Abstract

Aspheric surfaces are widely used because of their desirable characteristics. Such a surface can obtain nearly perfect imaging quality with fewer optical elements and reduce the size and mass of optical systems. Various machine systems have been developed based on modern deterministic polishing technologies for large aperture aspheric surfaces. Several factors affect the final precision of large aperture aspheric surfaces, such as the velocity limit of the machine and the path design. Excess velocity, which will be truncated automatically by the computer numerical control system, may cause the dwell time to deviate from the desired time. When a path designed on a two-dimensional surface map with equidistant pitch is projected onto an aspheric surface, the pitch changes as a result of the varied curvature of the aspheric surface. This may affect the removal map and cause some ripple errors. A multiregion distribution strategy, which includes velocity checking, is proposed in this study to avoid exceeding the velocity limits. The strategy can be used to modify local errors and edge effects. A three-dimensional spiral path generation method is also presented using an iterative method to ensure uniformity in the space length of the adjacent circle of the spiral path. This process can reduce the ripple error caused by the overlapping of tool paths. A polishing experiment was conducted, and the results proved the validity of the proposed strategies.

© 2013 Optical Society of America

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References

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  1. D. Anderson and J. Burge, “Optical fabrication,” in The Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds. (Marcel Dekker Inc., 2001), pp. 915–955.
  2. 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]
  3. M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
    [CrossRef]
  4. R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
    [CrossRef]
  5. W. Kordonski and S. Gorodkin, “Material removal in magnetorheological finishing of optics,” Appl. Opt. 50, 1984–1994 (2011).
    [CrossRef]
  6. W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
    [CrossRef]
  7. D. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and control of mid-spatial frequency wavefront errors in optical systems,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1.
  8. D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).
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    [CrossRef]
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  11. R. Aspden, R. McDonough, and F. R. Nitchie, “Computer assisted optical surfacing,” Appl. Opt. 11, 2739–2747 (1972).
    [CrossRef]
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    [CrossRef]
  13. C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Nonnull interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50, 3559–3569 (2011).
    [CrossRef]
  14. P. E. Murphy, T. G. Brown, and D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39, 2122–2129 (2000).
    [CrossRef]
  15. P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.
  16. D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
    [CrossRef]
  17. A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
    [CrossRef]
  18. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25, 785–790 (1986).
    [CrossRef]
  19. H.-Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
    [CrossRef]

2013 (1)

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

2012 (1)

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

2011 (4)

W. Kordonski and S. Gorodkin, “Material removal in magnetorheological finishing of optics,” Appl. Opt. 50, 1984–1994 (2011).
[CrossRef]

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Nonnull interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50, 3559–3569 (2011).
[CrossRef]

2010 (1)

H.-Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

2009 (1)

2006 (2)

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

2004 (2)

A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
[CrossRef]

T. Kim, J. H. Burge, Y. Lee, and S. Kim, “Null test for a highly paraboloidal mirror,” Appl. Opt. 43, 3614–3618 (2004).
[CrossRef]

2000 (1)

1996 (1)

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996).
[CrossRef]

1986 (1)

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

1972 (1)

Aikens, D.

D. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and control of mid-spatial frequency wavefront errors in optical systems,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1.

Aikens, D. M.

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996).
[CrossRef]

Anderson, D.

D. Anderson and J. Burge, “Optical fabrication,” in The Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds. (Marcel Dekker Inc., 2001), pp. 915–955.

Aspden, R.

Beaucamp, A. T. H.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Brown, T. G.

Burge, J.

P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.

D. Anderson and J. Burge, “Optical fabrication,” in The Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds. (Marcel Dekker Inc., 2001), pp. 915–955.

Burge, J. H.

Castelli, M.

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

Chen, X.

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Cheng, H. B.

H.-Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

DeGroote, J. E.

D. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and control of mid-spatial frequency wavefront errors in optical systems,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1.

Demmler, M.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Doubrovski, V.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Dunger, T.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Dunn, C.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

English, R. E.

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996).
[CrossRef]

Evans, R.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Freeman, R.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Gorodkin, S.

Gould, A.

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

Jones, R. A.

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

Jourdain, R.

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

Kim, D. W.

Kim, S.

Kim, S.-W.

Kim, T.

Kiontke, S.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Klinger, C.

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

Kordonski, W.

W. Kordonski and S. Gorodkin, “Material removal in magnetorheological finishing of optics,” Appl. Opt. 50, 1984–1994 (2011).
[CrossRef]

A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
[CrossRef]

Kordonski, W. I.

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

Krüger, M.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Lawson, J. K.

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996).
[CrossRef]

Lee, Y.

Liao, D.

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Luca, A.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Mandina, M.

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

Martin, H.

P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.

McCavana, G.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

McDonough, R.

Moore, D. T.

Morantz, P.

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

Morton, R.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Murphy, P. E.

Nelson, J. D.

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

Nitchie, F. R.

Riley, D.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Rost, D.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Shore, P.

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

Shorey, A.

A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
[CrossRef]

Shorey, A. B.

