Abstract

We propose an elliptical sub-aperture stitching (ESAS) method to measure the aspheric surfaces. In our method, the non-null configuration is used to overcome the disadvantages of the null testing. By adding the dynamic tilt, the different local nearly null fringe patterns are obtained and the corresponding phase data in the elliptical masks is extracted with negligible retrace errors. In order to obtain the full aperture result, a stitching algorithm is developed to stitch all the phase data together. We firstly show the principle of our method. Then the performance of the proposed method is analyzed by simulation experiments. In the end, practical examples are given to demonstrate the correctness of the proposed method. The stitching result shows a good agreement with the full-aperture null testing result.

© 2014 Optical Society of America

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  1. D. Malacara, Optical Shop Testing, (Wiley 2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
    [CrossRef]
  8. X. Hou, F. Wu, L. Yang, Q. Chen, “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15(20), 12890–12899 (2007).
    [CrossRef] [PubMed]
  9. P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
    [CrossRef]
  10. S. Chen, S. Li, Y. Dai, Z. Zheng, “Lattice design for subaperture stitching test of a concave paraboloid surface,” Appl. Opt. 45(10), 2280–2286 (2006).
    [CrossRef] [PubMed]
  11. P. F. Zhang, H. Zhao, X. A. Zhou, J. J. Li, “Sub-aperture stitching interferometry using stereovision positioning technique,” Opt. Express 18(14), 15216–15222 (2010).
    [CrossRef] [PubMed]
  12. M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
    [CrossRef]
  13. J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
    [CrossRef]
  14. Z. Malacara, Interferogram Analysis for Optical Testing, (The Chemical Rubber Company 2010).
  15. M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
    [CrossRef]

2010 (1)

2009 (2)

2007 (1)

2006 (1)

2004 (1)

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

2003 (3)

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

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
[CrossRef]

1996 (1)

1993 (1)

M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
[CrossRef]

1988 (1)

1981 (1)

C. J. Kim, J. C. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Abdulkadyrov, M. A.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Atad-Ettedgui, E.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Bennett, R. J.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Chen, Q.

Chen, S.

Cornejo-Rodriguez, A.

F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
[CrossRef]

Craig, S. C.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Dai, Y.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

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

Egan, I.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Escobar-Romero, F.

F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
[CrossRef]

Fleig, J.

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

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

Forbes, G.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

Forbes, G. W.

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

Granados-Agustin, F. S.

F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
[CrossRef]

Greivenkamp, J. E.

Hou, X.

Ignatov, A. N.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Kim, C. J.

C. J. Kim, J. C. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Koliopoulos, C. L.

Küchel, M. F.

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
[CrossRef]

Lawrence, G. N.

Li, J. J.

Li, S.

Liu, D.

Liu, Y. M.

Lowman, A. E.

Luo, Y.

Mazzoni, A.

M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
[CrossRef]

Melozzi, M.

M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
[CrossRef]

Murphy, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

Murphy, P. E.

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

Patrikeev, V. E.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Pezzati, L.

M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
[CrossRef]

Polyanchikov, A. V.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Pridnya, V. V.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Semenov, A. P.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Sharov, Y. A.

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Tian, C.

Tricard, M.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

Wang, L.

Wu, F.

Wyant, J. C.

C. J. Kim, J. C. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Yang, L.

Yang, Y.

Zhang, P. F.

Zhao, H.

Zheng, Z.

Zhou, X. A.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

C. J. Kim, J. C. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Opt. Eng. (1)

M. Melozzi, L. Pezzati, A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
[CrossRef]

Opt. Express (3)

Optics & Photonics News (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Optics & Photonics News 14(5), 38–43 (2003).
[CrossRef]

Proc. SPIE (4)

F. S. Granados-Agustin, F. Escobar-Romero, A. Cornejo-Rodriguez, “Testing a paraboloid mirror using annular subapertures without auxiliary optics,” Proc. SPIE 4829, 44–45 (2003).
[CrossRef]

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
[CrossRef]

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

M. A. Abdulkadyrov, A. N. Ignatov, V. E. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, A. P. Semenov, Y. A. Sharov, E. Atad-Ettedgui, I. Egan, R. J. Bennett, S. C. Craig, “M1 and M2 mirrors manufacturing for VISTA telescope. in Astronomical Telescopes and Instrumentation,” Proc. SPIE 5494, 374–381 (2004).
[CrossRef]

Other (2)

Z. Malacara, Interferogram Analysis for Optical Testing, (The Chemical Rubber Company 2010).

D. Malacara, Optical Shop Testing, (Wiley 2007).

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Figures (8)

Fig. 1
Fig. 1

Sketch of the local nearly null zone and fringe patterns. (a) no tilt. (b)with tilt.

