Abstract

We introduce a novel phase-shifting pixellated interferometer based on a liquid-crystal spatial light modulator and simulate the expected performance. The phase-shifted frames are captured simultaneously, which reduces problems arising from vibrations and air turbulence. The liquid-crystal spatial light modulator is flexible and can be configured to provide a large number of phase-shift levels and geometries to reduce measurement error.

© 2006 Optical Society of America

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References

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  1. K. Creath, in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D.W.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), pp. 94-140.
  2. J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
    [CrossRef]
  3. C. R. Mercer and K. Creath, Opt. Lett. 19, 916 (1994).
    [CrossRef] [PubMed]
  4. H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
    [CrossRef]
  5. M. J. Guardalben, L. Ning, N. Jain, D. J. Battaglia, and K. L. Marshall, Appl. Opt. 41, 1353 (2002).
    [CrossRef] [PubMed]
  6. G. D. Love, T. J. D. Oag, and A. K. Kirby, Opt. Express 13, 3491 (2005).
    [CrossRef] [PubMed]
  7. Y. Bitou, Opt. Lett. 28, 1576 (2003).
    [CrossRef] [PubMed]
  8. K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

2005 (1)

2004 (2)

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

2003 (1)

2002 (1)

1994 (2)

C. R. Mercer and K. Creath, Opt. Lett. 19, 916 (1994).
[CrossRef] [PubMed]

H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
[CrossRef]

Baker, K. L.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Battaglia, D. J.

Bitou, Y.

Creath, K.

C. R. Mercer and K. Creath, Opt. Lett. 19, 916 (1994).
[CrossRef] [PubMed]

K. Creath, in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D.W.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), pp. 94-140.

Gavel, D.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Guardalben, M. J.

Hayes, J.

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Jain, N.

Kadono, H.

H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
[CrossRef]

Kirby, A. K.

Love, G. D.

Marshall, K. L.

Mercer, C. R.

Millerd, J.

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Ning, L.

North-Morris, M.

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Novak, M.

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Oag, T. J.

Ogusu, M.

H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
[CrossRef]

Olivier, S. S.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Olsen, J.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Silva, D. A.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Stappaerts, E. A.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Toyooka, S.

H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
[CrossRef]

Tucker, J.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Wilks, S. C.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Wyant, J.

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Young, P. E.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

Appl. Opt. (1)

Opt. Commun. (1)

H. Kadono, M. Ogusu, and S. Toyooka, Opt. Commun. 110, 391 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Y. Bitou, Opt. Lett. 28, 1576 (2003).
[CrossRef] [PubMed]

K. L. Baker, E. A. Stappaerts, S. C. Wilks, D. Gavel, P. E. Young, J. Tucker, D. A. Silva, S. S. Olivier, and J. Olsen, Opt. Lett. 29, 1576 (2004).

C. R. Mercer and K. Creath, Opt. Lett. 19, 916 (1994).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. Millerd, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, in Proc. SPIE 5531, 304 (2004).
[CrossRef]

Other (1)

K. Creath, in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D.W.Robinson and G.T.Reid, eds. (Institute of Physics Publishing, 1993), pp. 94-140.

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Figures (5)

Fig. 1
Fig. 1

(a) Twyman–Green and (b) self-referencing point diffraction implementations of the single-shot, pixellated PSI that uses a LC-SLM: NPBS’s, nonpolarizing beam splitters; PBS, polarizing beam splitter; M, mirror; L’s, lenses; F’s, filters; P’s, polarizers.

Fig. 2
Fig. 2

Phase masks for the LC-SLM applied to obtain (a) three-, (b) four-, and (c) five-frame single-shot phase-shifting information.

Fig. 3
Fig. 3

Variance as a function of random phase errors in the phase step of the LC-SLM arising from miscalibration or dispersion for broadband illumination.

Fig. 4
Fig. 4

Effective spatial resolution obtainable with a four-bin macropixel reconstructing a sinusoidal phase with 16 subapertures per wavelength by use of various reconstruction algorithms. Int., interferometer.

Fig. 5
Fig. 5

Examination of the effective spatial resolution of the three algorithms as a function of the spatial sampling of the sinusoidal phase.

Equations (3)

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σ 2 1 ζ 0 ζ ( ϕ ζ 2 ) 2 d ϕ = ζ 2 12 .
Phase ( I 4 a ) = 0.25 { a tan ( I 4 a I 2 a I 1 a I 3 a ) + a tan ( I 4 a I 2 a I 1 b I 3 b ) + a tan ( I 4 a I 2 c I 1 c I 3 a ) + a tan ( I 4 a I 2 c I 1 d I 3 b ) } ,
Phase ( I 4 a ) = A tan [ I 4 a 0.5 ( I 2 a + I 2 c ) 0.25 ( I 1 a + I 1 b + I 1 c + I 1 d ) 0.5 ( I 3 a + I 3 b ) ] .

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