Abstract

Edge effect is regarded as one of the most difficult technical issues for fabricating large primary mirrors, especially for large polishing tools. Computer controlled active lap (CCAL) uses a large size pad (e.g., 1/3 to 1/5 workpiece diameters) to grind and polish the primary mirror. Edge effect also exists in the CCAL process in our previous fabrication. In this paper the material removal rules when edge effects happen (i.e. edge tool influence functions (TIFs)) are obtained through experiments, which are carried out on a Φ1090-mm circular flat mirror with a 375-mm-diameter lap. Two methods are proposed to model the edge TIFs for CCAL. One is adopting the pressure distribution which is calculated based on the finite element analysis method. The other is building up a parametric equivalent pressure model to fit the removed material curve directly. Experimental results show that these two methods both effectively model the edge TIF of CCAL.

© 2014 Optical Society of America

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References

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  2. M. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012).
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  3. M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE 7010, 70100L (2008).
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  4. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986).
    [Crossref]
  5. 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]
  6. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004).
    [Crossref] [PubMed]
  7. Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009).
    [Crossref]
  8. 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(7), 5656–5665 (2009).
    [Crossref] [PubMed]
  9. H. Hu, Y. Dai, X. Peng, and J. Wang, “Research on reducing the edge effect in magnetorheological finishing,” Appl. Opt. 50(9), 1220–1226 (2011).
    [Crossref] [PubMed]
  10. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
    [Crossref] [PubMed]
  11. H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).
  12. H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013).
    [Crossref] [PubMed]
  13. L. Haitao, Z. Zhige, W. Fan, F. Bin, and W. Yongjian, “Study on active lap tool influence function in grinding 1.8 m primary mirror,” Appl. Opt. 52(31), 7504–7511 (2013).
    [Crossref] [PubMed]
  14. F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).
  15. 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(24), 21850–21866 (2009).
    [Crossref] [PubMed]
  16. H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

2013 (2)

2012 (2)

2011 (2)

H. Hu, Y. Dai, X. Peng, and J. Wang, “Research on reducing the edge effect in magnetorheological finishing,” Appl. Opt. 50(9), 1220–1226 (2011).
[Crossref] [PubMed]

H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

2009 (3)

2008 (2)

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

M. Johns, “The Giant Magellan Telescope (GMT),” Proc. SPIE 6986, 698603 (2008).
[Crossref]

2004 (1)

2003 (1)

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]

1986 (1)

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986).
[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.

Beaucamp, A.

Bin, F.

Burge, J. H.

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]

Cayrel, M.

M. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012).
[Crossref]

Clampin, M.

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

Cordero-Davila, A.

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]

Cordero-Dávila, A.

Cuautle-Cortés, 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]

Dai, Y.

Evans, R.

Fan, B.

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

Fan, W.

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]

González-García, J.

Haitao, L.

Han, Y.

Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009).
[Crossref]

Hu, H.

Johns, M.

M. Johns, “The Giant Magellan Telescope (GMT),” Proc. SPIE 6986, 698603 (2008).
[Crossref]

Jones, R. A.

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986).
[Crossref]

Kim, D. W.

Kim, S. W.

Li, H.

Liu, H.

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

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]

Messelink, W.

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]

Park, W. H.

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]

Pedrayes-López, 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.

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]

Robledo-Sánchez, C.

Sayle, A.

Walker, D.

H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013).
[Crossref] [PubMed]

H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

Walker, D. D.

Wan, Y.

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

Wan, Y. J.

Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009).
[Crossref]

Wang, J.

Wu, F.

Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009).
[Crossref]

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

Yongjian, W.

Yu, G.

Zeng, Z.

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

Zhige, Z.

Appl. Opt. (3)

J. Eur. Opt. Soc. Rap. Publ. (1)

H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

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. Eng. (1)

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986).
[Crossref]

Opt. Express (4)

Proc. SPIE (5)

Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009).
[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. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012).
[Crossref]

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

Other (1)

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

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Figures (19)

Fig. 1
Fig. 1 Surface shape error profiles of the mirror after active lap grinding. The mirror edge is rolled down about 5–10 μm due to the skin pressure model.

