Abstract

Edge effect is regarded as one of the most difficult technical issues in a computer controlled optical surfacing (CCOS) process. Traditional opticians have to even up the consequences of the two following cases. Operating CCOS in a large overhang condition affects the accuracy of material removal, while in a small overhang condition, it achieves a more accurate performance, but leaves a narrow rolled-up edge, which takes time and effort to remove. In order to control the edge residuals in the latter case, we present a new concept of the ‘heterocercal’ tool influence function (TIF). Generated from compound motion equipment, this type of TIF can ‘transfer’ the material removal from the inner place to the edge, meanwhile maintaining the high accuracy and efficiency of CCOS. We call it the ‘heterocercal’ TIF, because of the inspiration from the heterocercal tails of sharks, whose upper lobe provides most of the explosive power. The heterocercal TIF was theoretically analyzed, and physically realized in CCOS facilities. Experimental and simulation results showed good agreement. It enables significant control of the edge effect and convergence of entire surface errors in large tool-to-mirror size-ratio conditions. This improvement will largely help manufacturing efficiency in some extremely large optical system projects, like the tertiary mirror of the Thirty Meter Telescope.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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  21. H. Hu and X. Zhang are preparing a manuscript to be called “Time-varying heterocercal tool and its application in large optical primary mirror with a central hole.”
  22. Delta Tau China technical support, “IMAC 400 details,” http://www.deltatau-china.com/html/xt/2449.html .
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    [Crossref]

2016 (1)

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

2015 (1)

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

2014 (2)

H. Hu, X. Luo, and H. Xin, “Layout optimization of equal-force supports for ultra large optical fabrication,” Acta Opt. Sin. 34(4), 0422003 (2014).
[Crossref]

H. Liu, F. Wu, Z. Zeng, B. Fan, and Y. Wan, “Edge effect modeling and experiments on active lap processing,” Opt. Express 22(9), 10761–10774 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2011 (2)

2009 (1)

2006 (2)

2004 (1)

2003 (1)

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

1990 (1)

J. Zimmerman, “Computer controlled optical surfacing for off-axis aspheric mirrors,” Proc. SPIE 1236, 663–668 (1990).
[Crossref]

1986 (1)

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 256785 (1986).
[Crossref]

1977 (1)

1965 (1)

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.

Bai, Y.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Beaucamp, A.

Burge, J. H.

Cabrera, V.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

Cole, G.

H. Hu, E. Qi, and G. Cole, “Research on sub-surface damage and its stress deformation in the process of large aperture and high diameter-to-thickness ratio TMT M3MP,” Proc. SPIE9682, 968244 (to be published).

Cordero-Davila, A.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “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, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

Dai, Y.

Deng, W.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Evans, R.

Fan, B.

Fang, H.

Ghim, Y. S.

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

Gonzalez, J.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

González-García, J.

Guo, P.

Hu, H.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

H. Hu, X. Luo, and H. Xin, “Layout optimization of equal-force supports for ultra large optical fabrication,” Acta Opt. Sin. 34(4), 0422003 (2014).
[Crossref]

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. Hu, E. Qi, and G. Cole, “Research on sub-surface damage and its stress deformation in the process of large aperture and high diameter-to-thickness ratio TMT M3MP,” Proc. SPIE9682, 968244 (to be published).

Jones, R. A.

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 256785 (1986).
[Crossref]

R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977).
[Crossref] [PubMed]

Kim, D. W.

Kim, G. C.

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

Kim, H. S.

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

Kim, S. W.

Leal-Cabrera, I.

Li, H.

Li, L.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Liu, H.

Luna-Aguilar, E.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

Luo, X.

H. Hu, X. Luo, and H. Xin, “Layout optimization of equal-force supports for ultra large optical fabrication,” Acta Opt. Sin. 34(4), 0422003 (2014).
[Crossref]

Messelink, W.

Nam, H. S.

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

Nunez-Alfonso, M.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

Park, W. H.

Pedrayes, M. H.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “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).

Qi, E.

H. Hu, E. Qi, and G. Cole, “Research on sub-surface damage and its stress deformation in the process of large aperture and high diameter-to-thickness ratio TMT M3MP,” Proc. SPIE9682, 968244 (to be published).

Rhee, H. G.

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

Robledo-Sanchez, C. I.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

Robledo-Sánchez, C.

Robledo-Sánchez, C. I.

Rupp, V.

Santiago-Alvarado, A.

Sayle, A.

Troy, M.

Walker, D.

Wan, Y.

Wang, J.

Wang, X.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Wu, F.

Xin, H.

H. Hu, X. Luo, and H. Xin, “Layout optimization of equal-force supports for ultra large optical fabrication,” Acta Opt. Sin. 34(4), 0422003 (2014).
[Crossref]

Yaitskova, N.

Yu, G.

Yu, J.

Zeng, Z.

Zhang, B.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Zhang, X.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Zheng, L.

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

Zimmerman, J.

