The empirical mode decomposition: a must-have tool in speckle interferometry?

Sébastien Equis; Pierre Jacquot

doi:10.1364/OE.17.000611

The empirical mode decomposition: a must-have tool in speckle interferometry?

Sébastien Equis and Pierre Jacquot

Optics Express
Vol. 17,
Issue 2,
pp. 611-623
(2009)
•https://doi.org/10.1364/OE.17.000611

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Sébastien Equis and Pierre Jacquot, "The empirical mode decomposition: a must-have tool in speckle interferometry?," Opt. Express 17, 611-623 (2009)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Discrete optical signal processing (070.2025)
- Speckle interferometry, metrology (120.6165)
- Fringe analysis (120.2650)
- Phase measurement (120.5050)

About this Article
History
- Original Manuscript: November 6, 2008
- Revised Manuscript: December 22, 2008
- Manuscript Accepted: December 23, 2008
- Published: January 7, 2009

Accessible

Open Access

Abstract

In a wider and wider range of research and engineering activities, there is a growing interest for full-field techniques, featuring nanometric sensitivities, and able to be addressed to dynamic behaviors characterization. Speckle interferometry (SI) techniques are acknowledged as good candidates to tackle this challenge. To get rid of the intrinsic correlation length limitation and simplify the unwrapping step, a straightforward approach lies in the pixel history analysis. The need of increasing performances in terms of accuracy and computation speed is permanently demanding new efficient processing techniques. We propose in this paper a fast implementation of the Empirical Mode Decomposition (EMD) to put the SI pixel signal in an appropriate shape for accurate phase computation. As one of the best way to perform it, the analytic method based on the Hilbert transform (HT) of the so-transformed signal will then be reviewed. For short evaluation, a zero-crossing technique which exploits directly the extrema finding step of the EMD will be presented. We propose moreover a technique to discard the under-modulated pixels which yield wrong phase evaluation. This work is actually an attempt to elaborate a phase extraction procedure which exploits all the reliable information in 3D, – two space and one time coordinates –, to endeavor to make the most of SI raw data.

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References

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Publication

Cf. Proceedings of the “Fringe” Conferences Series, as e.g.: W. Osten and W. Jüptner Eds., Elsevier (2001), W. Osten Ed., Springer (2005).
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J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[Crossref] [PubMed]
Colonna de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase-shifting,” Appl. Opt. 35, 5115–5121 (1996).
[Crossref]
L. Bruno, “Global approach for fitting 2D interferometric data,” Opt. Express 15, 4835–4847 (2007).
[Crossref] [PubMed]
E. Robin and V. Valle, “Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form,” Appl. Opt. 34, 7261–7269 (2005).
[Crossref]
M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]
D.J. Bone, H. -A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[Crossref] [PubMed]
K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns -Part I,” J. Opt. Soc. Am. A 18, 1862–1881 (2001).
[Crossref]
J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]
D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley-Interscience Publication, New-York, 1998).
H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]
M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999).
[Crossref]
V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[Crossref] [PubMed]
S. Equis, A. Baldi, and P. Jacquot, “Phase extraction in dynamic speckle interferometry by empirical mode decomposition,” in Proceedings of the International Conference in Experimental Mechanics, E.E. Gdoutos, ed. (Springer, Dordrecht, The Netherlands, 2007), pp. 719–720 & CD–Rom.
N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. -C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London Ser. A 454, 903–995 (1998).
[Crossref]
G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03 (2003).
N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. London Ser. A 459, 2317–2345 (2003).
[Crossref]
A. Federico and G. Kaufmann, “Evaluation of dynamic speckle activity using the empirical mode decomposition,” Opt. Commun. 267, 287–294 (2006).
[Crossref]
F. A. Marengo Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).
[Crossref]
S. Equis and P. Jacquot, “Phase extraction in dynamic speckle interferometry by empirical mode decomposition,” Strain (to be published).
R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, 1965).
E. Bedrosian, “A product theorem for Hilbert transforms,” Proc. IEEE 51, 868–869 (1963).
[Crossref]
D. Vakman, “On the analytic signal, the Teager-Kaiser algorithm, and other methods for defining amplitude and frequency,” IEEE Trans. Sig. Proc. 44, 791–797 (1996).
[Crossref]
B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568 (1992).
[Crossref]
M. LehmannDigital Speckle Pattern Interferometry and Related Techniques (John Wiley & Sons, Ltd, Chichester, 2001), Chap. 1.
G. Rilling, P. Flandrin, and P. Gonçalves “On Empirical Mode Decomposition and its algorithms”, Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).
K. Zeng and M. -X. He, “A simple boundary process technique for empirical mode decomposition,” IEEE Int. Geosci. Remote Sensing 6, 4258–4261 (2004).
N. Stevenson, M. Mesbah, and B. Boashash, “A sampling limit for the empirical mode decomposition,” in Proceedings of International Symposium on Signal Processing and its Applications ISSPA–05, 647–650 (2005).
[Crossref]
G. Rilling and P. Flandrin, “On the influence of sampling on the empirical mode decomposition,” in Proceedings of IEEE International Conference on Acoustic, Speech and Signal Processing ICASSP–06 (2006).
[Crossref]
http://perso.ens-lyon.fr/patrick.flandrin/publis.html
G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Sig. Proc. 56, 85–95 (2008).
[Crossref]
S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6841, 634138–1–634138–6 (2006).
[Crossref]
E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
[Crossref] [PubMed]
W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40, 529–541 (2003).
[Crossref]
www.qhull.org

