Abstract

The influence from the regular tool path to micro fabrication errors in deterministic finishing is studied through the simulations and experiments. The random pitch tool path based on the surface error distribution and the process parameters is designed to reduce this residual error when adopting the regular path to achieve the corrective polish. A nucleated glass flat mirror is polished with this method on the experimental installation UPF700-7 developed by ourselves. The surface accuracy is improved from the initial λ/30(RMS, 90%aperture, λ = 632.8nm) to the final λ/200 in 5 minutes and the medium-high spatial frequency errors induced by the regular path is restricted well at the same time. The accuracy of the simulation and the validity of the random pitch tool path are both proved through the experiments.

©2010 Optical Society of America

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References

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  1. S. D. Jacobs, W. I. Kordonski, D. Golini, I. V. Prokhorov, G. R. Gorodkin, and T. D. Strafford, “Deterministic Magnetorheological Finishing,” US, Patent, 5795212 (1998).
  2. 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]
  3. B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).
  4. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977).
    [Crossref] [PubMed]
  5. M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
    [Crossref]
  6. M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
    [Crossref]
  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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-958 .
    [Crossref] [PubMed]
  8. 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]
  9. J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
    [Crossref]
  10. D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).
  11. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-23-18942 .
    [Crossref]
  12. C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

2009 (1)

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

2008 (2)

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-23-18942 .
[Crossref]

2007 (3)

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[Crossref]

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

2003 (1)

1999 (1)

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]

1998 (1)

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

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]

1977 (1)

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]

Auerbach, J. M.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Brooks, D.

Canestrari, R.

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[Crossref]

Cotton, C. T.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Dumas, P.

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

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]

Dunn, C. R.

English, R. E.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[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]

Feng, S.

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

Freeman, R.

Ghigo, M.

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[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]

Hall, C.

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

Hallock, B.

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

Henesian, M. A.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

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]

Hunt, J. T.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Jones, R. A.

Kelly, J. H.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Kim, S.-W.

King, A.

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]

Lawson, J. K.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[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]

McCavana, G.

Messner, B.

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

Morton, R.

Novi, A.

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[Crossref]

Pitschke, E.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Rascher, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Sacks, R. A.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Schinhaerl, M.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Shoupe, M. J.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Smith, G.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Smith, L.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Sperber, P.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Spiga, D.

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[Crossref]

Stamp, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Supranowitz, C.

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

Trenholme, J. B.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Walker, D. D.

Williams, W. H.

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

Xiaoqiang, P.

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

Yifan, D.

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

Appl. Opt. (1)

Opt. Express (2)

Precis Eng (1)

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilization of time-variant influence functions on the computer controlled polishing,” Precis Eng 32(1), 47–54 (2008).
[Crossref]

Proc. SPIE (6)

M. Ghigo, R. Canestrari, D. Spiga, and A. Novi, “Correction of high spatial frequency errors on optical surfaces by means of ion beam figuring,” Proc. SPIE 6671, 667114 (2007).
[Crossref]

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]

B. Hallock, B. Messner, C. Hall, and C. Supranowitz, “Improvements in large window and optics production,” Proc. SPIE 6545, 645419 (2007).

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]

J. K. Lawson, J. M. Auerbach, R. E. English, M. A. Henesian, J. T. Hunt, R. A. Sacks, J. B. Trenholme, W. H. Williams, M. J. Shoupe, J. H. Kelly, and C. T. Cotton, “NIF optical specifications: the importance of the RMS gradient,” Proc. SPIE 3492, 336–343 (1998).
[Crossref]

C. Supranowitz, C. Hall, P. Dumas, and B. Hallock, “Improving surface figure and microroughness of IR materials and diamond turned surfaces with magnetorheological finishing (MRF®),” Proc. SPIE 6545, 64540S (2007).

Sci. China Ser. E: Technol. Sci. (1)

D. Yifan, S. Feng, and P. Xiaoqiang, “Restraint of mid-spatial frequency error in magnetorheological finishing (MRF) process by maxium entrophy method,” Sci. China Ser. E: Technol. Sci. 52, 3902 (2009).

Other (1)

S. D. Jacobs, W. I. Kordonski, D. Golini, I. V. Prokhorov, G. R. Gorodkin, and T. D. Strafford, “Deterministic Magnetorheological Finishing,” US, Patent, 5795212 (1998).

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Figures (16)

Fig. 1
Fig. 1 The typical raster tool path (a) and spiral tool path (b) adopted in MRF® process.

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Fig. 2
Fig. 2 Diagrammatic sketch for the surface removal with the MRF® removal function.

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Fig. 3
Fig. 3 The 2D map (a) and profile (b) of the first removal function for simulation.

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Fig. 4
Fig. 4 The 2D map (a) and profile (b) of the second removal function for simulation.

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Fig. 5
Fig. 5 Residual ripple alteration with the removal depth (a) and with the pitch (b).

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Fig. 6
Fig. 6 Initial figure error (a) and the polished surface (b) with 1mm pitch raster path.

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Fig. 7
Fig. 7 PSD for raster polished region.

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Fig. 8
Fig. 8 Profile along the line extracted from the polished surface measurement (a) in Fig. 7 and (b), (c) is the partial enlarged detail at the location 1 and 2.

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Fig. 9
Fig. 9 Initial figure error (a) and the polished surface (b) with 0.5mm pitch raster path.

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Fig. 10
Fig. 10 PSD for raster polished region.

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Fig. 11
Fig. 11 Profile along the line extracted from the polished surface measurement (a) in Fig. 10 and (b), (c) is the partial enlarged detail at the location 1 and 2.

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Fig. 12
Fig. 12 Spiral path through the diameter (a) and diagrammatic sketch of random pitch spiral path (b).

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Fig. 13
Fig. 13 Initial figure error (a) and the polished surface (b) with 1mm pitch spiral path.

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Fig. 14
Fig. 14 PSD for equilong pitch spiral polished region.

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Fig. 15
Fig. 15 Initial figure error (a) and the polished surface (b) with the random pitch spiral path.

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Fig. 16
Fig. 16 PSD for random pitch spiral polished region.

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Equations (6)

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

E ( x , y ) = r ( x , y ) ∗ t ( x , y ) .
E ( p ) = ∑ i = 1 n r ( p i ; p ) ⋅ t ( p i ) .
E ' ( p ' ) = ∑ i = 1 n r ( p i ; p ' ) ⋅ t ( p i ) .
σ E ( p ' ) = ∑ i = 1 n | r ( p i ; p ) − r ( p i ; p ' ) | ⋅ t ( p i ) .
σ E P V = 1 2 ∑ i = 1 n | r ( p i ) − r ( p i − 1 ) | r ( p i ) ⋅ D ⋅ Δ P 2 ≤ σ E r .
v a = D ⋅ Δ P / ∑ i = 1 n r ( p i ) ≥ v min .

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