Abstract

We propose a novel approach based on the generalized S-transform to retrieve optical phase distributions in temporal speckle pattern interferometry. The performance of the proposed approach is compared with those given by well-known techniques based on the continuous wavelet, the Hilbert transforms, and a smoothed time-frequency distribution by analyzing interferometric data degraded by noise, nonmodulating pixels, and modulation loss. The advantages and limitations of the proposed phase retrieval approach are discussed.

© 2008 Optical Society of America

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References

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  1. J. M. Huntley, in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), p. 59.
  2. A. Federico and G. H. Kaufmann, Opt. Eng. 41, 3209 (2002).
    [CrossRef]
  3. A. Federico and G. H. Kaufmann, Appl. Opt. 42, 7066 (2003).
    [CrossRef] [PubMed]
  4. A. Federico and G. H. Kaufmann, Proc. SPIE 5531, 127 (2004).
    [CrossRef]
  5. A. Federico and G. H. Kaufmann, Proc. SPIE 4933, 200 (2003).
    [CrossRef]
  6. V. D. Madjarova, H. Kadono, and S. Toyooka, Appl. Opt. 45, 7590 (2006).
    [CrossRef] [PubMed]
  7. S. Özder, Ö. Kokahan, E. Coskun, and H. Göktas, Opt. Lett. 32, 591 (2007).
    [CrossRef] [PubMed]
  8. R. G. Stockwell, “S-transform,” http://www.cora.nwra.com/~stockwel/.
  9. C. R. Pinnegard and L. Mansinha, SIAM J. Sci. Comput. (USA) 24, 1678 (2003).
    [CrossRef]
  10. C. R. Pinnegard and L. Mansinha, Signal Process. 84, 1167 (2004).
    [CrossRef]
  11. C. R. Pinnegard, Signal Process. 86, 2051 (2006).
    [CrossRef]
  12. E. Sejdic, I. Djurovic, and J. Jiang, in International Conference on Acoustic, Speech and Signal Processing (IEEE, 2007), p. III 1165.
  13. N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
    [CrossRef]
  14. F. A. Marengo Rodríguez, A. Federico, and G. H. Kaufmann, Opt. Commun. 275, 38 (2007).
    [CrossRef]

2007 (2)

S. Özder, Ö. Kokahan, E. Coskun, and H. Göktas, Opt. Lett. 32, 591 (2007).
[CrossRef] [PubMed]

F. A. Marengo Rodríguez, A. Federico, and G. H. Kaufmann, Opt. Commun. 275, 38 (2007).
[CrossRef]

2006 (2)

2004 (2)

C. R. Pinnegard and L. Mansinha, Signal Process. 84, 1167 (2004).
[CrossRef]

A. Federico and G. H. Kaufmann, Proc. SPIE 5531, 127 (2004).
[CrossRef]

2003 (3)

A. Federico and G. H. Kaufmann, Proc. SPIE 4933, 200 (2003).
[CrossRef]

A. Federico and G. H. Kaufmann, Appl. Opt. 42, 7066 (2003).
[CrossRef] [PubMed]

C. R. Pinnegard and L. Mansinha, SIAM J. Sci. Comput. (USA) 24, 1678 (2003).
[CrossRef]

2002 (1)

A. Federico and G. H. Kaufmann, Opt. Eng. 41, 3209 (2002).
[CrossRef]

1992 (1)

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Inf. Theory (1)

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Opt. Commun. (1)

F. A. Marengo Rodríguez, A. Federico, and G. H. Kaufmann, Opt. Commun. 275, 38 (2007).
[CrossRef]

Opt. Eng. (1)

A. Federico and G. H. Kaufmann, Opt. Eng. 41, 3209 (2002).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

A. Federico and G. H. Kaufmann, Proc. SPIE 5531, 127 (2004).
[CrossRef]

A. Federico and G. H. Kaufmann, Proc. SPIE 4933, 200 (2003).
[CrossRef]

SIAM J. Sci. Comput. (USA) (1)

C. R. Pinnegard and L. Mansinha, SIAM J. Sci. Comput. (USA) 24, 1678 (2003).
[CrossRef]

Signal Process. (2)

C. R. Pinnegard and L. Mansinha, Signal Process. 84, 1167 (2004).
[CrossRef]

C. R. Pinnegard, Signal Process. 86, 2051 (2006).
[CrossRef]

Other (3)

E. Sejdic, I. Djurovic, and J. Jiang, in International Conference on Acoustic, Speech and Signal Processing (IEEE, 2007), p. III 1165.

J. M. Huntley, in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), p. 59.

R. G. Stockwell, “S-transform,” http://www.cora.nwra.com/~stockwel/.

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Figures (3)

Fig. 1
Fig. 1

TSPI signal processed using the EMD method: (a) original signal, (b) filtered signal obtained after removing the first two lower frequency modes, and (c) filtered signal obtained after removing the first four lower-frequency modes.

Fig. 2
Fig. 2

(a) Phase derivative obtained from Fig. 1b; (b) phase derivative obtained from Fig. 1c, where the continuous curve corresponds to the GST, the dashed curve to the STFD, and the dashed-dotted curve with circles to the CWT; (c) phase corresponding to Fig. 1c obtained using the GST (continuous curve), the HT (dotted curve), and the STFD (triangles).

Fig. 3
Fig. 3

(a) TSPI signal; (b) phase derivative obtained using the GST (continuous curve), the STFD (triangles), and the CWT (dotted-dashed curve).

Equations (3)

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S ( τ , f , p ) = I ( t ) w G ( τ t , f , p ) exp ( i 2 π f t ) d t .
w G ( τ t , f , p 0 ) = ǀ f ǀ p 0 2 π exp [ f 2 ( τ t ) 2 2 p 0 2 ] .
S ( τ , f , p 0 ) = e 2 π i ǀ f ǀ τ 2 π CWT ( a , τ , ω 0 ) .

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