J. Zimmerman, “Computer controlled optical surfacing for off-axis aspheric mirrors,” Proc. SPIE 1236, 663–668 (1990).
[Crossref]

Acta Opt. Sin. (1)

H. Hu, X. Luo, and H. Xin, “Layout optimization of equal-force supports for ultra large optical fabrication,” Acta Opt. Sin. 34(4), 0422003 (2014).
[Crossref]

Appl. Opt. (7)

Int. J. Adv. Manuf. Technol. (2)

H. S. Nam, G. C. Kim, H. S. Kim, H. G. Rhee, and Y. S. Ghim, “Modeling of edge tool influence functions for computer controlled optical surfacing process,” Int. J. Adv. Manuf. Technol. 83(5-8), 911–917 (2016).
[Crossref]

L. Li, L. Zheng, W. Deng, X. Wang, X. Wang, B. Zhang, Y. Bai, H. Hu, and X. Zhang, “Optimized dwell time algorithm in magnetorheological finishing,” Int. J. Adv. Manuf. Technol. 81(5-8), 833–841 (2015).
[Crossref]

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), 256785 (1986).
[Crossref]

Opt. Express (4)

Proc. SPIE (2)

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez, M. Nunez-Alfonso, V. Cabrera, C. I. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003).
[Crossref]

J. Zimmerman, “Computer controlled optical surfacing for off-axis aspheric mirrors,” Proc. SPIE 1236, 663–668 (1990).
[Crossref]

Other (5)

H. Hu, E. Qi, and G. Cole, “Research on sub-surface damage and its stress deformation in the process of large aperture and high diameter-to-thickness ratio TMT M3MP,” Proc. SPIE9682, 968244 (to be published).

Wikipedia article, “Fish fin,” https://en.wikipedia.org/wiki/Fish_fin#AnchCaudal .

H. Hu and X. Zhang are preparing a manuscript to be called “Time-varying heterocercal tool and its application in large optical primary mirror with a central hole.”

Delta Tau China technical support, “IMAC 400 details,” http://www.deltatau-china.com/html/xt/2449.html .

V. G. Ford, “Tertiary mirror surface figure specification,” Thirty Meter Telescope Observatory Corporation document, TMT.OPT.SPE.12.001.DRF02, 2014, available at http://www.tmt.org/sites/default/files/documents/application/pdf/tmt%20-%20tertiary%20mirror%20surface%20figure%20specifications%2020121023.pdf .

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Figures (20)

Fig. 1
Fig. 1 Overhanging situation of 1.2m lap on the elliptic TMT M3 mirror (3.5m × 2.5m, supported by 144-point system in fabrication status [14]). a) 3 typical positions with the same overhang distance. b) Less overhang area in minor axis. c) More overhang area in major axis. d) Asymmetric overhang area in other directions.
Fig. 2
Fig. 2 Heterocercal concept.
Fig. 3
Fig. 3 Schematic diagram of the ‘heterocercal’ motion strategy.
Fig. 4
Fig. 4 Schematic diagram of velocity field of orbital and spin tool motion combination.
Fig. 5
Fig. 5 Instantaneous tool speed distribution in vector and contour map over the time period. a) Most overhang, status A (t = 0). b) Least overhang, status C (t = T/2).
Fig. 6
Fig. 6 Simulative heterocercal TIFs in the normalized color axis. a) k = 0.25. b) k = 0.00 (Orbital mode). c) k = 0.15. d) k = 0.30. e) k = 0.45.
Fig. 7
Fig. 7 Normalized material removal profile in X direction.
Fig. 8
Fig. 8 Scheme of the material removal profile of the edge TIFs. a) Orbital tool. b) Heterocercal tool.
Fig. 9
Fig. 9 TUE residuals of orbital tool and heterocercal tool.
Fig. 10
Fig. 10 3D model of the compound motion unit.
Fig. 11
Fig. 11 Schematic diagram of the control system for the compound motion unit.
Fig. 12
Fig. 12 Compound motion unit equipped with different sizes of tool bases. a) Normal status, equipped with a round base for ⌀400mm tool. b) Test status, equipped with a triangle base for ⌀90mm tool (still round tool-shape).
Fig. 13
Fig. 13 The working spot of the heterocercal TIF on a ⌀150mm workpiece. a) Measured spot. b) Normalized simulated spot. c) Simulative comparison.
Fig. 14
Fig. 14 Schematic diagram of the tool’s movement on the workpiece.
Fig. 15
Fig. 15 Edge TIF of the heterocercal tool.
Fig. 16
Fig. 16 Experimental result of the edge TIF profiles (a) and the simulative comparison (b).
Fig. 17
Fig. 17 Double-spiral tool path (blue dot line) and TIF orientation planning for an elliptic flat.
Fig. 18
Fig. 18 Initial surface error map of 3.5m × 2.5m elliptic flat (in μm).
Fig. 19
Fig. 19 Dwell time map. a) Orbital mode. b) Heterocercal mode, k = 0.25.
Fig. 20
Fig. 20 Residual error map after one simulative iteration of 1.2m round tool (in μm). a) Orbital mode. b) Heterocercal mode, k = 0.25.

Tables (2)

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Table 1 TIF types of round tools and the edge TIF profiles accordingly.

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Table 2 TIF experiment conditions

Equations (15)

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

Δz( x,y )=κp( x,y )v( x,y )Δt.
v( x,y,t )=s ω a , assuming ω a >0.
ω b =k ω a cos( 2π t T ), k>0, T= 2π ω a .
ω b =k ω a cosα, with ω a = dα / dt , ω b = dβ / dt .
v = v orbit + v spin =| OC | ω a e i( α+π/2 ) +| CP | ω b e i( β+ECP+π/2 ) .
v(x,y)= ω b 2 ( x 2 + y 2 )+2( ω a ω b ) ω b s( xcosα+ysinα )+ ( ω a ω b ) 2 s 2 .
p(x,y)= p 0 circ( xscosα r 0 , yssinα r 0 ).
Δz= t= t 0 t 0 +T κp( x,y )v( x,y )dt = α=0 2π κp( x,y )v( x,y ) dα ω a .
Δz=κ p 0 α=0 2π v( x,y,t ) dα ω a .
Δ z min 2 π , when x s 1 k .
D2s 2s k .
k= 2s D2s 2s D .
Δz= 1 D+2s y=D/2 s D/2 +s α=0 2π κp( x,y )v( x,y ) dα ω a .
TUR= S 3 S 1 ×100%.
β=ksinα+ θ 0 .

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