Abstract

Based on our previously reported annular subaperture reconstruction algorithm with Zernike annular polynomials and matrix method, we provide an experimental demonstration by testing a parabolic mirror with the complementary annular subaperture interferometric method. By comparing the results of annular subaperture method with that of the classical auto-collimation method, it is shown that the reconstruction results are in good agreement with the auto-collimation measurement. In addition, we discuss some limitations of characterizing annular subaperture measurement data with finite Zernike coefficients in our algorithm, and also show the possibility of characterizing higher spatial frequency information with adequate Zernike coefficients. It is believable that the reported method can be extended to test the surface shape of some large concave aspheric mirrors with acceptable accuracy.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
    [CrossRef]
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    [CrossRef]
  12. M. Tricard and P. E. Murphy, "Subaperture stitching for large aspheric surfaces," in Talk for NASA Tech Day 2006.
  13. S. Chen, S. Li, Y. Dai, and Z. Zheng, "Testing of large optical surfaces with subaperture stitching," Appl. Opt. 46, 3504-3509 (2007).
    [CrossRef] [PubMed]
  14. Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
    [CrossRef] [PubMed]
  15. M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).
  16. F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
    [CrossRef]
  17. J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology, of Applied Optics and Optical Engineering Series (Academic, 1992), Vol. 11 p. 28.
  18. X. Hou, F. Wu, L. Yang, and Q. Chen, "Comparison of annular wavefront interpretation with Zernike circle polynomials and annular polynomials," Appl. Opt. 45, 8893-8901 (2006).
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2007 (1)

2006 (2)

2005 (1)

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

2004 (1)

F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
[CrossRef]

2003 (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

2001 (1)

T. Hänsel, A. Nickel, and A. Schindler, "Stitching interferometry of aspherical surfaces," Proc. SPIE 4449, 265-273 (2001).
[CrossRef]

1997 (1)

M. Bray, "Stitching interferometer for large plano optics using a standard interferometer," Proc. SPIE 3134, 39-50 (1997).
[CrossRef]

1994 (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, "Measurement of large plane surface shapes by connecting small-aperture interferograms," Opt. Eng. 33, 608-613 (1994).
[CrossRef]

1993 (1)

M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).

1988 (1)

Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

1984 (1)

1983 (1)

1982 (2)

C. J. Kim, "Polynomial fit of interferograms," Appl. Opt. 21, 4521-4525 (1982).
[CrossRef] [PubMed]

J. G. Thunen and O. Y. Kwon, "Full aperture testing with subaperture test optics," Proc. SPIE 351, 19-27 (1982).

1981 (1)

1975 (1)

1968 (1)

Bray, M.

M. Bray, "Stitching interferometer for large plano optics using a standard interferometer," Proc. SPIE 3134, 39-50 (1997).
[CrossRef]

Chen, Q.

Chen, S.

Chow, W. W.

Cornejo, A.

Cornejo-Rodríguez, A.

F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
[CrossRef]

Dai, Y.

Day, R. D.

De Hainaut, C. R.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Dutton, D.

Erteza, A.

Escobar-Romero, J. F.

F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
[CrossRef]

Fleig, J.

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Forbes, G.

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Granados-Agustín, F.

F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
[CrossRef]

Hänsel, T.

T. Hänsel, A. Nickel, and A. Schindler, "Stitching interferometry of aspherical surfaces," Proc. SPIE 4449, 265-273 (2001).
[CrossRef]

Hou, X.

Kim, C. J.

Koliopoulos, C.

Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
[CrossRef] [PubMed]

Kwon, O. Y.

J. G. Thunen and O. Y. Kwon, "Full aperture testing with subaperture test optics," Proc. SPIE 351, 19-27 (1982).

Latta, M.

Lawrence, G.

Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
[CrossRef] [PubMed]

Lawrence, G. N.

Li, S.

Liu, Y. M.

Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
[CrossRef] [PubMed]

Mahajan, V. N.

Mazzoni, A.

M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).

Melozzi, M.

M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).

Murphy, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Murphy, P. E.

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

Negro, J. E.

Nickel, A.

T. Hänsel, A. Nickel, and A. Schindler, "Stitching interferometry of aspherical surfaces," Proc. SPIE 4449, 265-273 (2001).
[CrossRef]

Okada, K.

M. Otsubo, K. Okada, and J. Tsujiuchi, "Measurement of large plane surface shapes by connecting small-aperture interferograms," Opt. Eng. 33, 608-613 (1994).
[CrossRef]

Otsubo, M.

M. Otsubo, K. Okada, and J. Tsujiuchi, "Measurement of large plane surface shapes by connecting small-aperture interferograms," Opt. Eng. 33, 608-613 (1994).
[CrossRef]

Pezzati, L.

M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).

Rimmer, M. P.

Schindler, A.

T. Hänsel, A. Nickel, and A. Schindler, "Stitching interferometry of aspherical surfaces," Proc. SPIE 4449, 265-273 (2001).
[CrossRef]

Thunen, J. G.

J. G. Thunen and O. Y. Kwon, "Full aperture testing with subaperture test optics," Proc. SPIE 351, 19-27 (1982).

Tricard, M.

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Tsujiuchi, J.

