Abstract

In off-axis subapertures of most aspheres, astigmatism and coma dominate the aberrations with approximately quadratic and linear increase as the off-axis distance increases. A pair of counter-rotating Zernike plates is proposed to generate variable amount of Zernike terms Z4 and Z6, correcting most of the astigmatism and coma for subapertures located at different positions on surfaces of various aspheric shapes. The residual subaperture aberrations are then reduced within the vertical dynamic range of measurement of the interferometer. The plates are fabricated with computer generated holograms and the experimental results show the variable aberration correction effect without ghost fringes. The same plates are reconfigurable by counter-rotating to enable near-null test of various aspheres flexibly.

© 2014 Optical Society of America

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References

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  1. S. Chen, S. Li, Y. Dai, L. Ding, S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
    [CrossRef] [PubMed]
  2. S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
    [CrossRef]
  3. M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).
  4. S. Chang, A. Prata., “Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes,” J. Opt. Soc. Am. A 22(11), 2454–2464 (2005).
    [CrossRef] [PubMed]
  5. E. Acosta, S. Bará, “Variable aberration generators using rotated Zernike plates,” J. Opt. Soc. Am. A 22(9), 1993–1996 (2005).
    [CrossRef] [PubMed]
  6. J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
    [CrossRef]
  7. P. Murphy, G. Devries, and C. Brophy, “Stitching of near-nulled subaperture measurements,” US patent 2009/0251702 A1 (2009).
  8. S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
    [CrossRef]
  9. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Lincoln Lab. Tech. Rep. 854 (MIT Lincoln Laboratory, Lexington, Mass., 1989).
  10. M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
    [CrossRef]

2013 (1)

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

2010 (2)

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

2008 (1)

2005 (2)

2003 (1)

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

1999 (1)

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Acosta, E.

Antoine, P.

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Bará, S.

Bauer, M.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Bittner, H.

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Chang, S.

Chen, S.

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

Dai, Y.

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

DeVries, G.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Ding, L.

Ellis, K. S.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Erdmann, M.

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Fleig, J.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Forbes, G.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Fruit, M.

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Knapp, D. J.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Kulawiec, A.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Li, S.

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

Manhart, P. K.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Miladinovich, D.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Mills, J. P.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Mitchell, T. A.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Murphy, P.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Peng, X.

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

Prata, A.

Sparrold, S. W.

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

Tricard, M.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

Varin, J.-L.

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Zeng, S.

Zhao, C.

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

CIRP Annals Manufacturing Technology. (1)

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals Manufacturing Technology. 59, 547–550 (2010).

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

Opt. Eng. (1)

S. Chen, Y. Dai, S. Li, X. Peng, “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Chen, C. Zhao, S. Li, Y. Dai, “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307–315 (2013).
[CrossRef]

Proc. SPIE (2)

J. P. Mills, S. W. Sparrold, T. A. Mitchell, K. S. Ellis, D. J. Knapp, P. K. Manhart, “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201–208 (1999).
[CrossRef]

M. Fruit, P. Antoine, J.-L. Varin, H. Bittner, M. Erdmann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 274–285 (2003).
[CrossRef]

Other (2)

P. Murphy, G. Devries, and C. Brophy, “Stitching of near-nulled subaperture measurements,” US patent 2009/0251702 A1 (2009).

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Lincoln Lab. Tech. Rep. 854 (MIT Lincoln Laboratory, Lexington, Mass., 1989).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the counter-rotating Zernike plates.

Fig. 2
Fig. 2

Coordinate frames for off-axis subaperture.

Fig. 3
Fig. 3

(a) Subaperture lattice. (b) Optical layout of near-null subaperture test.

Fig. 4
Fig. 4

Near-null subaperture interferograms at different off-axis distances (λ = 632.8nm): (a) mirror 1 (peak-to-valley residual aberrations are 3.2 λ, 5.7 λ, 3.8 λ and 9.0 λ, respectively), (b) mirror 2 (peak-to-valley residual aberrations are 3.1 λ, 4.6 λ, 5.6 λ and 4.0 λ, respectively).

Fig. 5
Fig. 5

Near-null subaperture test with counter-rotating CGHs. (a) CGH in mount. (b) Set-up of near-null subaperture test.

Fig. 6
Fig. 6

Near-null subaperture wavefronts: (a) center (PV 2.522 λ, RMS 0.338 λ), (b) ring 1 (PV 3.035 λ, RMS 0.603 λ), (c) ring 2 (PV 5.359 λ, RMS 0.905 λ), (d) ring 3 (PV 4.015 λ, RMS 0.707 λ).

Fig. 7
Fig. 7

Subaperture wavefronts without CGHs counter-rotating: (a) ring 2 (PV 21.311 λ, RMS 3.669 λ), (b) ring 3 (irresolvable).

Fig. 8
Fig. 8

Near-null subaperture stitching result: (a) without stitching optimization, (b) with stitching optimization.

Tables (1)

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Table 1 Phase description of the two plates

Equations (9)

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x 2 + y 2 =2Rz( 1 e 2 ) z 2 .
( xcosβ+zsinβ+ x 0 ) 2 + y 2 +2R( xsinβzcosβ z 0 )+( 1 e 2 ) ( xsinβzcosβ z 0 ) 2 =0.
z z s = c 0 + c 1 x 2 + c 2 y 2 + c 3 x 3 + c 4 x y 2 .
Z 4 = x 2 y 2 , Z 6 =2x+3x( x 2 + y 2 ), Z 9 = x 3 3x y 2 .
P 4 = e 2 sin 2 β 4R 1 e 2 sin 2 β , P 6 = 1 e 2 sin 2 β 24 R 2 e 2 sinβcosβ( 43 e 2 sin 2 β ), P 9 = 1 e 2 sin 2 β 8 R 2 e 4 sin 3 βcosβ .
P 6 P 9 =1 4 3 1 e 2 sin 2 β .
Z=a Z 5 +b Z 7 =a ρ 2 sin2θ+b( 3 ρ 2 2 )ρsinθ.
W=2asin2α Z 4 +2bsinα Z 6 .
{ P 4i =2asin2 α i P 6i =2bsin α i .

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