2008 (1)

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Sig. Proc. 56, 85–95 (2008).
[Crossref]

2007 (2)

F. A. Marengo Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).
[Crossref]

L. Bruno, “Global approach for fitting 2D interferometric data,” Opt. Express 15, 4835–4847 (2007).
[Crossref] [PubMed]

2006 (3)

G. Rilling and P. Flandrin, “On the influence of sampling on the empirical mode decomposition,” in Proceedings of IEEE International Conference on Acoustic, Speech and Signal Processing ICASSP–06 (2006).
[Crossref]

A. Federico and G. Kaufmann, “Evaluation of dynamic speckle activity using the empirical mode decomposition,” Opt. Commun. 267, 287–294 (2006).
[Crossref]

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6841, 634138–1–634138–6 (2006).
[Crossref]

2005 (2)

E. Robin and V. Valle, “Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form,” Appl. Opt. 34, 7261–7269 (2005).
[Crossref]

N. Stevenson, M. Mesbah, and B. Boashash, “A sampling limit for the empirical mode decomposition,” in Proceedings of International Symposium on Signal Processing and its Applications ISSPA–05, 647–650 (2005).
[Crossref]

2004 (1)

K. Zeng and M. -X. He, “A simple boundary process technique for empirical mode decomposition,” IEEE Int. Geosci. Remote Sensing 6, 4258–4261 (2004).

2003 (4)

G. Rilling, P. Flandrin, and P. Gonçalves “On Empirical Mode Decomposition and its algorithms”, Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40, 529–541 (2003).
[Crossref]

N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. R. Soc. London Ser. A 459, 2317–2345 (2003).
[Crossref]

V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[Crossref] [PubMed]

2001 (1)

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns -Part I,” J. Opt. Soc. Am. A 18, 1862–1881 (2001).
[Crossref]

1999 (3)

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999).
[Crossref]

1998 (1)

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. -C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London Ser. A 454, 903–995 (1998).
[Crossref]

1996 (2)

D. Vakman, “On the analytic signal, the Teager-Kaiser algorithm, and other methods for defining amplitude and frequency,” IEEE Trans. Sig. Proc. 44, 791–797 (1996).
[Crossref]

Colonna de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase-shifting,” Appl. Opt. 35, 5115–5121 (1996).
[Crossref]

1993 (1)

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[Crossref] [PubMed]

1992 (1)

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568 (1992).
[Crossref]

1963 (1)

E. Bedrosian, “A product theorem for Hilbert transforms,” Proc. IEEE 51, 868–869 (1963).
[Crossref]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

An, W.

