takeda, H.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Takeshita, T.

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Tang, C.

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Tao, B.

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

Teixeira, R. C.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Ugural, A. C.

A. C. Ugural and A. C. Ugural, Stresses in Plates and Shells (McGraw-Hill Boston, 1999), Vol. 366.

A. C. Ugural and A. C. Ugural, Stresses in Plates and Shells (McGraw-Hill Boston, 1999), Vol. 366.

Uneda, M.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Van Hoof, C.

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

Vincent, G.

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

Wahi, R. P.

T. Kuttner and R. P. Wahi, “Modelling of internal stress distribution and deformation behaviour in the precipitation hardened superalloy SC16,” Mater. Sci. Eng., A 242(1-2), 259–267 (1998).
[Crossref]

Williamson, E. D.

L. H. Adams and E. D. Williamson, “The annealing of glass,” J. Franklin Inst. 190(6), 835–870 (1920).
[Crossref]

Winiarski, B.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Withers, P. J.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

Wong, L.

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Woo, T. C.

E. H. Lee, T. G. Rogers, and T. C. Woo, “Residual stresses in a glass plate cooled symmetrically from both surfaces,” J. Am. Ceram. Soc. 48(9), 480–487 (1965).
[Crossref]

Xie, R.

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Yamazaki, T.

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

Yi, A.

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

Zeuner, M.

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing: An established alternative for commercial applications,” Opt. Photonik 7(2), 56–58 (2012).
[Crossref]

Zhang, Z.

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Zhao, F.

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

Zhou, L.

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

Zhu, Y. W.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

Zuo, D. W.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

Ceram. Int. (1)

D. Liao, X. Chen, C. Tang, R. Xie, and Z. Zhang, “Characteristics of hydrolyzed layer and contamination on fused silica induced during polishing,” Ceram. Int. 40(3), 4479–4483 (2014).
[Crossref]

Curr. Appl. Phys. (1)

H. Aida, T. Doi, H. Takeda, H. Katakura, S.-W. Kim, K. Koyama, T. Yamazaki, and M. Uneda, “Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials,” Curr. Appl. Phys. 12(2), S41–S46 (2012).
[Crossref]

J. Am. Ceram. Soc. (2)

O. S. Narayanaswamy and R. Gardon, “Calculation of residual stresses in glass,” J. Am. Ceram. Soc. 52(10), 554–558 (1969).
[Crossref]

E. H. Lee, T. G. Rogers, and T. C. Woo, “Residual stresses in a glass plate cooled symmetrically from both surfaces,” J. Am. Ceram. Soc. 48(9), 480–487 (1965).
[Crossref]

J. Eng. Ind. (1)

B. Tao, P. He, L. Shen, and A. Yi, “Annealing of compression molded aspherical glass lenses,” J. Eng. Ind. 136(1), 011008 (2013).
[Crossref]

J. Franklin Inst. (1)

L. H. Adams and E. D. Williamson, “The annealing of glass,” J. Franklin Inst. 190(6), 835–870 (1920).
[Crossref]

J. Integr. Circuits Syst. (1)

R. C. Teixeira, K. De Munck, P. De Moor, K. Baert, B. Swinnen, C. Van Hoof, and A. Knüttel, “Stress analysis on ultra thin ground wafers,” J. Integr. Circuits Syst. 3(2), 113–121 (2008).
[Crossref]

J. Visualized Exp. (1)

T. Suratwala, R. Steele, M. Feit, R. Dylla-Spears, R. Desjardin, D. Mason, L. Wong, P. Geraghty, P. Miller, and N. Shen, “Convergent polishing: a simple, rapid, full aperture polishing process of high quality optical flats & spheres,” J. Visualized Exp. 94(94), e51965 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

T. Takeshita, N. Makimoto, H. Nogami, R. Sawada, and T. Kobayashi, “Simulation and fabrication of a MEMS optical scanner device considering deformation caused by internal stress,” Jpn. J. Appl. Phys. 55(10S), 10TA11 (2016).
[Crossref]

