Abstract

Applying the iterative stitching algorithm, we demonstrate the power of subaperture testing through experiments. Naturally the algorithm applies to flats, spherical or aspheric surfaces. We first apply it to a silicon carbide flat mirror with larger aperture than the interferometer’s. The testing results help to obtain a high-precision mirror through five iterations of ion beam figuring. The second experiment is 37-subaperture testing of a large spherical mirror. Good consistence is observed between the stitching result and the full aperture test result using a Zygo interferometer. Finally we study the applicability of the algorithm to subaperture testing of a parabolic surface. The stitching result is consistent with the auto-collimation test result. Furthermore, the surface is tested with annular subapertures and also retrieved by our algorithm successfully.

© 2008 Optical Society of America

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References

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  1. S. Y. Chen, S. Y. Li, and Y. F. Dai, "Iterative algorithm for subaperture stitching interferometry for general surfaces," J. Opt. Soc. Am. A 22, 1929-1936 (2005).
    [CrossRef]
  2. 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]
  3. S. Y. Chen, S. Y. Li, Y. F. Dai, and Z. W. Zheng, "Testing of large optical surfaces with subaperture stitching," Appl. Opt. 46, 3504-3509 (2007).
    [CrossRef] [PubMed]
  4. P. Murphy, J. Fleig, G. Forbes,  et al., "Subaperture stitching interferometry for testing mild aspheres," Proc. SPIE 6293, 62930J-1-62930J-10 (2006).
    [CrossRef]
  5. J. G. Thunen and O. Y. Kwon, "Full aperture testing with subaperture test optics," Proc. SPIE 351, 19-27 (1982).
  6. W. W. Chow and G. N. Lawrence, "Method for subaperture testing interferogram reduction," Opt. Lett. 8, 468-470 (1983).
    [CrossRef] [PubMed]
  7. T. W. Stuhlinger, "Subaperture optical testing: experimental verification," Proc. SPIE 656, 118-127 (1986).
  8. M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
    [CrossRef]
  9. 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]
  10. S. H. Tang, "Stitching: high-spatial-resolution microsurface measurements over large areas," Proc. SPIE 3479, 43-49 (1998).
    [CrossRef]
  11. M. Sjöedahl and B. F. Oreb, "Stitching interferometric measurement data for inspection of large optical components," Opt. Eng. 41, 403-408 (2002).
    [CrossRef]
  12. L. Zhou, Y. F. Dai, X. H. Xie,  et al.,"Model and method to determine dwell time in ion beam figuring," Nanotechnology and Precision Engineering 5, 107-112 (2007).
  13. X. Hou, F. Wu, L. Yang, and Q. Chen,"Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method," Opt. Express 15, 12890-12899 (2007).
    [CrossRef] [PubMed]

2007 (3)

2006 (1)

2005 (1)

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]

2002 (1)

M. Sjöedahl and B. F. Oreb, "Stitching interferometric measurement data for inspection of large optical components," Opt. Eng. 41, 403-408 (2002).
[CrossRef]

1998 (1)

S. H. Tang, "Stitching: high-spatial-resolution microsurface measurements over large areas," Proc. SPIE 3479, 43-49 (1998).
[CrossRef]

1991 (1)

M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
[CrossRef]

1986 (1)

T. W. Stuhlinger, "Subaperture optical testing: experimental verification," Proc. SPIE 656, 118-127 (1986).

1983 (1)

1982 (1)

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

Chen, M. Y.

M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
[CrossRef]

Chen, Q.

Chen, S. Y.

Cheng, W. M.

M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
[CrossRef]

Chow, W. W.

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]

Hou, X.

Kwon, O. Y.

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

Lawrence, G. N.

Li, S. Y.

Murphy, P. E.

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]

Oreb, B. F.

M. Sjöedahl and B. F. Oreb, "Stitching interferometric measurement data for inspection of large optical components," Opt. Eng. 41, 403-408 (2002).
[CrossRef]

Sjöedahl, M.

M. Sjöedahl and B. F. Oreb, "Stitching interferometric measurement data for inspection of large optical components," Opt. Eng. 41, 403-408 (2002).
[CrossRef]

Stuhlinger, T. W.

T. W. Stuhlinger, "Subaperture optical testing: experimental verification," Proc. SPIE 656, 118-127 (1986).

Tang, S. H.

S. H. Tang, "Stitching: high-spatial-resolution microsurface measurements over large areas," Proc. SPIE 3479, 43-49 (1998).
[CrossRef]

Thunen, J. G.

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

Wang, C. W.

M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
[CrossRef]

Wu, F.

Xie, X. H.

L. Zhou, Y. F. Dai, X. H. Xie,  et al.,"Model and method to determine dwell time in ion beam figuring," Nanotechnology and Precision Engineering 5, 107-112 (2007).

Yang, L.

Zheng, Z. W.

Zhou, L.

L. Zhou, Y. F. Dai, X. H. Xie,  et al.,"Model and method to determine dwell time in ion beam figuring," Nanotechnology and Precision Engineering 5, 107-112 (2007).

Appl. Opt. (1)

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

Nanotechnology and Precision Engineering (1)

L. Zhou, Y. F. Dai, X. H. Xie,  et al.,"Model and method to determine dwell time in ion beam figuring," Nanotechnology and Precision Engineering 5, 107-112 (2007).

Opt. Eng. (1)

M. Sjöedahl and B. F. Oreb, "Stitching interferometric measurement data for inspection of large optical components," Opt. Eng. 41, 403-408 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (5)

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

T. W. Stuhlinger, "Subaperture optical testing: experimental verification," Proc. SPIE 656, 118-127 (1986).

M. Y. Chen, W. M. Cheng, and C. W. Wang, "Multiaperture overlap-scanning technique for large-aperture test," Proc. SPIE 1553, 626-635 (1991).
[CrossRef]

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]

S. H. Tang, "Stitching: high-spatial-resolution microsurface measurements over large areas," Proc. SPIE 3479, 43-49 (1998).
[CrossRef]

Other (1)

P. Murphy, J. Fleig, G. Forbes,  et al., "Subaperture stitching interferometry for testing mild aspheres," Proc. SPIE 6293, 62930J-1-62930J-10 (2006).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

SAT of a SiC flat mirror.

Fig. 2.
Fig. 2.

Measured subapertures and retrieved full aperture error of the SiC flat mirror.

Fig. 3.
Fig. 3.

Final results of the SiC flat mirror

Fig. 4.
Fig. 4.

Full aperture error of the spherical mirror.

Fig. 5.
Fig. 5.

Experimental setup for testing a parabolic mirror.

Fig. 6.
Fig. 6.

Measured subapertures of the parabolic mirror.

Fig. 7.
Fig. 7.

Measured annular subapertures of the parabolic mirror.

Fig. 8.
Fig. 8.

Full aperture error of the parabolic mirror obtained from conventional null test as well as two different SAT methods (all with coma removed).

Tables (1)

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Table 1. Comparison between the SASL algorithm and the conventional algorithm

Equations (3)

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[ x , y , z ] = [ β u , β ν , ϕ ]
[ x , y , z ] = [ ( r + ϕ ) β u , ( r + ϕ ) β ν , r ts ( r + ϕ ) 1 β 2 ( u 2 + ν 2 ) ]
f i w j , i = g i −1 [ x j , i , y j , i , z j , i , 1 ] T

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