Abstract

We present a theoretical modeling method to predict the ring tool influence function (TIF) based on the computer-controlled active lap process. The gap on the lap-grinding layer is considered, and its influence on the ring TIF is analyzed too. The relationship between the shape of the ring TIF and the lap-workpiece rotation speed ratio is discussed in this paper. The recipe for calculating dwell time for axisymmetric fabrication is discussed. The grinding process of a 1.8 m primary mirror is improved based on these results. The grinding process is accomplished after 30 circles of grinding, and the surface shape error is from PV 82 μm RMS 16.4 μm reduced to PV 13.5 μm RMS 2.5 μm.

© 2013 Optical Society of America

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  1. H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
    [CrossRef]
  2. D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
    [CrossRef]
  3. D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
    [CrossRef]
  4. H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
    [CrossRef]
  5. H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
    [CrossRef]
  6. H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
    [CrossRef]
  7. B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
    [CrossRef]
  8. F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).
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    [CrossRef]
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  11. 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).
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    [CrossRef]
  14. D. W. Kim, S. W. Kim, and J. H. Burge, “Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions,” Opt. Express 17, 21850–21866 (2009).
    [CrossRef]
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    [CrossRef]
  18. Y. Li and D. Wang, “New design deforming controlling system of the active stressed lap,” Proc. SPIE 7018, 701833 (2008).
    [CrossRef]
  19. M. Chen, Y. Feng, Y. Wan, L. Yang, and B. Fan, “Neural network based surface shape modeling of stressed lap optical polishing,” Appl. Opt. 49, 1350–1354 (2010).
    [CrossRef]
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  21. A. Cordero-Davila, J. Gonzalez-Garcia, M. Pedrayes-Lopez, L. A. Aguilar-Chiu, J. Cuautle-Cortes, and C. Robledo-Sanchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43, 1250–1254 (2004).
    [CrossRef]
  22. “Adaptive quadrature,” Wikipedia, http://en.wikipedia.org/wiki/Adaptive_quadrature .

2013 (1)

2011 (1)

2010 (5)

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

M. Chen, Y. Feng, Y. Wan, L. Yang, and B. Fan, “Neural network based surface shape modeling of stressed lap optical polishing,” Appl. Opt. 49, 1350–1354 (2010).
[CrossRef]

C. Miao, J. C. Lambropoulos, and S. D. Jacob, “Process parameter effects on material removal in magnetorheological finishing of borosilicate glass,” Appl. Opt. 49, 1951–1963 (2010).
[CrossRef]

Z. Li, S. Li, Y. Dai, and X. Peng, “Optimization and application of influence function in abrasive jet polishing,” Appl. Opt. 49, 2947–2953 (2010).
[CrossRef]

2009 (1)

2008 (2)

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Y. Li and D. Wang, “New design deforming controlling system of the active stressed lap,” Proc. SPIE 7018, 701833 (2008).
[CrossRef]

2007 (1)

L. Zhang and Z. Zeng, “Structural optimization of active stressed lap,” Opt. Electron. Eng. 34, 11–15 (2007).

2006 (1)

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

2005 (1)

2004 (2)

A. Cordero-Davila, J. Gonzalez-Garcia, M. Pedrayes-Lopez, L. A. Aguilar-Chiu, J. Cuautle-Cortes, and C. Robledo-Sanchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43, 1250–1254 (2004).
[CrossRef]

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

1999 (1)

H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
[CrossRef]

1994 (2)

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[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]

1992 (1)

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

1990 (1)

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

1927 (1)

F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).

Aguilar-Chiu, L. A.

Allen, R. G.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
[CrossRef]

Anderson, D.

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Anderson, D. S.

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Angel, J. R. P.

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Burge, J.

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[CrossRef]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Burge, J. H.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

D. W. Kim, S. W. Kim, and J. H. Burge, “Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions,” Opt. Express 17, 21850–21866 (2009).
[CrossRef]

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
[CrossRef]

Chen, M.

Chen, Q.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

Cordero-Davila, A.

Cuautle-Cortes, J.

Cuerden, B.

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Dai, Y.

David, W.

Davison, W. B.

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Deng, J.

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

DeRigne, S. T.

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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Fan, B.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

M. Chen, Y. Feng, Y. Wan, L. Yang, and B. Fan, “Neural network based surface shape modeling of stressed lap optical polishing,” Appl. Opt. 49, 1350–1354 (2010).
[CrossRef]

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Feng, Y.

