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.

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

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

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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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