Fig. 2
Fig. 2

The first simulation result. (a)global fringe patterns .(b) local fringe patterns with different masks. (c) extracted phase data. (d) stitching result. (e) ideal result. (f) differences between stitching and ideal result.

Fig. 3
Fig. 3

The second simulation result.(a) fringe patterns with different tilts .(b) extracted phase data. (c) stitching result. (d) ideal result. (e)differences between stitching and ideal result.

Fig. 4
Fig. 4

Testing ability of our proposed method with respect to conic constant ( K ) and numerical aperture ( N A ) . (a) the full aperture could be tested with dynamic tilts for the fringe aliasing are not occurred. (b)only the area in the red circle could be tested due to the fringe aliasing in the area outside of the red circle. (c)the area filled by oblique line can be measured and the red circle locates the turning point with K = 1 .

Fig. 5
Fig. 5

The testing ability of our method with respect to the different aspheric coefficient A

Fig. 6
Fig. 6

Experimental setup: an adjustment stage with 5 degrees of freedom is used to add dynamic tilt and an attenuation filter is used to obtain the interferograms with high contrast.

Fig. 7
Fig. 7

Testing result of concave ellipsoid. (a) nine fringe patterns. (b)stitching result with surface sag removed(PV = 0.2213wave, RMS = 0.0176wave). (c)null testing result(PV = 0.198 wave, RMS = 0.015wave). (d)residual error(PV = 0.0929 wave, RM S = 0.0117wave). (wave = 0.6328 um)

Fig. 8
Fig. 8

Testing result of convex hyperboloid. (a) nine fringe patterns. (b)stitching result with surface sag removed(PV = 0.1872wave, RMS = 0.0211wave). (c)null testing result(PV = 0.190 wave, RM S = 0.022wave). (d)residual error(PV = 0.062 wave, RM S = 0.065wave). (wave = 0.6328 um)

Equations (11)

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{ ϕ A ( x , y ) = ϕ O ( x , y ) + P A + T A x · x + T A y · y ϕ B ( x , y ) = ϕ O ( x , y ) + P B + T B x · x + T B y · y ,
F = u 1 j = 1 M m = 1 N 1 n = m + 1 N σ j [ ϕ m j o ( x , y ) ϕ n j o ( x , y ) ( ( P m x P n x ) + ( T m x T n x ) x + ( T m y T n y ) y ] 2 d x d y / N j + u 2 i = 1 N s i ( ϕ i ( x , y ) ( P i + T i x x + T i y y ) ) 2 d x d y / N i ,
A [ E 1 T ... E N T ] T = b ,
A R j = u 1 [ ( 1 , 1 ) ( 1 , x ) ( 1 , y ) ( x , 1 ) ( x , x ) ( x , y ) ( y , 1 ) ( y , x ) ( y , y ) ] ,
b r j = u 1 [ ( 1 , ϕ m j o ( x , y ) ϕ n j o ( x , y ) ) ( x , ϕ m j o ( x , y ) ϕ n j o ( x , y ) ) ( y , ϕ m j o ( x , y ) ϕ n j o ( x , y ) ) ] ,
A F i = u 2 [ ( 1 , 1 ) ( 1 , x ) ( 1 , y ) ( x , 1 ) ( x , x ) ( x , y ) ( y , 1 ) ( y , x ) ( y , y ) ] ,
b f i = u 2 [ ( 1 , ϕ i ( x , y ) ) ( x , ϕ i ( x , y ) ) ( y , ϕ i ( x , y ) ) ] ,
A = j = 1 M [ U m j A R j U m j T + U n j A R j U n j T U m j A R j U n j T U n j A R j U m j T ] + i = 1 N U i A F i U i T ,
b = j = 1 M [ ( U m i U n i ) · b r i ] + i = 1 N U i b f i ,
Z ( s ) = c · s 2 1 + 1 ( 1 + K ) · c 2 · s 2 + A · s 4 + B · s 6 + C · s 8 + D · s 10 + ,
W ( x , y ) x λ 2 · ( Δ x ) ,

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