Abstract

Optical surfaces can be accurately figured by computer controlled optical surfacing (CCOS) that uses well characterized sub-diameter polishing tools driven by numerically controlled (NC) machines. The motion of the polishing tool is optimized to vary the dwell time of the polisher on the workpiece according to the desired removal and the calibrated tool influence function (TIF). Operating CCOS with small and very well characterized TIF achieves excellent performance, but it takes a long time. This overall polishing time can be reduced by performing sequential polishing runs that start with large tools and finish with smaller tools. In this paper we present a variation of this technique that uses a set of different size TIFs, but the optimization is performed globally – i.e. simultaneously optimizing the dwell times and tool shapes for the entire set of polishing runs. So the actual polishing runs will be sequential, but the optimization is comprehensive. As the optimization is modified from the classical method to the comprehensive non-sequential algorithm, the performance improvement is significant. For representative polishing runs we show figuring efficiency improvement from ~88% to ~98% in terms of residual RMS (root-mean-square) surface error and from ~47% to ~89% in terms of residual RMS slope error.

© 2009 OSA

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  1. R. A. Jones, “Computer control for grinding and polishing,” Photon. Spectra , 34–39 (1963).
  2. R. Aspden, R. McDonough, and F. R. Nitchie., “Computer assisted optical surfacing,” Appl. Opt. 11(12), 2739–2747 (1972).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  5. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25, 785–790 (1986).
  6. J. R. Johnson, and E. Waluschka, “Optical fabrication-process modeling-analysis tool box,” in Manufacturing and metrology tooling for the Solar-A Soft X-Ray Telescope, W.R. Sigman, L.V. Burns, C.G. Hull-Allen, A.F. Slomba, and R.G. Kusha, eds., Proc. SPIE 1333, 106–117 (1990).
  7. 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(8), 958–964 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. S. D. Jacobs, “International innovations in optical finishing,” in Current Developments in Lens Design and Optical Engineering V, P.Z. Mouroulis, W.J. Smith, and R.B. Johnson, eds., Proc. SPIE 5523, 264–272 (2004).
  11. J. H. Burge, S. Benjamin, D. Caywood, C. Noble, M. Novak, C. Oh, R. Parks, B. Smith, P. Su, M. Valente, and C. Zhao, “Fabrication and testing of 1.4-m convex off-axis aspheric optical surfaces,” in Optical Manufacturing and Testing VIII, J. H. Burge; O. W. Fähnle and R. Williamson, eds., Proc. SPIE 7426, 74260L1–12 (2009).
  12. M. Johns, “The Giant Magellan Telescope (GMT),” in Extremely Large Telescopes: Which Wavelengths? T. E. Andersen, eds., Proc. SPIE 6986, 698603 1–12 (2008).
  13. J. Nelson, and G. H. Sanders, “The status of the Thirty Meter Telescope project,” in Ground-based and Airborne Telescopes II, L. M. Stepp and R. Gilmozzi, eds., Proc. SPIE 7012, 70121A1–18 (2008).
  14. D. D. Walker, A. P. Doel, R. G. Bingham, D. Brooks, A. M. King, G. Peggs, B. Hughes, S. Oldfield, C. Dorn, H. McAndrews, G. Dando, and D. Riley, “Design Study Report: The Primary and Secondary Mirrors for the Proposed Euro50 Telescope” (2002), http://www.zeeko.co.uk/papers/dl/New%20Study%20Report%20V%2026.pdf .
  15. T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, J.R.P. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 214–225 (2003).
  16. A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 towards a European ELT,” in Ground-based and Airborne Telescopes, L. M. Stepp, eds., Proc. SPIE 6267, 626725 1–10 (2006).
  17. R. E. Parks, “Specifications: Figure and Finish are not enough,” in An optical Believe It or Not: Key Lessons Learned, M. A. Kahan, eds., Proc. SPIE 7071, 70710B1–9 (2008).
  18. J. M. Hill, “Optical Design, Error Budget and Specifications for the Columbus Project Telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, eds., Proc. SPIE 1236, 86–107 (1990).
  19. 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] [PubMed]
  20. A. P. Bogodanov, “Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool,” Sov. J. Opt. Technol. 52, 409–413 (1985).
  21. C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithms for ion beam milling of optical components,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 1752, 54–62 (1992).
  22. M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
    [CrossRef]
  23. H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40(9), 1936–1943 (2001).
    [CrossRef]
  24. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in C (Cambridge, 1988)
  25. C. Bob, Crawford, Don Loomis, Norm Schenck, and Bill Anderson, Optical Engineering and Fabrication Facility, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, (personal communication, 2008).
  26. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Edge tool influence function library using the parametric edge model for computer controlled optical surfacing,” in Optical Manufacturing and Testing VIII, J. H. Burge; O. W. Fähnle and R. Williamson, Proc. SPIE 7426, 74260G1–12 (2009).
  27. P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).
  28. A. Heller, “Safe and sustainable energy with LIFE” (2009), https://str.llnl.gov/AprMay09/pdfs/05.09.02.pdf .
  29. H. H. Barrett, and K. J. Myers, Foundations of Image Science (Wiley, 2004)
  30. D. W. Kim, and S. W. Kim, “Novel simulation technique for efficient fabrication of 2m class hexagonal segments for extremely large telescope primary mirrors,” in Optical Design and Testing II, Y. Wang, Z. Weng, S. Ye and J. M. Sasian, eds., Proc. SPIE 5638, 48–59 (2005).

