Abstract

The calculation of the dwell time plays a crucial role in polishing precision large optics. Although some studies have taken place, it remains a challenge to develop a calculation algorithm which is absolutely stable, together with a high convergence ratio and fast solution speed even for extremely large mirrors. For this aim, we introduced a self-adaptive iterative algorithm to calculate the dwell time in this paper. Simulations were conducted in bonnet polishing (BP) to test the performance of this method on a real 430mm×430mm fused silica part with the initial surface error PV=1741.29nm, RMS=433.204nm. The final surface residual error in the clear aperture after two simulation steps turned out to be PV=11.7nm, RMS=0.5nm. The results confirm that this method is stable and has a high convergence ratio and fast solution speed even with an ordinary computer. It is notable that the solution time is usually just a few seconds even on a 1000mm×1000mm part. Hence, we believe that this method is perfectly suitable for polishing large optics. And not only can it be applied to BP, but it can also be applied to other subaperture deterministic polishing processes.

© 2014 Optical Society of America

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  1. R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra 17, 34–39 (1983).
  2. L. N. Allen and R. E. Keim, “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33–50 (1989).
  3. S. C. West, H. M. Martin, R. H. Nagel, R. S. Young, W. B. Davison, T. J. Trebisky, S. T. Derigne, and B. B. Hille, “Practical design and performance of the stressed-lap polishing tool,” Appl. Opt. 33, 8094–8100 (1994).
    [CrossRef]
  4. W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
    [CrossRef]
  5. W. Fähnle, H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surfaces,” Appl. Opt. 37, 6771–6773 (1998).
    [CrossRef]
  6. J. W. Carr, “Atmospheric pressure plasma processing for damage-free optics and surfaces,” Eng. Res. Dev. Technol. 3, 31–39 (1999).
  7. R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).
  8. D. D. Walker, R. Freeman, R. Morton, G. McCavana, and A. Beaucamp, “Use of the ‘Precessions’TM process for prepolishing and correcting 2D & 2(1/2)D form,” Opt. Express 14, 11787–11795 (2006).
    [CrossRef]
  9. G. Yu, D. D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51, 6637–6640 (2012).
    [CrossRef]
  10. H. Li, D. D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21, 370–381 (2013).
    [CrossRef]
  11. H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).
  12. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16, 218–224 (1977).
    [CrossRef]
  13. S. R. Wilson and J. R. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–324 (1987).
    [CrossRef]
  14. S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74–81 (1988).
    [CrossRef]
  15. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
    [CrossRef]
  16. P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599–611 (2000).
    [CrossRef]
  17. C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
    [CrossRef]
  18. C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).
  19. H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
    [CrossRef]
  20. L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).
  21. W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).
  22. J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell-time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
    [CrossRef]
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    [CrossRef]
  24. F. Shi, “Study on the key techniques of magnetorheological finishing for high-precision optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2009) [in Chinese].
  25. C. Song, Y. Dai, and X. Peng, “Model and algorithm based on accurate realization of dwell time in magnetorheological finishing,” Appl. Opt. 49, 3676–3683 (2010).
    [CrossRef]
  26. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003).
    [CrossRef]
  27. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).
  28. D. W. Kim and S. W. Kim, “Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes,” Opt. Express 13, 910–917 (2005).
    [CrossRef]
  29. C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
    [CrossRef]
  30. H. Li, D. D. Walker, G. Yu, and W. Zhang, “Modeling and validation of polishing tool influence functions for manufacturing segments for an extremely large telescope,” Appl. Opt. 52, 5781–5787 (2013).
    [CrossRef]
  31. C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).
  32. H. Fang, P. Guo, and J. Yu, “Dwell function algorithm in fluid jet polishing,” Appl. Opt. 45, 4291–4296 (2006).
    [CrossRef]
  33. L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008) [in Chinese].

2013 (3)

2012 (1)

2010 (2)

C. Song, Y. Dai, and X. Peng, “Model and algorithm based on accurate realization of dwell time in magnetorheological finishing,” Appl. Opt. 49, 3676–3683 (2010).
[CrossRef]

H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).

2009 (3)

2007 (2)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

2006 (2)

2005 (1)

2003 (1)

2001 (1)

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[CrossRef]

2000 (2)

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599–611 (2000).
[CrossRef]

1999 (1)

J. W. Carr, “Atmospheric pressure plasma processing for damage-free optics and surfaces,” Eng. Res. Dev. Technol. 3, 31–39 (1999).