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Fig. 2
Fig. 2 Sketch of CCAL in edge figuring.

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Fig. 3
Fig. 3 Definition of lap overhang ratio, Slap.

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Fig. 4
Fig. 4 Sketch of parametric equivalent pressure curve model.

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Fig. 5
Fig. 5 Parametric pressure curves for various overhang ratio, Slap (α = –2Slap + 0.8, β = 3, and ε = 0.2).

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Fig. 6
Fig. 6 FEA model for pressure analysis when active lap overhang mirror edge (Slap = 0.3).

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Fig. 7
Fig. 7 Center pressure curves for different rigidity soft layer (Slap = 0.3, and Em is Young’s modulus of the workpiece).

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Fig. 8
Fig. 8 Active lap edge ring TIF experimental setup (a) and measuring method (b).

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Fig. 9
Fig. 9 Edge ring TIFs from the experiments.

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Fig. 10
Fig. 10 Fitted parametric pressure curves. Normalized by the pressure when active lap inside the mirror. The zero position on the x axis is the mirror edge, and the negative direction of the x axis is toward the mirror center (α0.1 = 1.559, α0.2 = 1.101, α0.3 = 0.540, β = 18.511, and ε = 0.642).

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Fig. 11
Fig. 11 Comparison between predicted TIFs and measured TIFs.

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Fig. 12
Fig. 12 Gaussian fitted α-Slap curve (a) and the family of edge ring TIFs calculated based on this curve (b).

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Fig. 13
Fig. 13 Comparison between the experimental TIF and theoretic TIFs with different Es, Slap = 0.3.

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Fig. 14
Fig. 14 Pressure distribution FEA results for different overhang ratios: (a) Slap = 0.05, (b) Slap = 0.1, (c) Slap = 0.15, (d) Slap = 0.2, (e) Slap = 0.25, (f) Slap = 0.3, (g) Slap = 0.35, and (h) Slap = 0.4 (Es = 20.78 MPa).

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Fig. 15
Fig. 15 Center pressure curves from FEA results (a) and edge ring TIF family calculated based on these pressure curves (b).

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Fig. 16
Fig. 16 Comparison between predicted TIFs from FEA results and measured TIFs.

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Fig. 17
Fig. 17 Normalized fit error, Err, for the parametric and FEA model at different overhang ratios.

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Fig. 18
Fig. 18 Simulation results for CCAL piston target removal process. Curves are normalized by the target removal profile.

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Fig. 19
Fig. 19 Simulation results for CCAL arbitrary target removal process.

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Tables (2)

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Table 1 Material properties for FEA

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Table 2 Parameters for edge ring TIF experiments

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Equations (9)

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dz(x,y)=k⋅P(x,y)⋅V(x,y)⋅dt,
TIF A ( e ) = ω 1 2 π ∑ M → N k ⋅ P ( ρ , θ , e ) ⋅ V ( ρ , θ , e ) ⋅ d t ,
TIF A ( e ) = k 2 π ∫ − ϕ ϕ P ( ρ , θ , e ) ⋅ V ( ρ , θ , e ) ⋅ d θ ,
P E ( ρ , e ) ⋅ ∫ − ϕ ϕ V ⋅ d θ = ∫ − ϕ ϕ P ( ρ , θ , e ) ⋅ V ⋅ d θ .
TIF A (e)= k 2π P E (ρ,e)⋅ ∫ −ϕ ϕ V ⋅dθ.
κ map (x,α,β,γ,δ,ε)= κ 0 ⋅{1+ S lap ε ⋅[ f 1 (x,α,β)+ f 2 (x,γ,δ)]},
P E ( x , α , β , ε ) = p s ⋅ [ 1 + S l a p ε ⋅ f ( x , α , β ) ] ,
f(x,a,β)= β⋅ (x+ W lap ⋅α) 2 ( W lap ⋅α) 2 Θ(x+ W lap ⋅α),
Err= ∑ | TIF Model − TIF Measure | ∑ TIF Measure ⋅100(%).

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