Abstract

In phase-shifting interferometry experiments, the accuracy of the phase shift is a major issue. Many experimental and data analyses are done to cancel phase-shift errors inherent to the modulation techniques used. We propose to remove most of the phase-shift error by recourse to a frequency-shifting method. This approach can be applied to both holography and interferometry. We validate the idea with a holographic experiment.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Creath, in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349-393.
    [CrossRef]
  2. I. Yamaguchi and T. Zhang, Opt. Lett. 18, 31 (1997).
  3. K. Kinnstaetter, A. W. Lohmann, J. Schwider, and N. Streibl, Appl. Opt. 27, 5082 (1988).
    [CrossRef] [PubMed]
  4. E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 39, 4070 (2000).
    [CrossRef]
  5. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, Appl. Opt. 22, 3421 (1983).
    [CrossRef] [PubMed]
  6. P. Hariharan, B. F. Oreb, and T. Eiju, Appl. Opt. 26, 2504 (1987).
    [CrossRef] [PubMed]
  7. G. Lai and T. Yatagai, J. Opt. Soc. Am. A 8, 822 (1991).
    [CrossRef]
  8. K. G. Larkin and B. F. Oreb, J. Opt. Soc. Am. A 9, 1740 (1992).
    [CrossRef]
  9. P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
    [CrossRef]
  10. J. Schmit and K. Creath, Appl. Opt. 34, 3610 (1995).
    [CrossRef] [PubMed]
  11. B. Gutman and H. Weber, Appl. Opt. 37, 7624 (1998).
    [CrossRef]
  12. J. M. Huntley, J. Opt. Soc. Am. A 15, 2233 (1998).
    [CrossRef]
  13. C. S. Guo, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, Opt. Lett. 27, 1687 (2002).
    [CrossRef]
  14. L. Z. Cai, Q. Liu, and X. L. Yang, Opt. Lett. 29, 183 (2004).
    [CrossRef] [PubMed]
  15. L. Z. Cai, Y. R. Wang, Q. Liu, X. F. Meng, and M. Z. He, Appl. Opt. 45, 1193 (2006).
    [CrossRef] [PubMed]
  16. X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, Opt. Lett. 31, 1966 (2006).
    [CrossRef] [PubMed]
  17. L. Z. Cai, Q. Liu, and X. L. Yang, Opt. Lett. 28, 1808 (2003).
    [CrossRef] [PubMed]
  18. J. A. Ferrari and E. Garbusi, Opt. Lett. 29, 1257 (2004).
    [CrossRef] [PubMed]
  19. L. Z. Cai, Q. Liu, and X. L. Yang, Opt. Lett. 29, 1259 (2004).
    [CrossRef]
  20. F. Le Clerc, L. Collot, and M. Gross, Opt. Lett. 25, 716 (2000).
    [CrossRef]
  21. U. Schnars, J. Opt. Soc. Am. A 11, 977 (1994).
    [CrossRef]
  22. T. Kreis, in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.
    [CrossRef]
  23. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, Opt. Lett. 29, 1668 (2004).
    [CrossRef] [PubMed]
  24. T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
    [CrossRef]
  25. I. Yamaguchi, J. I. Kato, S. Ohta, and J. Mizuno, Appl. Opt. 40, 6177 (2001).
    [CrossRef]

2006 (2)

2004 (4)

2003 (1)

2002 (1)

2001 (1)

2000 (2)

1998 (2)

1997 (2)

I. Yamaguchi and T. Zhang, Opt. Lett. 18, 31 (1997).

T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
[CrossRef]

1995 (1)

1994 (2)

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

U. Schnars, J. Opt. Soc. Am. A 11, 977 (1994).
[CrossRef]

1992 (1)

1991 (1)

1988 (1)

1987 (1)

1983 (1)

Adams, M.

T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
[CrossRef]

Burow, R.

Cai, L. Z.

Collot, L.

Creath, K.

J. Schmit and K. Creath, Appl. Opt. 34, 3610 (1995).
[CrossRef] [PubMed]

K. Creath, in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349-393.
[CrossRef]

Cuche, E.

Deason, V. A.

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Depeursinge, C.