1998 (1)

1996 (1)

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[CrossRef]

1995 (1)

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

1994 (1)

1992 (1)

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

1989 (1)

L. N. Allen and R. E. Keim, “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33–50 (1989).

1988 (1)

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74–81 (1988).
[CrossRef]

1987 (1)

S. R. Wilson and J. R. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–324 (1987).
[CrossRef]

1983 (1)

R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra 17, 34–39 (1983).

1977 (1)

1927 (1)

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Allen, L. N.

L. N. Allen and R. E. Keim, “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33–50 (1989).

Beaucamp, A.

Bifano, T. G.

P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599–611 (2000).
[CrossRef]

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Bingham, R. G.

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

Brooks, D.

D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003).
[CrossRef]

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

Carnal, C. L.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Carr, J. W.

J. W. Carr, “Atmospheric pressure plasma processing for damage-free optics and surfaces,” Eng. Res. Dev. Technol. 3, 31–39 (1999).

Dai, Y.

C. Song, Y. Dai, and X. Peng, “Model and algorithm based on accurate realization of dwell time in magnetorheological finishing,” Appl. Opt. 49, 3676–3683 (2010).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

Davison, W. B.

Deng, W.

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Derigne, S. T.

Drueding, T. W.

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Egert, C. M.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Evans, R.

Fähnle, W.

Fang, H.

Fawcett, S. C.

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Feinberg, M. R.

Frankena, H. J.

Freeman, R.

Guo, P.

Guo, Y.

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Hille, B. B.

Horenstein, M. N.

Hylton, K. W.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

Jacobs, S.

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[CrossRef]

Jiao, C.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

Jones, R. A.

R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra 17, 34–39 (1983).

R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16, 218–224 (1977).
[CrossRef]

Kang, H.

H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).

Keim, R. E.

L. N. Allen and R. E. Keim, “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33–50 (1989).

Kim, D. H.

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

Kim, D. W.

Kim, J.

H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).

Kim, S. W.

King, A.

Kordonski, W.

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[CrossRef]

Lee, H.

H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[CrossRef]

Li, H.

Li, S.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

Lu, Z.

Martin, H. M.

McCavana, G.

McNeil, J. R.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74–81 (1988).
[CrossRef]

S. R. Wilson and J. R. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–324 (1987).
[CrossRef]

Messelink, W.

Morton, R.

Nagel, R. H.

Pan, R.

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

Peng, X.

Peng, Y.

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Preston, F. W.

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Reicher, D. W.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74–81 (1988).
[CrossRef]

Riley, D.

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

Sandri, G.

Sayle, A.

Shanbhag, P. M.

Shi, F.

F. Shi, “Study on the key techniques of magnetorheological finishing for high-precision optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2009) [in Chinese].

Shi, Y.

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Song, C.

Sun, Z.

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Trebisky, T. J.

van Brug, H.

Walker, D. D.

Wang, C.

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Wang, T.

Wang, X.

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Wang, Z.

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

West, S. C.

Wilson, S. R.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74–81 (1988).
[CrossRef]

S. R. Wilson and J. R. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–324 (1987).
[CrossRef]

Wu, J.

Xie, X.

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

Xie, Y.

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

Xu, Q.

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Yang, M.

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[CrossRef]

Yang, X.

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

Young, R. S.

Yu, G.

Yu, J.

Zhang, H.

Zhang, W.

Zhang, X.

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Zheng, L.

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Zhou, L.

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008) [in Chinese].

Appl. Opt. (10)

R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16, 218–224 (1977).
[CrossRef]

P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion beam machining of millimeter scale optics,” Appl. Opt. 39, 599–611 (2000).
[CrossRef]

W. Fähnle, H. van Brug, and H. J. Frankena, “Fluid jet polishing of optical surfaces,” Appl. Opt. 37, 6771–6773 (1998).
[CrossRef]

S. C. West, H. M. Martin, R. H. Nagel, R. S. Young, W. B. Davison, T. J. Trebisky, S. T. Derigne, and B. B. Hille, “Practical design and performance of the stressed-lap polishing tool,” Appl. Opt. 33, 8094–8100 (1994).
[CrossRef]

J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell-time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
[CrossRef]

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
[CrossRef]

H. Fang, P. Guo, and J. Yu, “Dwell function algorithm in fluid jet polishing,” Appl. Opt. 45, 4291–4296 (2006).
[CrossRef]

C. Song, Y. Dai, and X. Peng, “Model and algorithm based on accurate realization of dwell time in magnetorheological finishing,” Appl. Opt. 49, 3676–3683 (2010).
[CrossRef]

G. Yu, D. D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51, 6637–6640 (2012).
[CrossRef]

H. Li, D. D. Walker, G. Yu, and W. Zhang, “Modeling and validation of polishing tool influence functions for manufacturing segments for an extremely large telescope,” Appl. Opt. 52, 5781–5787 (2013).
[CrossRef]

Chin. Opt. Lett. (1)

Eng. Res. Dev. Technol. (1)

J. W. Carr, “Atmospheric pressure plasma processing for damage-free optics and surfaces,” Eng. Res. Dev. Technol. 3, 31–39 (1999).

