Abstract

The edge effect could not be avoided in most optical manufacturing methods based on the theory of computer controlled optical surfacing. The difference between the removal function at the workpiece edge and that inside it is also the primary cause for edge effect in magnetorheological finishing (MRF). The change of physical dimension and removal ratio of the removal function is investigated through experiments. The results demonstrate that the situation is different when MRF “spot” is at the leading edge or at the trailing edge. Two methods for reducing the edge effect are put into practice after analysis of the processing results. One is adopting a small removal function for dealing with the workpiece edge, and the other is utilizing the removal function compensation. The actual processing results show that these two ways are both effective on reducing the edge effect in MRF.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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2010

2009

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

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, 5656–5665 (2009).
[CrossRef] [PubMed]

2008

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

2006

2004

1999

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Aguilar-Chiu, L. A.

Burge, J. H.

Cordero-Dávila, A.

Cuautle-Cortés, J.

Dai, Y.

Dumas, P.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

A. Shorey, A. Jones, P. Dumas, and M. Tricard, “Improved edge performance in magnetorheological finishing (MRF)” (QED Technologies, Inc.), http://optics.nasa.gov/tech_days/tech_days_2004/docs/17%20Aug%202004/15%20QED%20Edge%20Effects.pdf.

Fang, H.

Feng, S.

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

Geiss, Andreas

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Golini, D.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

González-García, J.

Gorodkin, G. R.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Guo, P.

Hao, H.

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

Hogan, S.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Hu, Hao

Jacobs, S. D.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Jones, A.

A. Shorey, A. Jones, P. Dumas, and M. Tricard, “Improved edge performance in magnetorheological finishing (MRF)” (QED Technologies, Inc.), http://optics.nasa.gov/tech_days/tech_days_2004/docs/17%20Aug%202004/15%20QED%20Edge%20Effects.pdf.

Kim, D. W.

Kim, S. W.

Kordonski, W. I.

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Park, W. H.

Pedrayes-López, M.

Peng, X.

Pitschke, E.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Prokhorov, I. V.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Rascher, R.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Robledo-Sánchez, C.

Schinhaerl, M.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Shorey, A.

A. Shorey, A. Jones, P. Dumas, and M. Tricard, “Improved edge performance in magnetorheological finishing (MRF)” (QED Technologies, Inc.), http://optics.nasa.gov/tech_days/tech_days_2004/docs/17%20Aug%202004/15%20QED%20Edge%20Effects.pdf.

Shorey, A. B.

A. B. Shorey, “Mechanisms of material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).

Smith, G.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Smith, L.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Sperber, P.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Stamp, R.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Strafford, T. D.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

Tricard, M.

A. Shorey, A. Jones, P. Dumas, and M. Tricard, “Improved edge performance in magnetorheological finishing (MRF)” (QED Technologies, Inc.), http://optics.nasa.gov/tech_days/tech_days_2004/docs/17%20Aug%202004/15%20QED%20Edge%20Effects.pdf.

Xiaoqiang, P.

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

Yifan, D.

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

Yu, J.

Appl. Math. Model.

M. Schinhaerl, G. Smith, R. Stamp, R. Rascher, L. Smith, E. Pitschke, P. Sperber, and Andreas Geiss, “Mathematical modelling of influence functions in computer-controlled polishing,” Appl. Math. Model. 32, 2888–2924 (2008).
[CrossRef]

Appl. Opt.

J. Natl. Univ. Defense Technol.

H. Hao, P. Xiaoqiang, D. Yifan, and S. Feng, “Algorithm and implementation of magnetorheological finishing with spiral scan mode,” J. Natl. Univ. Defense Technol. 31, 5–9 (2009) (in Chinese).

Opt. Express

Proc. SPIE

D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” Proc. SPIE 3782, 80–91 (1999).
[CrossRef]

Other

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, “Deterministic magnetorheological finishing,” U.S. patent 5,795,212 (18 August 1998).

A. Shorey, A. Jones, P. Dumas, and M. Tricard, “Improved edge performance in magnetorheological finishing (MRF)” (QED Technologies, Inc.), http://optics.nasa.gov/tech_days/tech_days_2004/docs/17%20Aug%202004/15%20QED%20Edge%20Effects.pdf.

A. B. Shorey, “Mechanisms of material removal in magnetorheological finishing (MRF) of glass,” Ph.D. dissertation (University of Rochester, 2000).

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Figures (10)

Fig. 1
Fig. 1

Schematic drawing of the MR fluid flow state (a) at the leading edge, (b) away from edges, and (c) at the trailing edge.

Fig. 2
Fig. 2

Results of the first mirror figure error correction: (a) initial figure error, (b) figure error after MRF on full aperture, (c) figure error after MRF on 85% aperture.

Fig. 3
Fig. 3

Results of the second mirror figure error correction: (a) initial figure error, (b) figure error after MRF on full aperture, (c) figure error after MRF on 85% aperture.

Fig. 4
Fig. 4

Actual removal function at the leading edge: (a) result from the interferometer, (b) concrete removal function.

Fig. 5
Fig. 5

Comparison of the actual removal function and the ideal one: (a) ideal removal function at leading edge, (b) comparison of the MRR and VRR.

Fig. 6
Fig. 6

Actual removal function at the trailing edge: (a) result from the interferometer, (b) concrete removal function.

Fig. 7
Fig. 7

Comparison of the actual removal function and the ideal one: (a) ideal removal function at trailing edge, (b) comparison of the MRR and VRR.

Fig. 8
Fig. 8

Manufacturing results using the small removal function method: (a) initial figure error, (b) removal function used in the experiment, (c) figure error after the first iteration, (d) figure error after the second iteration.

Fig. 9
Fig. 9

Fitting curve of the VRR ratio.

Fig. 10
Fig. 10

Manufacturing results using the compensation method: (a) initial figure error, (b) figure error after MRF.

Equations (3)

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f ( x ) = { p 1 x n + p 2 x n 1 + + p n x + p n + 1 , x x 0 0 , x > x 0 .
F m × n = [ F 1 1 F 1 2 F 1 k F 1 n F 2 1 F 2 2 F 2 k F 2 n F i 1 F i 2 F i k F i n F m 1 F m 2 F m k F m n ] .
F × T = Q .

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