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40, 529–541 (2003).
[Crossref]

Bachor, H. -A.

D.J. Bone, H. -A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[Crossref] [PubMed]

Baldi, A.

S. Equis, A. Baldi, and P. Jacquot, “Phase extraction in dynamic speckle interferometry by empirical mode decomposition,” in Proceedings of the International Conference in Experimental Mechanics, E.E. Gdoutos, ed. (Springer, Dordrecht, The Netherlands, 2007), pp. 719–720 & CD–Rom.

Bedrosian, E.

E. Bedrosian, “A product theorem for Hilbert transforms,” Proc. IEEE 51, 868–869 (1963).
[Crossref]

Boashash, B.

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568 (1992).
[Crossref]

Bone, D. J.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns -Part I,” J. Opt. Soc. Am. A 18, 1862–1881 (2001).
[Crossref]

Bone, D.J.

D.J. Bone, H. -A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[Crossref] [PubMed]

Botello, S.

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, 1965).

Bruno, L.

L. Bruno, “Global approach for fitting 2D interferometric data,” Opt. Express 15, 4835–4847 (2007).
[Crossref] [PubMed]

Carlsson, T. E.

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40, 529–541 (2003).
[Crossref]

Cherbuliez, M.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999).
[Crossref]

Creath, K.

K. Creath, Interferogram Analysis (Institute of Physics Publishing, Bristol, UK, 1993), Chap. 4.

Equis, S.

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6841, 634138–1–634138–6 (2006).
[Crossref]

S. Equis and P. Jacquot, “Phase extraction in dynamic speckle interferometry by empirical mode decomposition,” Strain (to be published).

Fan, K. L.

Federico, A.

A. Federico and G. Kaufmann, “Evaluation of dynamic speckle activity using the empirical mode decomposition,” Opt. Commun. 267, 287–294 (2006).
[Crossref]

Flandrin, P.

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Sig. Proc. 56, 85–95 (2008).
[Crossref]

G. Rilling, P. Flandrin, and P. Gonçalves “On Empirical Mode Decomposition and its algorithms”, Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03 (2003).

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley-Interscience Publication, New-York, 1998).

Gloersen, P.

Gonçalves, P.

G. Rilling, P. Flandrin, and P. Gonçalves “On Empirical Mode Decomposition and its algorithms”, Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03 (2003).

He, M. -X.

K. Zeng and M. -X. He, “A simple boundary process technique for empirical mode decomposition,” IEEE Int. Geosci. Remote Sensing 6, 4258–4261 (2004).

Huang, N. E.

Huntley, J. M.

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[Crossref] [PubMed]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Jacquot, P.

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6841, 634138–1–634138–6 (2006).
[Crossref]

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999).
[Crossref]

Colonna de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase-shifting,” Appl. Opt. 35, 5115–5121 (1996).
[Crossref]

S. Equis and P. Jacquot, “Phase extraction in dynamic speckle interferometry by empirical mode decomposition,” Strain (to be published).

Kadono, H.

V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[Crossref] [PubMed]

Kaufmann, G.

A. Federico and G. Kaufmann, “Evaluation of dynamic speckle activity using the empirical mode decomposition,” Opt. Commun. 267, 287–294 (2006).
[Crossref]

Kaufmann, G. H.

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Larkin, K. G.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns -Part I,” J. Opt. Soc. Am. A 18, 1862–1881 (2001).
[Crossref]

Lega, Colonna de

Colonna de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase-shifting,” Appl. Opt. 35, 5115–5121 (1996).
[Crossref]

Lega, X. Colonna de

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999).
[Crossref]

Lehmann, M.

M. LehmannDigital Speckle Pattern Interferometry and Related Techniques (John Wiley & Sons, Ltd, Chichester, 2001), Chap. 1.