Int. J. Mod. Phys. B (1)

W. Kordonski and S. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2837–2848 (1996).
[CrossRef]

J. Mech. Eng. (1)

C. Wang, Y. Guo, Z. Wang, R. Pan, and Y. Xie, “Dynamic removal function modeling of bonnet tool polishing on optics elements,” J. Mech. Eng. 49, 19–25 (2013) [in Chinese].
[CrossRef]

J. Mech. Sci. Tech. (1)

H. Lee, J. Kim, and H. Kang, “Airbag tool polishing for aspherical glass lens molds,” J. Mech. Sci. Tech. 24, 153–158 (2010).

J. Soc. Glass Technol. (1)

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).

Nanotechnol. Precis. Eng. (1)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nanotechnol. Precis. Eng. 5, 107–112 (2007).

Opt. Eng. (1)

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40, 1936–1943 (2001).
[CrossRef]

Opt. Express (4)

Opt. Precis. Eng. (1)

W. Deng, L. Zheng, Y. Shi, X. Wang, and X. Zhang, “Dwell-time algorithm based on matrix algebra and regularization method,” Opt. Precis. Eng. 15, 1009–1015 (2007).

Photonics Spectra (1)

R. A. Jones, “Computer control for grinding and polishing,” Photonics Spectra 17, 34–39 (1983).

Precis. Eng. (1)

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Proc. SPIE (5)

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54–62 (1992).

L. N. Allen and R. E. Keim, “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33–50 (1989).

R. G. Bingham, D. D. Walker, D. H. Kim, D. Brooks, R. Freeman, and D. Riley, “A novel automated process for aspheric surfaces,” Proc. SPIE 4093, 445–448 (2000).

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[CrossRef]

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[CrossRef]

Other (3)

F. Shi, “Study on the key techniques of magnetorheological finishing for high-precision optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2009) [in Chinese].

C. Wang, Z. Wang, X. Yang, Z. Sun, Y. Peng, Y. Guo, and Q. Xu, “Modeling of the static tool influence function of bonnet polishing based on FEA,” Int. J. Adv. Manuf. Technol. (to be published).

L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008) [in Chinese].

Supplementary Material (2)

» Media 1: MOV (1814 KB)     
» Media 2: MOV (1793 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

Tool movement model in BP.

Fig. 2.
Fig. 2.

Schematic diagram of the material removal process of BP.

Fig. 3.
Fig. 3.

Flow chart of the self-adaptive iterative algorithm.

Fig. 4.
Fig. 4.

Measured TIFs used in the simulation. (a) TIF1, diameter=30mm and (b) TIF2, diameter=16mm.

Fig. 5.
Fig. 5.

Initial surface error map of the fused silica part. (a) Measurement results from the interferometer and (b) the preprocessed surface error.

Fig. 6.
Fig. 6.

Surface residual error after the first simulation process using the self-adaptive iterative algorithm. (a) The whole surface and (b) 400mm×400mm of the center part. (The simulation process is provided in the accompanying movie clip, Media 1.)

Fig. 7.
Fig. 7.

Solution results of (a) the dwell-time distribution and (b) the velocity distribution.

Fig. 8.
Fig. 8.

Surface residual error after the second simulation process using the self-adaptive iterative algorithm. (a) The whole surface and (b) 400mm×400mm of the center part.

Fig. 9.
Fig. 9.

Surface error shape. (a) The initial surface error and (b) the surface residual error of the central 400mm×400mm area after the simulation polishing process when ξ=0.3235 (0.3235=0.9522).

Fig. 10.
Fig. 10.

Changing curve of the final surface residual convergent RMS and its convergence ratio vary with the damping factor.

Fig. 11.
Fig. 11.

Surface error shape. (a) The initial surface error and (b) the surface residual error of the central 970mm×970mm area after the simulation polishing process. (The simulation process is provided in the accompanying movie clip, Media 2.)

Equations (8)

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Δh(x,y)=k·p(x,y)·v(x,y),
H(x,y)=R(x,y)**D(x,y).
E(x,y)=H0(x,y)H(x,y),
VR=ΩR(x,y)dxdy,
D0=H0/VR,
E0=H0R**D0.
H0=H0min(H0).
rnr×1=Bnr×nttnt×1,

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