2009 (1)

2005 (1)

2003 (1)

2002 (1)

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

2001 (1)

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40(9), 1936–1943 (2001).
[CrossRef]

1996 (1)

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

1986 (1)

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25, 785–790 (1986).

1985 (1)

A. P. Bogodanov, “Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool,” Sov. J. Opt. Technol. 52, 409–413 (1985).

1983 (1)

R. A. Jones, “Computer-controlled polishing of telescope mirror segments,” Opt. Eng. 22, 236–240 (1983).

1974 (1)

1972 (1)

1963 (1)

R. A. Jones, “Computer control for grinding and polishing,” Photon. Spectra , 34–39 (1963).

Ando, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

Aspden, R.

Bogodanov, A. P.

A. P. Bogodanov, “Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool,” Sov. J. Opt. Technol. 52, 409–413 (1985).

Brooks, D.

Burge, J. H.

Deguchi, A.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

Denker, C. J.

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Didkovsky, L. I.

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Freeman, R.

Goode, P. R.

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Jones, R. A.

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25, 785–790 (1986).

R. A. Jones, “Computer-controlled polishing of telescope mirror segments,” Opt. Eng. 22, 236–240 (1983).

R. A. Jones, “Computer control for grinding and polishing,” Photon. Spectra , 34–39 (1963).

Kim, D. W.

Kim, S. W.

King, A.

Kuhn, J. R.

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Lee, H.

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40(9), 1936–1943 (2001).
[CrossRef]

McCavana, G.

McDonough, R.

Morton, R.

Nakamura, N.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

Negishi, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

Nitchie, F. R.

Park, W. H.

Shannon, R. R.

Takimoto, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

Wagner, R. E.

Walker, D. D.

Wang, H.

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Yang, M.

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40(9), 1936–1943 (2001).
[CrossRef]

Appl. Opt. (2)

J. Jpn. Soc. Precis. Eng. (1)

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, and N. Nakamura, “Studies on super-smooth polishing (2nd report),” J. Jpn. Soc. Precis. Eng. 62, 408–412 (1996).
[CrossRef]

J. Korean Astron. Soc. (1)

P. R. Goode, C. J. Denker, L. I. Didkovsky, J. R. Kuhn, and H. Wang, “1.6 m Solar Telescope in Big Bear – the NST,” J. Korean Astron. Soc. 35, 1–8 (2002).

Opt. Eng. (3)

H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. 40(9), 1936–1943 (2001).
[CrossRef]

R. A. Jones, “Computer-controlled polishing of telescope mirror segments,” Opt. Eng. 22, 236–240 (1983).

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25, 785–790 (1986).

Opt. Express (3)

Photon. Spectra (1)

R. A. Jones, “Computer control for grinding and polishing,” Photon. Spectra , 34–39 (1963).

Sov. J. Opt. Technol. (1)

A. P. Bogodanov, “Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool,” Sov. J. Opt. Technol. 52, 409–413 (1985).

Other (18)

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithms for ion beam milling of optical components,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 1752, 54–62 (1992).

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” in Window and Dome Technologies VIII, R. W. Tustison, eds., Proc. SPIE 5078, 90–96 (2003).

J. R. Johnson, and E. Waluschka, “Optical fabrication-process modeling-analysis tool box,” in Manufacturing and metrology tooling for the Solar-A Soft X-Ray Telescope, W.R. Sigman, L.V. Burns, C.G. Hull-Allen, A.F. Slomba, and R.G. Kusha, eds., Proc. SPIE 1333, 106–117 (1990).

S. D. Jacobs, “International innovations in optical finishing,” in Current Developments in Lens Design and Optical Engineering V, P.Z. Mouroulis, W.J. Smith, and R.B. Johnson, eds., Proc. SPIE 5523, 264–272 (2004).

J. H. Burge, S. Benjamin, D. Caywood, C. Noble, M. Novak, C. Oh, R. Parks, B. Smith, P. Su, M. Valente, and C. Zhao, “Fabrication and testing of 1.4-m convex off-axis aspheric optical surfaces,” in Optical Manufacturing and Testing VIII, J. H. Burge; O. W. Fähnle and R. Williamson, eds., Proc. SPIE 7426, 74260L1–12 (2009).

M. Johns, “The Giant Magellan Telescope (GMT),” in Extremely Large Telescopes: Which Wavelengths? T. E. Andersen, eds., Proc. SPIE 6986, 698603 1–12 (2008).

J. Nelson, and G. H. Sanders, “The status of the Thirty Meter Telescope project,” in Ground-based and Airborne Telescopes II, L. M. Stepp and R. Gilmozzi, eds., Proc. SPIE 7012, 70121A1–18 (2008).