M. Otsubo, K. Okada, and J. Tsujiuchi, "Measurement of large plane surface shapes by connecting small-aperture interferograms," Opt. Eng. 33, 608-613 (1994).
[CrossRef]

Wu, F.

Wu, S.

Wyant, J. C.

Yang, L.

Zheng, Z.

Appl. Opt. (8)

Appl.Opt. (2)

X. Hou, F. Wu, L. Yang, and Q. Chen, "Comparison of annular wavefront interpretation with Zernike circle polynomials and annular polynomials," Appl. Opt. 45, 8893-8901 (2006).
[CrossRef] [PubMed]

Y. M. Liu, G. Lawrence, and C. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt. 27, 4504-4513 (1988).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, "Measurement of large plane surface shapes by connecting small-aperture interferograms," Opt. Eng. 33, 608-613 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Photonics News (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, "Stitching interferometry: A flexible solution for surface metrology," Opt. Photonics News 14, 38-43 (2003).
[CrossRef]

Opt.Eng. (1)

M. Melozzi, L. Pezzati, and A. Mazzoni, "Testing aspheric surfaces using mulitiple annular interferograms," Opt. Eng. 32, 1073-1079 (1993).

Opt.Rev. (1)

F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, "Testing parabolic surfaces with annular subaperture interferograsm," Opt. Rev. 11, 82-86 (2004).
[CrossRef]

Proc. SPIE (4)

P. E. Murphy, J. Fleig, G. Forbes, and M. Tricard, "High precision metrology of demes and aspheric optics," Proc. SPIE 5786,112-121 (2005).
[CrossRef]

M. Bray, "Stitching interferometer for large plano optics using a standard interferometer," Proc. SPIE 3134, 39-50 (1997).
[CrossRef]

T. Hänsel, A. Nickel, and A. Schindler, "Stitching interferometry of aspherical surfaces," Proc. SPIE 4449, 265-273 (2001).
[CrossRef]

J. G. Thunen and O. Y. Kwon, "Full aperture testing with subaperture test optics," Proc. SPIE 351, 19-27 (1982).

Other (3)

MetroPro Manual, Version 7.4.2,2001, Zygo corporation,http://www.zygo.com

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

J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology, of Applied Optics and Optical Engineering Series (Academic, 1992), Vol. 11 p. 28.

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Figures (10)

Fig. 1.
Fig. 1.

Subaperture configurations for testing aspheric surface: ( a ) non-overlapping circle subapertures, (b) overlapping circle subapertures, (c) overlapping annular subapertures, (d) complementary annular subapertures.

Fig. 2.
Fig. 2.

Geometry of annular subaperture interferometric method.

Fig. 3.
Fig. 3.

Simulated interferograms from aspheric surface tested with spherical wavefront, showing the change of null fringe and resolvable subaperture area with the increase of d..

Fig. 4.
Fig. 4.

Experimental setup for testing a parabolic mirror with annular subaperture method.

Fig. 5.
Fig. 5.

Experiment results: ( a) interferogram , (b) surface map of the inner subaperture after masking (PV=1.989 λ , rms=4. 667 λ); (c) interferogram, (d) surface map of the outer subaperture after masking (PV=4.051 λ, rms=2.365 λ).

Fig. 6.
Fig. 6.

Reconstruction result removed piston, tilts, defocus and coma: (a) 2-D plot, (b) 3-D plot (PV= 0..331 λ, rms= 0.055 λ).

Fig. 7.
Fig. 7.

Results of auto-collimation measurement removed piston, tilts, defocus and coma: (a) 2-D plot, (b) 3-D plot based on the phase data (PV= 0.323 λ, rms= 0.061 λ); (c) and 2-D plot, (d) 3-D plot based on the first 36-term Zernike fitting (PV= 0.311 λ, rms= 0.054 λ).

Fig. 8.
Fig. 8.

Non-null measurement result for: (a) full-aperture (PV= 4.198 λ, rms= 1.092 λ), (b) and annular subaperture method (PV=4.124 λ, rms= 1.139 λ).

Fig. 9.
Fig. 9.

Graphics representation of the inner subaperture data removed piston, tilts and power: (a) the 2-D plot, (b) the corresponding profile, (c) the corresponding 3-D plot, (d) the 3-D plot with 36-term Zernike fitting, (e) the 3-D plot with 100-term Zernike fitting, (f) the 3-D plot with 230-term Zernike fitting.

Fig. 10.
Fig. 10.

Residual surface map of the 36-term Zernike fitting for (a) the inner subaperture, (b) and the outer subaperture. Note the local irregularity and higher spatial-frequency information.

Tables (1)

Tables Icon

Table 1 Comparison of the residual rms value of Zernike fitting with different term number

Equations (3)

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

W ( P , Θ , ε 0 ) = k = 1 K i = 1 4 b ki Z ki ( ρ k , θ , ε k ) + i = 5 L B i Z i ( P , Θ , ε 0 ) ,
W ( P , Θ , ε 0 ) = k = 1 K i = 1 L a ki Z ki ( ρ k , θ , ε k ) ,
k = 1 K i = 1 L a ki Z ki ( ρ k , θ , ε k ) = k = 1 K i = 1 4 b ki Z ki ( ρ k , θ , ε k ) + i = 5 L B i Z i ( P , Θ , ε 0 ) .

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