Gao, P.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

Gonzalez-Garcia, J.

Hille, B. B.

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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Jacob, S. D.

Jiang, W.

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

Ketelsen, D. A.

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[CrossRef]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Kim, D. W.

Kim, S. W.

Kingsley, J. S.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Kittrell, W. C.

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Lambropoulos, J. C.

Li, H.

Li, S.

Li, X.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

Li, Y.

Y. Li and D. Wang, “New design deforming controlling system of the active stressed lap,” Proc. SPIE 7018, 701833 (2008).
[CrossRef]

Li, Z.

Ling, N.

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

Luo, X.

Lutz, R. D.

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Martin, H.

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Martin, H. M.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
[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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Miao, C.

Miller, S. M.

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Nagel, R. H.

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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Pedrayes-Lopez, M.

Peng, X.

Preston, F.

F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).

Robledo-Sanchez, C.

Trebisky, T. J.

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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

Tuell, M.

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

Tuell, M. T.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

Wan, Y.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

M. Chen, Y. Feng, Y. Wan, L. Yang, and B. Fan, “Neural network based surface shape modeling of stressed lap optical polishing,” Appl. Opt. 49, 1350–1354 (2010).
[CrossRef]

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Wang, D.

Y. Li and D. Wang, “New design deforming controlling system of the active stressed lap,” Proc. SPIE 7018, 701833 (2008).
[CrossRef]

West, S. C.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Yang, L.

M. Chen, Y. Feng, Y. Wan, L. Yang, and B. Fan, “Neural network based surface shape modeling of stressed lap optical polishing,” Appl. Opt. 49, 1350–1354 (2010).
[CrossRef]

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Young, R. S.

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]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

Yu, G.

Zeng, Z.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

L. Zhang and Z. Zeng, “Structural optimization of active stressed lap,” Opt. Electron. Eng. 34, 11–15 (2007).

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

Zhang, L.

L. Zhang and Z. Zeng, “Structural optimization of active stressed lap,” Opt. Electron. Eng. 34, 11–15 (2007).

Zhang, W.

Zhang, X.

Zhao, C.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

Zheng, L.

Zhou, J.

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

Zobrist, T.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

Appl. Opt. (7)

High Power Laser and Particle Beams (1)

Z. Zeng, J. Deng, X. Li, N. Ling, and W. Jiang, “Investigation of deformation experiment for active polishing lap,” High Power Laser and Particle Beams 16, 555–559 (2004).

J. Soc. Glass Technol. (1)

F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).

Opt. Electron. Eng. (1)

L. Zhang and Z. Zeng, “Structural optimization of active stressed lap,” Opt. Electron. Eng. 34, 11–15 (2007).

Opt. Express (2)

Proc. SPIE (9)

B. Fan, Y. Wan, L. Yang, Z. Zeng, J. Deng, and X. Li, “The grind and polish prediction of computer controlled active lap,” Proc. SPIE 6148, 61480Z (2006).
[CrossRef]

Y. Li and D. Wang, “New design deforming controlling system of the active stressed lap,” Proc. SPIE 7018, 701833 (2008).
[CrossRef]

H. Martin, D. Anderson, J. R. P. Angel, R. H. Nagel, S. C. West, and R. S. Young, “Progress in the stressed-lap polishing of a 1.8  m f/1 mirror,” Proc. SPIE 1236, 682–690 (1990).
[CrossRef]

D. S. Anderson, J. R. P. Angel, J. Burge, W. B. Davison, S. T. DeRigne, B. B. Hille, D. A. Ketelsen, W. C. Kittrell, H. M. Martin, R. H. Nagel, T. J. Trebisky, S. C. West, and R. S. Young, “Stressed-lap polishing of 3.5  m f/1.5 and 1.8  m f/1.0 mirrors,” Proc. SPIE 1531, 260–269 (1992).
[CrossRef]

D. Anderson, H. Martin, J. Burge, D. A. Ketelsen, and S. C. West, “Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory,” Proc. SPIE 2199, 199–210 (1994).
[CrossRef]

H. M. Martin, R. G. Allen, and J. H. Burge, “Polishing of a 6.5  m f/1.25 mirror for the first Magellan telescope,” Proc. SPIE 3739, 47–55 (1999).
[CrossRef]

H. M. Martin, J. H. Burge, B. Cuerden, W. B. Davison, J. S. Kingsley, R. D. Lutz, S. M. Miller, and M. Tuell, “Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope,” Proc. SPIE 7018, 70180G (2008).
[CrossRef]

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4  m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7709, 77390A (2010).
[CrossRef]

B. Fan, Z. Zeng, X. Li, Q. Chen, P. Gao, J. Zhou, and Y. Wan, “Grinding and polishing technology by computer controlled active lap for Φ1250  mm F/1.5 aspheric mirror,” Proc. SPIE 7654, 765409 (2010).
[CrossRef]

Other (1)

“Adaptive quadrature,” Wikipedia, http://en.wikipedia.org/wiki/Adaptive_quadrature .