D. D. Walker, A. P. Doel, R. G. Bingham, D. Brooks, A. M. King, G. Peggs, B. Hughes, S. Oldfield, C. Dorn, H. McAndrews, G. Dando, and D. Riley, “Design Study Report: The Primary and Secondary Mirrors for the Proposed Euro50 Telescope” (2002), http://www.zeeko.co.uk/papers/dl/New%20Study%20Report%20V%2026.pdf .

T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 Extremely Large Telescope,” in Future Giant Telescopes, J.R.P. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 214–225 (2003).

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 towards a European ELT,” in Ground-based and Airborne Telescopes, L. M. Stepp, eds., Proc. SPIE 6267, 626725 1–10 (2006).

R. E. Parks, “Specifications: Figure and Finish are not enough,” in An optical Believe It or Not: Key Lessons Learned, M. A. Kahan, eds., Proc. SPIE 7071, 70710B1–9 (2008).

J. M. Hill, “Optical Design, Error Budget and Specifications for the Columbus Project Telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, eds., Proc. SPIE 1236, 86–107 (1990).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in C (Cambridge, 1988)

C. Bob, Crawford, Don Loomis, Norm Schenck, and Bill Anderson, Optical Engineering and Fabrication Facility, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, (personal communication, 2008).

D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Edge tool influence function library using the parametric edge model for computer controlled optical surfacing,” in Optical Manufacturing and Testing VIII, J. H. Burge; O. W. Fähnle and R. Williamson, Proc. SPIE 7426, 74260G1–12 (2009).

A. Heller, “Safe and sustainable energy with LIFE” (2009), https://str.llnl.gov/AprMay09/pdfs/05.09.02.pdf .

H. H. Barrett, and K. J. Myers, Foundations of Image Science (Wiley, 2004)

D. W. Kim, and S. W. Kim, “Novel simulation technique for efficient fabrication of 2m class hexagonal segments for extremely large telescope primary mirrors,” in Optical Design and Testing II, Y. Wang, Z. Weng, S. Ye and J. M. Sasian, eds., Proc. SPIE 5638, 48–59 (2005).

Supplementary Material (3)

» Media 1: AVI (1468 KB)     
» Media 2: AVI (1861 KB)     
» Media 3: AVI (1725 KB)     

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Figures (8)

Fig. 1
Fig. 1

Orbital (left) and spin (right) tool motion with their parametric edge TIFs [19].

Fig. 2
Fig. 2

Flow chart for the non-sequential optimization technique using the gradient descent method

Fig. 6
Fig. 6

Complementary TIF library

Fig. 3
Fig. 3

Optimization results for Case 1.1-1.4

Fig. 4
Fig. 4

Randomly generated 1.6m target removal map (surface RMS: 701nm, slope error RMS: 0.522arcsed, error volume: 1.31cm3)

Fig. 5
Fig. 5

(Media 1, Media 2, Media 3) Three simulation results for 1.6m NST target removal map.

Fig. 6
Fig. 6

Complementary TIF library (continued)

Fig. 6
Fig. 6

Complementary TIF library (continued)

Tables (3)

Tables Icon

Table 3 Parameters for the TIF library generation g

Tables Icon

Table 1 Parameters for the polishing simulation

Tables Icon

Table 2 Surface specifications before and after polishing process for Case 2.1-2.3 e

Equations (11)

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

R e m o v a l _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) = D w e l l _ t i m e _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) * * T I F ( x T I F , y T I F , x w o r k p i e c e , y w o r k p i e c e )
F O M t o t a l R S S R M S _ e r r o r s = i = 1 6 C i F O M i 2
F O M 1 R M S o f P o s i t i v e E r r o r M a p = M + { e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F O M 2 R M S o f N e g a t i v e E r r o r M a p = M { e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F O M 3 R M S o f x S l o p e M a p = M { x e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F O M 4 R M S o f y S l o p e M a p = M { y e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F O M 5 R M S o f x C u r v a t u r e M a p = M { 2 x 2 e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F O M 6 R M S o f y C u r v a t u r e M a p = M { 2 y 2 e r r o r _ m a p ( x , y ) } 2 d x d y / M d x d y
F E R M S i n i t i a l _ e r r o r _ m a p R M S r e s i d u a l _ e r r o r _ m a p R M S i n i t i a l _ e r r o r _ m a p 100                     ​ ​ [ % ] .
F F [ R e m o v a l _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) ] = F F [ D w e l l _ t i m e _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) * * T I F ( x T I F , y T I F ) ] = F F [ D w e l l _ t i m e _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) ] F F [ T I F ( x T I F , y T I F ) ]
D w e l l _ t i m e _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) = F F 1 [ F F [ R e m o v a l _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) ] F F [ T I F ( x T I F , y T I F ) ] ] = F F 1 [ F F [ T a r g e t _ r e m o v a l _ m a p ( x w o r k p i e c e , y w o r k p i e c e ) ] F F [ T I F ( x T I F , y T I F ) ] ]

Metrics