Dong, G. Y.

Eiju, T.

Elssner, K.-E.

Ferrari, J. A.

Garbusi, E.

Gross, M.

Grzanna, J.

Guo, C. S.

Gutman, B.

Hariharan, P.

He, M. Z.

Huntley, J. M.

Jueptner, W. P.

T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
[CrossRef]

Kato, J. I.

Kinnstaetter, K.

Kreis, T.

T. Kreis, in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.
[CrossRef]

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
[CrossRef]

Lai, G.

Larkin, K. G.

Lassahn, G. D.

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Lassahn, J. K.

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Le Clerc, F.

Liao, J.

Liu, Q.

Lohmann, A. W.

Marquet, P.

Meng, X. F.

Merkel, K.

Mizuno, J.

Ohta, S.

Oreb, B. F.

Schmit, J.

Schnars, U.

U. Schnars, J. Opt. Soc. Am. A 11, 977 (1994).
[CrossRef]

Schwider, J.

Shen, X. X.

Spolaczyk, R.

Streibl, N.

Taylor, P. L.

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Wang, H. T.

Wang, Y. R.

Weber, H.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yaroslavsky, L. P.

Yatagai, T.

Zhang, F.

Zhang, L.

Zhang, T.

Zhu, Y. Y.

Appl. Opt. (8)

J. Opt. Soc. Am. A (4)

Opt. Eng. (1)

P. L. Taylor, G. D. Lassahn, J. K. Lassahn, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Opt. Lett. (9)

Proc. SPIE (1)

T. M. Kreis, M. Adams, and W. P. Jueptner, Proc. SPIE 3098, 224 (1997).
[CrossRef]

Other (2)

K. Creath, in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349-393.
[CrossRef]

T. Kreis, in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Phase-shifting digital holography setup. L, main laser; BS, beam splitter; AOM1, AOM2, acousto-optic modulators; BE, beam expander; M, mirror; A1, A2, light attenuators; USAF, transmission USAF 1951 test pattern; CCD, CCD camera; E L , E I , E LO , and E, laser, illumination, LO and object fields; ω AOM 1 2 , driving frequencies of the AOMs.

Fig. 2
Fig. 2

USAF target k-space 1024 × 1024 holograms E ̃ ( k x , k y ) displayed on a logarithmic scale for E ̃ ( k x , k y ) 2 at (a) Δ ω = + 2.5 Hz and (b) Δ ω = 2.5 Hz . The centers of white circles 1 and 2 correspond to the true and the twin images, respectively.

Fig. 3
Fig. 3

(a) Weight W + 1 of the true image peak as a function of the heterodyne frequency Δ ω in hertz. The vertical axis is in logarithmic scale arbitrary units. The points correspond to experimental data: Δ ω = 5 to + 5 Hz with 0.1 Hz increments. The solid gray curve is theoretical, Eq. (5). (b) Weight W 1 of the twin image.

Fig. 4
Fig. 4

(a), (b) USAF target reconstructed image on a linear scale for the field intensity E x , y , z 2 with z = 194.5 mm ( 4096 × 4096   pixels ) . (a) Δ ω = + 2.5 Hz (true image), (b) Δ ω = 2.5 Hz (twin image). (c), (d) Enlargemt ( 512 × 512   pixels ) of the center of the true (c) and the twin (d) image. Pixel size is 6.7 μ m × 6.7 μ m .

Equations (6)

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

Δ ω ω LO ω I = ω AOM 2 ω AOM 1 .
Δ φ ( Δ ω ) = 2 π Δ ω ω CCD .
E = A m = 0 3 ( j ) m I m = A [ ( I 0 I 2 ) ± j ( I 1 I 3 ) ] ,
W ± 1 = C ± 1 E ̃ k x , k y 2 ,
W ± 1 ( Δ ω ) = B η 2 ( Δ ω ) m = 0 3 j m e j m Δ φ ( Δ ω ) 2 .
η ( Δ ω ) = 1 Δ φ ( Δ ω ) φ = 0 Δ φ ( Δ ω ) e j φ d φ = 1 e j Δ φ ( Δ ω ) Δ φ ( Δ ω ) .

Metrics