Abstract

Based on our previously proposed subaperture stitching and localization (SASL) algorithm, we present strategies and a prototype for testing of large optical surfaces with subaperture stitching. First, several strategies are introduced to deal with new problems when applying the SASL algorithm to large surfaces. The uncertainty of the lateral scale of the interferometer is compensated in the same manner as that of the radii of best-fit spheres in the algorithm. Then the coarse–fine stitching strategy is proposed to stitch tens of subapertures efficiently. Second, a prototype for testing of large surfaces with subaperture stitching is developed with a welded structural base. The model of kinematics is built to determine the initial configuration of each subaperture, according to the records of nulling motion. The uncertainty of linear motion is required to be no more than 1 mm, taking advantage of the large range of convergence of the SASL algorithm. Finally we present an experiment to verify the validity of the method and the prototype. A spherical surface is tested and successfully stitched with 37 subapertures.

© 2007 Optical Society of America

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References

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  1. J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
    [CrossRef]
  2. M. Tricard and P. E. Murphy, "Subaperture stitching for large aspheric surfaces," in Talk for NASA Tech Day 2005.
  3. M. Tricard and P. E. Murphy, "Subaperture stitching interferometry for large aspheric optics," in Talk for NASA Tech Day 2006.
  4. S. Y. Chen, S. Y. Li, and Y. F. Dai, "An iterative algorithm for subaperture stitching interferometry for general surface," J. Opt. Soc. Am. A 22, 1929-1936 (2005).
    [CrossRef]
  5. S. Y. Chen, S. Y. Li, Y. F. Dai, and Z. W. Zheng, "Iterative algorithm for subaperture stitching test with spherical interferometers," J. Opt. Soc. Am. A 23, 1219-1226 (2006).
    [CrossRef]
  6. S. Y. Chen, S. Y. Li, Y. F. Dai, and Z. W. Zheng, "Lattice design for subaperture stitching test of a concave paraboloid surface," Appl. Opt. 45, 2280-2286 (2006).
    [CrossRef] [PubMed]
  7. R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

2006 (3)

2005 (2)

2003 (1)

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

1994 (1)

R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Chen, S. Y.

Dai, Y. F.

Dumas, P.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

Fleig, J.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

Forbes, G. W.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

Li, S. Y.

Li, Z. X.

R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Murphy, P. E.

M. Tricard and P. E. Murphy, "Subaperture stitching interferometry for large aspheric optics," in Talk for NASA Tech Day 2006.

M. Tricard and P. E. Murphy, "Subaperture stitching for large aspheric surfaces," in Talk for NASA Tech Day 2005.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

Murray, R.

R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Sastry, S. S.

R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Tricard, M.

M. Tricard and P. E. Murphy, "Subaperture stitching interferometry for large aspheric optics," in Talk for NASA Tech Day 2006.

M. Tricard and P. E. Murphy, "Subaperture stitching for large aspheric surfaces," in Talk for NASA Tech Day 2005.

Zheng, Z. W.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Proc. SPIE (1)

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," Proc. SPIE 5188, 296-307 (2003).
[CrossRef]

Other (3)

M. Tricard and P. E. Murphy, "Subaperture stitching for large aspheric surfaces," in Talk for NASA Tech Day 2005.

M. Tricard and P. E. Murphy, "Subaperture stitching interferometry for large aspheric optics," in Talk for NASA Tech Day 2006.

R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

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Figures (6)

Fig. 1
Fig. 1

(Color online) SASI prototype.

Fig. 2
Fig. 2

Equivalent kinematic mechanism of the SASI.

Fig. 3
Fig. 3

Lattice of the tested surface.

Fig. 4
Fig. 4

(Color online) Measured central and outmost subapertures.

Fig. 5
Fig. 5

Flow chart of stitching.

Fig. 6
Fig. 6

(Color online) Results of full test and SAT.

Equations (16)

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[ x y z ] = [ r + ϕ r t s u r + ϕ r t s v r t s r + ϕ r t s r t s 2 u 2 v 2 ] ,
f i w j , i = g i 1 [ r i + ϕ j , i r t s u j , i , r i + ϕ j , i r t s v j , i , r t s r i + ϕ j , i r t s r t s 2 u j , i 2 v j , i 2 , 1 ] T ,
S E ( 3 ) = { exp ( t = 1 6 m t ξ ^ t ) } ,
ξ ^ = ( ω ^ v 0 0 )
g i S E ( 3 ) / G 0 = { exp ( t = 1 h m t η ^ t ) G 0 } ,
min F = μ 1 σ 2 + μ 2 σ o 2 ,
σ 2 = i = 1 s j = 1 N i f i w j , i x j , i , n j , i 2 / i = 1 s N i ,
σ o 2 = i = 1 s 1 k = i + 1 s j o = 1 N o i k ( f k w i k j o , k x i k j o , k , n i k j o , k f i w i k j o , i x i k j o , k , n i k j o , k ) 2 / N o ,
[ x y z ] = [ r + ϕ r t s γ u r + ϕ r t s γ v r t s r + ϕ r t s r t s 2 γ 2 u 2 γ 2 v 2 ] .
[ x y z ] = [ ( r + ϕ ) β u ( r + ϕ ) β v r t s ( r + ϕ ) 1 β 2 ( u 2 + v 2 ) ] ,
f i w j , i = g i 1 [ ( r i + ϕ j , i ) β i u j , i , ( r i + ϕ j , i ) β i v j , i , r t s ( r i + ϕ j , i ) 1 β i 2 ( u j , i 2 + v j , i 2 ) , 1 ] T .
{ g i l + 1 = g i l exp ( t = 1 h m t , i η ^ t ) g i l ( I + t = 1 h m t , i η ^ t ) r i l + 1 = r i l + r ˜ i β i l + 1 = β i l + β ˜ i = 1 , , s .
g i = g 0 exp { ξ ^ z z } exp { ξ ^ b b } exp { ξ ^ x x } exp { ξ ^ y y } exp { ξ ^ c c } ,
g 0 = [ 1 0 0 0 0 1 0 0 0 0 1 r t s r c 0 0 0 1 ] , ξ ^ x = [ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ] ,
ξ ^ y = [ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ] , ξ ^ z = [ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ] ,
ξ ^ b = [ 0 0 0 0 0 0 r c l 1 0 l r c 0 0 0 0 0 0 ] , ξ ^ c = [ 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ] .

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