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

Simms, J.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Tam, H.-Y.

H.-Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

Tang, C.

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Tian, C.

Tricard, M.

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
[CrossRef]

Walker, D. D.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Wei, T.

Wei, X.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Xie, R.

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Yang, Y.

Youngworth, R. N.

D. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and control of mid-spatial frequency wavefront errors in optical systems,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1.

Yu, G.

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

Yuan, Z.

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Zeuner, M.

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

Zhao, C.

P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.

Zhou, P.

P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.

Zhuo, Y.

Appl. Opt. (5)

J. Fluids Eng. (1)

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR Jet(TM)) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

J. Mater. Process. Technol. (1)

H.-Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

JEOS RP (1)

D. Liao, Z. Yuan, C. Tang, R. Xie, and X. Chen, “Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing,” JEOS RP 8, 13031 (2013).

Laser Focus World (1)

J. D. Nelson, A. Gould, C. Klinger, and M. Mandina, “High frequency and random motion rapidly smoothes optical surfaces,” Laser Focus World 47 (10), 71–74 (2011).

Opt. Eng. (1)

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

Opt. Express (1)

Proc. SPIE (5)

M. Demmler, M. Zeuner, A. Luca, T. Dunger, D. Rost, S. Kiontke, and M. Krüger, “Ion beam figuring of silicon aspheres,” Proc. SPIE 7934, 793416 (2011).
[CrossRef]

R. Jourdain, M. Castelli, P. Morantz, and P. Shore, “Plasma surface figuring of large optical components,” Proc. SPIE 8430, 843011 (2012).
[CrossRef]

J. K. Lawson, D. M. Aikens, and R. E. English, “Power spectral density specifications for high-power laser systems,” Proc. SPIE 2775, 345–356 (1996).
[CrossRef]

D. D. Walker, A. T. H. Beaucamp, V. Doubrovski, C. Dunn, R. Evans, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, G. Yu, and X. Wei, “Commissioning of the first Precessions 1.2  m CNC polishing machines for large optics,” Proc. SPIE 6288, 62880P (2006).
[CrossRef]

A. Shorey, W. Kordonski, and M. Tricard, “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99–107 (2004).
[CrossRef]

Other (3)

P. Zhou, H. Martin, C. Zhao, and J. Burge, “Mapping distortion correction for GMT interferometric test,” in Optical Fabrication and Testing, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW3D.2.

D. Anderson and J. Burge, “Optical fabrication,” in The Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds. (Marcel Dekker Inc., 2001), pp. 915–955.

D. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and control of mid-spatial frequency wavefront errors in optical systems,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuA1.

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Figures (12)

Fig. 1.
Fig. 1.

Diagram sketch of a five-axis machine system.

Fig. 2.
Fig. 2.

Diagram of the gesture of the URF stayed on a point on the workpiece.

Fig. 3.
Fig. 3.

Diagram of aspheric surface fabrication.

Fig. 4.
Fig. 4.

Velocity smoothing using the moving window averaging method: (a) original and (b) smoothened velocity curves.

Fig. 5.
Fig. 5.

Diagram of the multiregion distribution.

Fig. 6.
Fig. 6.

Diagram of the surface error distribution showing (a) the surface error map, (b) the binary image of the region divided by the target surface, and (c) the design result with the raster path.

Fig. 7.
Fig. 7.

Multiregion distribution strategy used for edge error modification: (a) initial surface error with edge effect, (b) designed region and path, and (c) surface error after edge modification.

Fig. 8.
Fig. 8.

Spiral path and its projection on the aspherical surface.

Fig. 9.
Fig. 9.

Peak-to-valley as a function of pitch: (a) result from Tam’s paper [19] with ellipse removal function and (b) result from the current study with the axisymmetric removal function.

Fig. 10.
Fig. 10.

Diagram of the iterative method.

Fig. 11.
Fig. 11.

3-D spiral path for the aspheric surface showing (a) an isometric view and (b) a top view.

Fig. 12.
Fig. 12.

Polishing results for the aspheric surface: (a) initial surface error, (b) the final surface errors, and (c) average PSD curve of the final surface errors.

Tables (2)

Tables Icon

Table 1. Results from the Iterative Method

Tables Icon

Table 2. Design Data of the Null Compensator

Equations (8)

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

Δd(x,y)=f(x,y)g(x,y),
gr(x,y)=κ·gn(sx,sy),
Vr=1111κ·gr(sx,sy)dxdy,
ttotal=Vtotal/Vr.
z=f(x,y)=cr21+1(k+1)c2r2+Ajr2j+
{Ci=arctan(nyinxi)θi=arctan(y0x0)Bi=arctan(nzi1nzi2)Xi=LsinBixi2+yi2cos(Ciθi)Yi=xi2+yi2sin(Ciθi)Zi=ziL(1cosBi).
dL=TL(x,y)gr(x,y)=1vH1111κgn(sx,sy)dxdy=Vr/vH,
dH=TH(x,y)gr(x,y)=1vL1111κgn(sx,sy)dxdy=Vr/vL,

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