Abstract

Edge mis-figure is regarded as one of the most difficult technical issues for manufacturing the segments of extremely large telescopes, which can dominate key aspects of performance. A novel edge-control technique has been developed, based on ‘Precessions’ polishing technique and for which accurate and stable edge tool influence functions (TIFs) are crucial. In the first paper in this series [D. Walker Opt. Express 20, 19787–19798 (2012)], multiple parameters were experimentally optimized using an extended set of experiments. The first purpose of this new work is to ‘short circuit’ this procedure through modeling. This also gives the prospect of optimizing local (as distinct from global) polishing for edge mis-figure, now under separate development. This paper presents a model that can predict edge TIFs based on surface-speed profiles and pressure distributions over the polishing spot at the edge of the part, the latter calculated by finite element analysis and verified by direct force measurement. This paper also presents a hybrid-measurement method for edge TIFs to verify the simulation results. Experimental and simulation results show good agreement.

© 2013 OSA

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References

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  1. 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. Express20(18), 19787–19798 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  4. H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).
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    [CrossRef]
  6. R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2012

2011

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

2009

2004

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]

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
[CrossRef]

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

2003

2000

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000).
[CrossRef]

1990

T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990).
[CrossRef]

1986

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

1974

1927

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).

Abdulkadyrov, M. A.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Aguilar-Chiu, L. A.

Beaucamp, A.

Brooks, D.

Burge, J.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Burge, J. H.

Cayrel, M.

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
[CrossRef]

Cordero-Dávila, A.

Cuautle-Cortés, J.

Cuerden, H. B.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Evans, R.

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. Express20(18), 19787–19798 (2012).
[CrossRef] [PubMed]

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

Freeman, R.

Geyl, R.

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
[CrossRef]

Gilmozzi, R.

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

González-García, J.

Ignatov, A. N.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[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.

King, A.

Li, H.

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. Express20(18), 19787–19798 (2012).
[CrossRef] [PubMed]

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

Martin, H. M.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Mast, T. S.

T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990).
[CrossRef]

McCavana, G.

Messelink, W.

Miller, S. M.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Morton, R.

Nelson, J. E.

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000).
[CrossRef]

T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990).
[CrossRef]

Park, W. H.

Patrikeev, V.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Pedrayes-López, M.

Polyanchikov, A. V.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Preston, F. W.

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).

Pridnya, V. V.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Robledo-Sánchez, C.

Semenov, A. P.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Shannon, R. R.

Sharov, Y. A.

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

Smith, B.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Tarreau, M.

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
[CrossRef]

Wagner, R. E.

Walker, D. D.

Yu, G.

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. Express20(18), 19787–19798 (2012).
[CrossRef] [PubMed]

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

Zhao, C.

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

Appl. Opt.

J. Eur. Opt. Soc. Rap. Pub.

H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

J. Soc. Glass Technol.

F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).

Opt. Eng.

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

Opt. Express

Proc. SPIE

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004).
[CrossRef]

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000).
[CrossRef]

R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004).
[CrossRef]

A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004).
[CrossRef]

T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990).
[CrossRef]

Other

H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).

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Figures (14)

Fig. 1
Fig. 1

The sketch of the tool lift process for edge control (reproduced from Paper 1)

Fig. 2
Fig. 2

Sketch of space movement of the tool of the precess.

Fig. 3
Fig. 3

Velocity relation of any point in contact zone.

Fig. 4
Fig. 4

Surface velocity distribution normalized simulation results: R160 tool, Z-offset: 2.8mm, Precess angle: 10°.

Fig. 5
Fig. 5

The elements and the restraints on the FEM model for R160mm tool.

Fig. 6
Fig. 6

The absolute pressure distribution simulation results (R160mm tool, 2.8mm Z-offset, 60mm spot-size).

Fig. 7
Fig. 7

The absolute pressure distribution simulation results (Overhang: 5mm, 15mm, 20mm, 25mm).

Fig. 8
Fig. 8

The sketch of the set-up of the force measurement.

Fig. 9
Fig. 9

The force with different Z-offset measurement result of R160mm bonnet tool.

Fig. 10
Fig. 10

The schematic diagram of interpolating 3D TIF at the edge, where (a) 2D scanning and interpolating boundary of TIF (b) Interpolating of 3D in the vicinity of edge of TIF.

Fig. 11
Fig. 11

The results of stitched 3D IFs at the edge (Overhang: 5mm, 15mm, 20mm, 25mm).

Fig. 12
Fig. 12

Comparison of modeling and experimental results of edge TIFs.

Fig. 13
Fig. 13

Preliminary modelling result of edge removal profile, using modelled TIF data.

Fig. 14
Fig. 14

Edge control results (200mm cross corners, Zerodur hexagonal part).

Tables (1)

Tables Icon

Table 1 Materials Characteristics for Modeling

Equations (9)

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

Δh(x,y)=kν(x,y)p(x,y)
R(x,y)= 1 T 0 T Δh(x,y)dt= 1 T 0 T kν(x,y)p(x,y)dt
T= 2π / ω 0
R(r)= 1 T 0 T kv(x,y)p(x,y)dt= k 2π θ 0 θ 0 v(x,y)p(x,y)dθ
v ' p1 (x,y)=2cosρ (Rd) 1 s(sα)(sβ)(sγ) ω 0
α= [ (Rr) 2 + x 2 + y 2 ] 1/2 ; β=(Rd) (cosρ) 1 ; γ= [ y 2 + [(Rd)tgρx] 2 ] 1/2 ; s= 1 2 αβγ v p2 =rω
v p (x,y)= ( v ' p1 (x,y)) 2 + ( v p2 (x,y)) 2 +2cosα v ' p1 (x,y) v p2 (x,y)
f= A p(x,y)dxdy
f R160 =16.43kg

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