Abstract

A novel subaperture stitching interferometry is developed to measure the surface deformation of the lens by utilizing the mechanical vibration induced from a motorized stage. The interferograms of different subapertures are acquired on the fly while the tested optics is rotating against its symmetrical axis. The measurement throughput and the subaperture positioning accuracy are improved simultaneously by adopting both the synchronous rotational scanning mechanism and the non-uniform phase shifting algorithm. The experimental measurement shows the stitched phase RMS error of 0.0037 waves proving the feasibility of the proposed phase acquisition method.

© 2013 OSA

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    [CrossRef]
  3. E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. 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]
  7. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
    [CrossRef]
  8. Y.-M. Liu, G. N. Lawrence, and C. L. Koliopoulos, “Subaperture testing of aspheres with annular zones,” Appl. Opt. 27(21), 4504–4513 (1988).
    [CrossRef] [PubMed]
  9. M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993).
    [CrossRef]
  10. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. S. Chen, S. Li, and Y. Dai, “Iterative algorithm for subaperture stitching interferometry for general surfaces,” J. Opt. Soc. Am. A 22(9), 1929–1936 (2005).
    [CrossRef] [PubMed]
  14. P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
    [CrossRef]

2013 (1)

2012 (1)

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

2008 (1)

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE 7063, 706316 (2008).
[CrossRef]

2006 (1)

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

2005 (1)

2004 (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

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]

2001 (1)

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

1994 (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[CrossRef]

1993 (1)

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

1988 (1)

1983 (1)

1980 (1)

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19(5), 195679 (1980).
[CrossRef]

Brock, N. J.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Burge, J. H.

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE 7063, 706316 (2008).
[CrossRef]

Chang, H. S.

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

Chen, S.

Chen, Y. A.

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

Chen, Y. C.

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

Chen, Y.-C.

Chow, W. W.

Dai, Y.

DeVries, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

Drauschke, A.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

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.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[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]

Forbes, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[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]

Hayes, J. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Kley, E.-B.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Koliopoulos, C. L.

Lawrence, G. N.

Lee, C.-M.

Li, S.

Liang, C. W.

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

Liang, C.-W.

Lin, P. C.

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[CrossRef]

Lin, P.-C.

Liu, Y.-M.

Loomis, J. S.

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19(5), 195679 (1980).
[CrossRef]

Mazzoni, A.

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

Melozzi, M.

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

Miladinovic, D.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

Millerd, J. E.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Murphy, P.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

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]

North-Morris, M. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

O'Donohue, S.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

Okada, K.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 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(2), 608–613 (1994).
[CrossRef]

Pezzati, L.

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

Rockstroh, W.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Schmidt, H.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Tsujiuchi, J.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[CrossRef]

Wittig, L.-C.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Wyant, J. C.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Wyrowski, F.

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Zhao, C.

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE 7063, 706316 (2008).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Eng. (3)

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19(5), 195679 (1980).
[CrossRef]

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[CrossRef]

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

Opt. Lett. (1)

Proc. SPIE (6)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE 7063, 706316 (2008).
[CrossRef]

P. C. Lin, Y. A. Chen, H. S. Chang, C. W. Liang, and Y. C. Chen, “Aberration compensation and position scanning of a subaperture stitching algorithm,” Proc. SPIE 8494, 84940L, 84940L-8 (2012).
[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]

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[CrossRef]

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE 4440, 135–144 (2001).
[CrossRef]

Other (1)

D. Malacara, Optical shop testing (Wiley-Interscience, 2007).

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Figures (4)

Fig. 1
Fig. 1

(a) The proposed subaperture interferometer setup; note that there are three axes for optical null and one axis for the rotational measurement. (b) The tested area forms a ring surface at same radial height of the tested surface during the rotational measurement.

Fig. 2
Fig. 2

(a) The potential vibration range during the stage rotation. (b) The decomposition of vibration into longitudinal direction vibration and transverse direction vibration, which induce random phase shift and tilts respectively during the phase acquisition.

Fig. 3
Fig. 3

60 interferograms located at 12 different subapertures are taken in five rotation cycles. Note the random distribution of the piston phase shifting across these rotational cycles.

Fig. 4
Fig. 4

(a) The single full aperture measurement. (b) The stitched subapertures measurement. (c) The stitching error map. (d) The map of subaperture overlapping times.

Equations (3)

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I i (x,y)= I dc (x,y)+ I ac (x,y)cos[ ϕ(x,y)+ p i +x T i x +y T i y ], for i=1,2,...,M,
S= k K ij N [ ( φ i (k)+ δ i + α i x+ β i y+ κ i ( x 2 + y 2 ) )( φ j (k)+ δ j + α j x+ β j y+ κ j ( x 2 + y 2 ) ) ] 2 ,
σ( k )= 1 N( k ) i=1 N( k ) [ φ ^ i ( k ) φ avg ( k ) ] 2 ,

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