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

Full Article  |  PDF Article
OSA Recommended Articles
Parametric modeling of edge effects for polishing tool influence functions

Dae Wook Kim, Won Hyun Park, Sug-Whan Kim, and James H. Burge
Opt. Express 17(7) 5656-5665 (2009)

Modeling of edge effect in subaperture tool influence functions of computer controlled optical surfacing

Songlin Wan, Xiangchao Zhang, Xiaoying He, and Min Xu
Appl. Opt. 55(36) 10223-10228 (2016)

Edge control in a computer controlled optical surfacing process using a heterocercal tool influence function

Haixiang Hu, Xin Zhang, Virginia Ford, Xiao Luo, Erhui Qi, Xuefeng Zeng, and Xuejun Zhang
Opt. Express 24(23) 26809-26824 (2016)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. M. Johns, “The Giant Magellan Telescope (GMT),” Proc. SPIE 6986, 698603 (2008).
    [Crossref]
  2. M. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012).
    [Crossref]
  3. M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE 7010, 70100L (2008).
    [Crossref]
  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. 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).

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]

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.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2

Sketch of CCAL in edge figuring.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3

Definition of lap overhang ratio, Slap.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4

Sketch of parametric equivalent pressure curve model.

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5

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

Download Full Size | PPT Slide | PDF

Fig. 6
Fig. 6

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

Download Full Size | PPT Slide | PDF

Fig. 7
Fig. 7

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

Download Full Size | PPT Slide | PDF

Fig. 8
Fig. 8

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

Download Full Size | PPT Slide | PDF

Fig. 9
Fig. 9

Edge ring TIFs from the experiments.

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

Fig. 11
Fig. 11

Comparison between predicted TIFs and measured TIFs.

Download Full Size | PPT Slide | PDF

Fig. 12
Fig. 12

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

Download Full Size | PPT Slide | PDF

Fig. 13
Fig. 13

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

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

Fig. 15
Fig. 15

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

Download Full Size | PPT Slide | PDF

Fig. 16
Fig. 16

Comparison between predicted TIFs from FEA results and measured TIFs.

Download Full Size | PPT Slide | PDF

Fig. 17
Fig. 17

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

Download Full Size | PPT Slide | PDF

Fig. 18
Fig. 18

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

Download Full Size | PPT Slide | PDF

Fig. 19
Fig. 19

Simulation results for CCAL arbitrary target removal process.

Download Full Size | PPT Slide | PDF

Tables (2)

Tables Icon

Table 1 Material properties for FEA

View Table | View all tables in this article
Tables Icon

Table 2 Parameters for edge ring TIF experiments

View Table | View all tables in this article

Equations (9)

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

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(%).

Metrics