Abstract

Computer controlled polishing requires accurate knowledge of the tool influence function (TIF) for the polishing tool (i.e. lap). While a linear Preston’s model for material removal allows the TIF to be determined for most cases, nonlinear removal behavior as the tool runs over the edge of the part introduces a difficulty in modeling the edge TIF. We provide a new parametric model that fits 5 parameters to measured data to accurately predict the edge TIF for cases of a polishing tool that is either spinning or orbiting over the edge of the workpiece.

© 2009 Optical Society of America

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References

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  1. M. Johns, "The Giant Magellan Telescope (GMT)," Proc. SPIE 6986, 698603 (2008).
    [CrossRef]
  2. M. Clampin, "Status of the James Webb Space Telescope (JWST)," Proc. SPIE 7010, 70100L (2008).
    [CrossRef]
  3. R. Aspden, R. McDonough, and F. R. Nitchie, Jr, "Computer assisted optical surfacing," Appl. Opt. 11, 2739-2747 (1972).
    [CrossRef] [PubMed]
  4. R. E. Wagner and R. R. Shannon, "Fabrication of aspherics using a mathematical model for material removal," Appl. Opt. 13, 1683-1689 (1974).
    [CrossRef] [PubMed]
  5. D. J. Bajuk, "Computer controlled generation of rotationally symmetric aspheric surfaces," Opt. Eng. 15, 401-406 (1976).
  6. R. A. Jones, "Grinding and polishing with small tools under computer control," Opt. Eng. 18, 390-393 (1979).
  7. R. A. Jones, "Computer-controlled polishing of telescope mirror segments," Opt. Eng. 22, 236-240 (1983).
  8. R. A. Jones, "Computer-controlled optical surfacing with orbital tool motion," Opt. Eng. 25, 785-790 (1986).
  9. J. R. Johnson and E. Waluschka, "Optical fabrication-process modeling-analysis tool box," Proc. SPIE 1333, 106-117 (1990).
    [CrossRef]
  10. R. A. Jones and W. J. Rupp, "Rapid optical fabrication with CCOS," Proc. SPIE 1333, 34-43 (1990).
    [CrossRef]
  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).
    [CrossRef] [PubMed]
  12. D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
    [CrossRef]
  13. E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
    [CrossRef]
  14. 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] [PubMed]
  15. B. C. Crawford, D. Loomis, N. Schenck, and B. Anderson, Optical Engineering and Fabrication Facility, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, (personal communication, 2008).
  16. D. W. Kim, College of Optical Sciences, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, W. H. Park, and J. H. Burge are preparing a manuscript to be called "Edge tool influence function model including tool stiffness and bending effects."
  17. D. W. Kim, College of Optical Sciences, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, and J. H. Burge are preparing a manuscript to be called "Time scale dependent conformable tool."

2008

M. Johns, "The Giant Magellan Telescope (GMT)," Proc. SPIE 6986, 698603 (2008).
[CrossRef]

M. Clampin, "Status of the James Webb Space Telescope (JWST)," Proc. SPIE 7010, 70100L (2008).
[CrossRef]

2005

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).
[CrossRef] [PubMed]

2004

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

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] [PubMed]

2003

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

1990

J. R. Johnson and E. Waluschka, "Optical fabrication-process modeling-analysis tool box," Proc. SPIE 1333, 106-117 (1990).
[CrossRef]

R. A. Jones and W. J. Rupp, "Rapid optical fabrication with CCOS," Proc. SPIE 1333, 34-43 (1990).
[CrossRef]

1986

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

1983

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

1979

R. A. Jones, "Grinding and polishing with small tools under computer control," Opt. Eng. 18, 390-393 (1979).

1976

D. J. Bajuk, "Computer controlled generation of rotationally symmetric aspheric surfaces," Opt. Eng. 15, 401-406 (1976).

1974

1972

Aguilar-Chiu, L. A.

Aspden, R.

Bajuk, D. J.

D. J. Bajuk, "Computer controlled generation of rotationally symmetric aspheric surfaces," Opt. Eng. 15, 401-406 (1976).

Beaucamp, A. T.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Brooks, D.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Cabrera-Pelaez, V. H.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Cassie, M.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Clampin, M.

M. Clampin, "Status of the James Webb Space Telescope (JWST)," Proc. SPIE 7010, 70100L (2008).
[CrossRef]

Cordero-Davila, A.

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] [PubMed]

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Cuautle-Cortes, J.

Cuautle-Cortez, J.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Doubrovski, V.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Dunn, C.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Freeman, R.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Gonzalez Garcia, J.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Gonzalez-Garcia, J.

Johns, M.

M. Johns, "The Giant Magellan Telescope (GMT)," Proc. SPIE 6986, 698603 (2008).
[CrossRef]

Johnson, J. R.

J. R. Johnson and E. Waluschka, "Optical fabrication-process modeling-analysis tool box," Proc. SPIE 1333, 106-117 (1990).
[CrossRef]

Jones, R. A.

R. A. Jones and W. J. Rupp, "Rapid optical fabrication with CCOS," Proc. SPIE 1333, 34-43 (1990).
[CrossRef]

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, "Grinding and polishing with small tools under computer control," Opt. Eng. 18, 390-393 (1979).

Kim, D. W.

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).
[CrossRef] [PubMed]

Kim, S. W.

