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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013

2012

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. SPIE8494, 84940L, 84940L-8 (2012).
[CrossRef]

2008

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE7063, 706316 (2008).
[CrossRef]

2006

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE6293, 62930J (2006).
[CrossRef]

2005

2004

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. SPIE5531, 304–314 (2004).
[CrossRef]

2003

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE5188, 296–307 (2003).
[CrossRef]

2001

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE4440, 135–144 (2001).
[CrossRef]

1994

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

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

1988

1983

1980

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. SPIE5531, 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. SPIE7063, 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. SPIE8494, 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. SPIE8494, 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. SPIE8494, 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. SPIE6293, 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. SPIE4440, 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. SPIE5188, 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. SPIE6293, 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. SPIE5188, 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. SPIE6293, 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. SPIE5188, 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. SPIE5531, 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. SPIE4440, 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. SPIE8494, 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. SPIE8494, 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. SPIE6293, 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. SPIE5531, 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. SPIE6293, 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. SPIE5188, 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. SPIE5531, 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. SPIE5531, 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. SPIE6293, 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. SPIE4440, 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. SPIE4440, 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. SPIE4440, 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. SPIE5531, 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. SPIE4440, 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. SPIE7063, 706316 (2008).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

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

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

Opt. Lett.

Proc. SPIE

E.-B. Kley, W. Rockstroh, H. Schmidt, A. Drauschke, F. Wyrowski, and L.-C. Wittig, “Investigation of large null-CGH realization,” Proc. SPIE4440, 135–144 (2001).
[CrossRef]

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE5188, 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. SPIE6293, 62930J (2006).
[CrossRef]

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. SPIE5531, 304–314 (2004).
[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. SPIE8494, 84940L, 84940L-8 (2012).
[CrossRef]

C. Zhao and J. H. Burge, “Stitching of off-axis sub-aperture null measurements of an aspheric surface,” Proc. SPIE7063, 706316 (2008).
[CrossRef]

Other

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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