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Figures (13)

Fig. 1.
Fig. 1.

Motion of mirror and active lap in grinding (a) and the sketch for removed material calculation (b), where the arc MN is the route the mirror surface point A moves across the lap in one running circle.

Fig. 2.
Fig. 2.

Ring TIFs of the active lap at different locations (i.e., different e). The removed materials are normalized by the maximum value of the TIF with e equal to 760 mm. The other parameters are P=const, ω=1.

Fig. 3.
Fig. 3.

Gap layout for grind layer (a) and for polyurethane pad (b).

Fig. 4.
Fig. 4.

Ring TIFs for different running circle times with circular gap (a) and grid gap (b). e=500mm, ω=1, P=constant. The blue dash line represents the TIF without a gap (i.e., only the center hole is considered). The red solid line is for the TIF with a gap after one running circle. The green, cyan, and magenta solid lines are for the average TIFs with gaps after 5, 10, and 40 times running circles, respectively. Each running circle starts with different θ0 (uniformly distributed on [0, 2π]).

Fig. 5.
Fig. 5.

Difference from the ideal TIF curve, normalized by the maximum value of ideal TIF.

Fig. 6.
Fig. 6.

Relative velocity distribution for different ω (e=500mm).

Fig. 7.
Fig. 7.

Maximum of relative velocity varying with ω (e=500mm).

Fig. 8.
Fig. 8.

Ring TIFs of active lap with different ω (e=500mm). The lap center hole is not considered.

Fig. 9.
Fig. 9.

Active lap ring TIF experimental setup (a), (b) and measure method (c).

Fig. 10.
Fig. 10.

TIF comparison between the experiments and the theoretical prediction. [The lap position e is 175 mm, the mirror rotate speed is 2.7 rpm, and the lap rotate speed is (a) 6 rpm, (b) 6rpm, and (c) 3.7rpm.]

Fig. 11.
Fig. 11.

Active lap smooth capability for different ω. (The active lap is moved from 160 to 760 mm; 60 lap positions and 100 sample points were used.)

Fig. 12.
Fig. 12.

Convergent curve of 1.8 m primary mirror in the grinding.

Fig. 13.
Fig. 13.

Final surface shape error of the 1.8 m primary mirror after the grinding process. (unit: μm).

Tables (1)

Tables Icon

Table 1. Dimensions of 1.8 m Honeycomb Primary Mirror

Equations (18)

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

dz(x,y)=k·P(x,y)·V(x,y)·dt,
RA(ρA,e,ω)=MNk·P(ρA,θ,e)·V(ρA,θ,e,ω)·dt,
RA(ρA,e,ω)=k0TP(ρA,θ,e)·V(ρA,θ,e,ω)·dt,
RA(ρA,e,ω)=kω1θAθAP(ρA,θ,e)·V(ρA,θ,e,ω)·dθ,
V=ω1[(1ω)yA,(ω1)xAω·e],
V(ρA,θ,e,ω)=ω1e2ω2+ρA2(1ω)22eρAω(ω1)cos(θ).
RA(ρA,e,ω)=kθAθAP(ρA,θ,e)·Vr(ρA,θ,e,ω)·dθ,
TIF(e,ω)=RA(ρA,e,ω),{ρAR:|ρAe|rL}.
G(ρA,θ,e,θ0)={1,Ais not in the gap0,Ais in the gap.
RA(ρA,e,ω,θ0)=kθAθAP(ρA,θ,e)·G(ρA,θ,e,θ0)·Vr(ρA,θ,e,ω)·dθ.
Vr=[(1ω)yA,(ω1)xAω·e],
MRj=i=1nti·TIFj(ei,ωi),j=1,2,m,
TIFj(ei,ωi)=RA(ρj,ei,ωi),
MRj=i=1nti·TIFji,j=1,2,m.
TIF·t=MR,
t=TIFMR.
{mint12TIF·tMR22st.t0.
E=12TIF·tMR22.

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