Mater. Sci. Eng., A (1)

T. Kuttner and R. P. Wahi, “Modelling of internal stress distribution and deformation behaviour in the precipitation hardened superalloy SC16,” Mater. Sci. Eng., A 242(1-2), 259–267 (1998).
[Crossref]

Opt. Lasers Eng. (1)

K. Ramesh and V. Ramakrishnan, “Digital photoelasticity of glass: A comprehensive review,” Opt. Lasers Eng. 87, 59–74 (2016).
[Crossref]

Opt. Photonik (1)

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing: An established alternative for commercial applications,” Opt. Photonik 7(2), 56–58 (2012).
[Crossref]

Plasma Sources Sci. Technol. (1)

H. Paetzelt, G. Böhm, and T. Arnold, “Etching of silicon surfaces using atmospheric plasma jets,” Plasma Sources Sci. Technol. 24(2), 025002 (2015).
[Crossref]

Procedia CIRP (1)

F. Zhao, L. Zhou, Z. Fan, and Z. Dai, “Research on Surface Processing of Quartz Wafer Based on Magnetorheological Finishing and Ion Beam Figuring,” Procedia CIRP 71, 496–499 (2018).
[Crossref]

Vak. Forsch. Prax. (1)

T. Arnold, G. Boehm, I. Eichentopf, M. Janietz, J. Meister, and A. Schindler, “Plasma Jet Machining: A novel technology for precision machining of optical elements,” Vak. Forsch. Prax. 22(4), 10–16 (2010).
[Crossref]

Other (7)

D. W. Kim, H. M. Martin, and J. H. Burge, “Calibration and optimization of computer-controlled optical surfacing for large optics,” in Optical Manufacturing and Testing IX (International Society for Optics and Photonics, 2011), Vol. 8126, p. 812615.

D. C. Harris, “History of magnetorheological finishing,” in Window and Dome Technologies and Materials XII (International Society for Optics and Photonics, 2011), Vol. 8016, p. 80160N.

R. L. Hibbard, Design of Precision Mounts for Optimizing the Conversion Efficiency of KDP Crystals for the National Ignition Facility (Lawrence Livermore National Lab., CA (United States), 1998).

C. R. Forest, M. Akilian, G. Vincent, A. Lamure, and M. L. Schattenburg, “Thin glass optic and silicon wafer deformation and kinematic constraint,” in Submitted to Proceedings of the 18th Annual Meeting, (The American Society for Precision Engineering, 2003), Vol. 29.

B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J. C. Hanan, G. S. Schajer, and P. J. Withers, “Comparative analysis of shot-peened residual stresses using micro-hole drilling, micro-slot cutting, X-ray diffraction methods and finite-element modelling,” in Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9, K. B. Zimmerman, ed. (Springer, 2016), pp. 215–223.

A. C. Ugural and A. C. Ugural, Stresses in Plates and Shells (McGraw-Hill Boston, 1999), Vol. 366.

J. Li, Y. W. Zhu, D. W. Zuo, K. Lin, and M. Li, “Fixed abrasive lapping and polishing of hard brittle materials,” in Key Engineering Materials, F. H. Wohlbier, ed. (Trans Tech Publ, 2010), Vol. 426, pp. 589–592.

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Figures (9)