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).
[CrossRef] [PubMed]

King, A.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Libert, M.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Luna-Aguilar, E.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

McCavana, G.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

McDonough, R.

Morton, R.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Nitchie, F. R.

Nunez-Alfonso, M.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Pedrayes-Lopez, M.

Pedrayes-Lopez, M. H.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Riley, D.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Robledo-Sanchez, C.

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] [PubMed]

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

Rupp, W. J.

R. A. Jones and W. J. Rupp, "Rapid optical fabrication with CCOS," Proc. SPIE 1333, 34-43 (1990).
[CrossRef]

Shannon, R. R.

Simms, J.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Wagner, R. E.

Walker, D. D.

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

Waluschka, E.

J. R. Johnson and E. Waluschka, "Optical fabrication-process modeling-analysis tool box," Proc. SPIE 1333, 106-117 (1990).
[CrossRef]

Appl. Opt.

Opt. Eng.

D. J. Bajuk, "Computer controlled generation of rotationally symmetric aspheric surfaces," Opt. Eng. 15, 401-406 (1976).

R. A. Jones, "Grinding and polishing with small tools under computer control," Opt. Eng. 18, 390-393 (1979).

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.

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).
[CrossRef] [PubMed]

Proc. SPIE

D. D. Walker, A. T. Beaucamp, D. Brooks, V. Doubrovski, M. Cassie, C. Dunn, R. Freeman, A. King, M. Libert, G. McCavana, R. Morton, D. Riley, and J. Simms, "New results from the Precessions polishing process scaled to larger sizes," Proc. SPIE 5494, 71-80 (2004).
[CrossRef]

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, "Edge effects with Preston equation," Proc. SPIE 4840, 598-603 (2003).
[CrossRef]

M. Johns, "The Giant Magellan Telescope (GMT)," Proc. SPIE 6986, 698603 (2008).
[CrossRef]

M. Clampin, "Status of the James Webb Space Telescope (JWST)," Proc. SPIE 7010, 70100L (2008).
[CrossRef]

J. R. Johnson and E. Waluschka, "Optical fabrication-process modeling-analysis tool box," Proc. SPIE 1333, 106-117 (1990).
[CrossRef]

R. A. Jones and W. J. Rupp, "Rapid optical fabrication with CCOS," Proc. SPIE 1333, 34-43 (1990).
[CrossRef]

Other

B. C. Crawford, D. Loomis, N. Schenck, and B. Anderson, Optical Engineering and Fabrication Facility, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, (personal communication, 2008).

D. W. Kim, College of Optical Sciences, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, W. H. Park, and J. H. Burge are preparing a manuscript to be called "Edge tool influence function model including tool stiffness and bending effects."

D. W. Kim, College of Optical Sciences, University of Arizona, 1630 E. University Blvd, Tucson, Arizona 85721, and J. H. Burge are preparing a manuscript to be called "Time scale dependent conformable tool."

Supplementary Material (2)

» Media 1: AVI (639 KB)     
» Media 2: AVI (621 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

x-profiles of the pressure distribution, p(x,y), under the tool-workpiece contact area: linear pressure distribution model. (left), static FEA results. (right).

Fig. 2.
Fig. 2.

Orbital (left) and spin (right) tool motion with the basic edge TIF.

Fig. 3.
Fig. 3.

Degrees of freedom of the κ map (in x-profile) using five parameters.

Fig. 4.
Fig. 4.

x-Profiles of κ maps for various overhang ratio, STIF . (α=0.2, β=2, γ=0.2, δ=1 and ε=0.2).

Fig. 5.
Fig. 5.

Measured vs simulated removal profiles: orbital tool motion (α=0.2, β=4, γ=0.4, δ=20, and ε=1.5).

Fig. 6.
Fig. 6.

Measured vs simulated removal profiles: spin tool motion case (α=0.4, β=6 γ=0.3, δ=-3, and ε=0.9).

Fig. 7.
Fig. 7.

Measured (with RMS error bars) vs simulated (using different edge TIF models) edge removal profiles for the orbital tool motion case.

Fig. 8.
Fig. 8.

Normalized fit residual, ∆, of the simulated removal profiles using different TIF models for orbital and spin tool motion cases.

Tables (2)

Tables Icon

Table 1. Normalized parametric edge TIFsa

Tables Icon

Table 2. Edge TIF experiment conditions

Equations (8)

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

Δ z ( x , y ) = κ · P ( x , y ) · V T ( x , y ) · Δ t ( x , y )
A p ( x , y ) dxdy = f 0
A ( x x ' ) · p ( x x ' , y ) dxdy = 0
p ( x , y ) = c 1 · x + c 2
f 1 ( x , α , β ) = β ( W TIF · α ) 2 · ( x + W TIF · α ) 2 · Θ ( x + W TIF · α )
f 2 ( x , γ , δ ) = δ ( W TIF . γ ) 2 · ( x W TIF + W TIF · S TIF + W TIF · γ ) 2 · Θ ( x W TIF + W TIF · S TIF + W TIF · γ )
κ map ( x , α , β , γ , δ , ε ) = κ 0 · { 1 + S TIF ε · ( f 1 + f 2 ) }
Δ = normalized fit residual = RMS of ( data mode l ) RMS of data · 100 ( % )

Metrics