Fig. 1.
Fig. 1. Distribution of the internal stress in the cylindrical coordinates. (a) The plate in the cylindrical coordinates. (b) The stress distribution in a section of the plate.
Fig. 2.
Fig. 2. Force and moment balance relation in the thinning process. (a) The force and moment of the removed part on the ultra-thin plate balance the internal stress remained after annealing. (b) The ultra-thin plate is deformed and its internal stress is redistributed after the material removed.
Fig. 3.
Fig. 3. Placement of the samples in the annealing process. The left picture shows the exploded view, and the right picture shows the cross section of a single sample.
Fig. 4.
Fig. 4. Annealing schedule.
Fig. 5.
Fig. 5. Schematic of the thinning method.
Fig. 6.
Fig. 6. Surface figure of the measuring surface at different thickness, (a) 3.00 m, (b) 1.09 mm, (c) 0.61 mm, (d) 0.34 mm.
Fig. 7.
Fig. 7. Deflection of the sample at different thickness.
Fig. 8.
Fig. 8. Theoretical and experimental results of the deflection with the thickness of (a) 0.61 mm, (b) 1.09 mm and 0.34 mm.
Fig. 9.
Fig. 9. Internal stress at different thickness.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

σ 0 ( z ) = a z 2 + b z + c ,
h 0 2 h 0 2 σ 0 ( z ) d z = 0 ,
σ 0 ( z ) = 1 3 a [ ( h 0 2 ) 2 3 z 2 ] .
h 0 2     ( h 0 2 h ) σ 0 ( z ) d z F = 0 ,
h 0 2     ( h 0 2 h ) ( z + h 0 2 ) σ 0 ( z ) d z M M F = 0 ,
σ 0 ( z )   =   σ 0 ( z ) E / E ( 1 ν ) ( 1 ν ) ,
Γ = a h 0 2 2 E / E ( 1 ν ) ( 1 ν ) ,
z = z h 0 ,
h = h h 0 ,
F = F [ E / E ( 1 ν ) ( 1 ν ) ] h 0 ,
M F = M F [ E / E ( 1 ν ) ( 1 ν ) ] h 0 2 ,
M = M [ E / E ( 1 ν ) ( 1 ν ) ] h 0 2 ,
σ 0 ( z ) = Γ ( 1 6 2 z 2 ) .
F = Γ ( 2 3 h 3 h 2 + 1 3 h ) .
σ F = F h = Γ ( 2 3 h 2 h + 1 3 ) .
M F = 1 2 ( 1 2 h ) ( z + 1 2 ) σ F d z   =   Γ ( 1 3 h 4 1 2 h 3 + 1 6 h 2 ) .
M = 1 2     ( 1 2 h ) ( z + 1 2 ) σ 0 ( z ) d z M F = 1 6 Γ ( h 4 h 3 ) .
σ M ( z ) = 12 M ( z   +   1 h 2 ) h 3 .
σ M ( z ) = 2 Γ ( h 1 ) z + Γ ( h 1 ) 2 .
σ ( z )   =   σ 0 ( z ) σ F σ M ( z ) .
σ ( z )   =   Γ [ 2 z 2 + 2 ( h 1 ) z + ( 1 3 h 2 + h 1 2 ) ] .
4 w = ( d 2 d r 2 + 1 r d d r ) ( d 2 w d r 2 + 1 r dw d r ) = 0 ,
2 = d 2 d r 2 + 1 r d d r .
D = E h 3 12 ( 1 ν 2 ) .
w = w h 0 ,
r = r h 0 ,
D = D [ E / E ( 1 ν ) ( 1 ν ) ] h 0 3 = h 3 12 ( 1   +   ν ) .
4 w = ( d 2 d r 2 + 1 r d d r ) ( d 2 w d r 2 + 1 r d w d r ) = 0.
w = c 1 + c 2 r 2 + c 3 r 2 ln r + c 4 ln r ,
lim r 0 w = c 1 + lim r 0 c 4 ln r = 0.
D d d r ( d 2 w d r 2 + 1 r d w d r ) = 0.
M = D ( d 2 w d r 2 + ν r d w d r ) .
c 2 = M 2 D ( 1 + ν ) .
c 2 = Γ ( 1 h ) .
w = Γ ( 1 h ) r 2 .
σ ( z ) = { [ 2 z 2 + 2 ( h 1 ) z + ( 1 3 h 2 + h 1 2 ) ] ( 1 h ) r 2 w 0 < h < 1 Γ ( 1 6 2 z 2 ) h   =   1 .

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