Liu, H. H.

Long, S. R.

Madjarova, V. D.

V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[Crossref] [PubMed]

Marroquin, J. L.

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

Mesbah, M.

Oldfield, M. A.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns -Part I,” J. Opt. Soc. Am. A 18, 1862–1881 (2001).
[Crossref]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley-Interscience Publication, New-York, 1998).

Qu, W.

Rilling, G.

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Sig. Proc. 56, 85–95 (2008).
[Crossref]

G. Rilling, P. Flandrin, and P. Gonçalves “On Empirical Mode Decomposition and its algorithms”, Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).

G. Rilling, P. Flandrin, and P. Gonçalves, “On empirical mode decomposition and its algorithms,” in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03 (2003).

Rivera, M.

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

Robin, E.

E. Robin and V. Valle, “Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form,” Appl. Opt. 34, 7261–7269 (2005).
[Crossref]

Rodriguez, F. A. Marengo

Rodriguez–Vera, R.

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

Saldner, H.

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[Crossref] [PubMed]

Sandeman, R. J.

D.J. Bone, H. -A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[Crossref] [PubMed]

Servin, M.

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

Shen, S. S. P.

Shen, Z.

Shih, H. H.

Stevenson, N.

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Toyooka, S.

V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[Crossref] [PubMed]

Tung, C. C.

Vakman, D.

D. Vakman, “On the analytic signal, the Teager-Kaiser algorithm, and other methods for defining amplitude and frequency,” IEEE Trans. Sig. Proc. 44, 791–797 (1996).
[Crossref]

Valle, V.

E. Robin and V. Valle, “Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form,” Appl. Opt. 34, 7261–7269 (2005).
[Crossref]

Vikhagen, E.

E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
[Crossref] [PubMed]

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Wu, M. C.

Yen, N. -C.

Zeng, K.

K. Zeng and M. -X. He, “A simple boundary process technique for empirical mode decomposition,” IEEE Int. Geosci. Remote Sensing 6, 4258–4261 (2004).

Zheng, Q.

Appl. Opt. (6)

E. Robin and V. Valle, “Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form,” Appl. Opt. 34, 7261–7269 (2005).
[Crossref]

D.J. Bone, H. -A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[Crossref] [PubMed]

E. Vikhagen, “Nondestructive testing by use of TV holography and deformation phase gradient calculation,” Appl. Opt. 29, 137–144 (1990).
[Crossref] [PubMed]

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[Crossref] [PubMed]

Colonna de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase-shifting,” Appl. Opt. 35, 5115–5121 (1996).
[Crossref]

J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez–Vera, and M. Servin, “Regularization methods for processsing fringe-pattern images,” Appl. Opt. 38, 788–794 (1999).
[Crossref]

IEEE Int. Geosci. Remote Sensing (1)

K. Zeng and M. -X. He, “A simple boundary process technique for empirical mode decomposition,” IEEE Int. Geosci. Remote Sensing 6, 4258–4261 (2004).

IEEE Trans. Sig. Proc. (2)

D. Vakman, “On the analytic signal, the Teager-Kaiser algorithm, and other methods for defining amplitude and frequency,” IEEE Trans. Sig. Proc. 44, 791–797 (1996).
[Crossref]

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Sig. Proc. 56, 85–95 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

J. Opt. Soc. Am. A (1)

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Supplementary Material (3)

» Media 1: MOV (2912 KB)

» Media 2: MOV (2691 KB)

» Media 3: MOV (2000 KB)

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Fig. 1. A typical temporal pixel signal experimentally obtained in SI (gray levels in ordinate and time measured in frame number in abscissa).

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Fig. 2. Standard EMD algorithm.

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Fig. 3. Standard deviation of the difference between the extracted phase from the 1^st IMF and the theoretical phase with an upper bound.

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Fig. 4. (a) averaged criterion δ for 10 iterations of sifting process, (b) EMD filter model (cubic spline kernel) with simulations in solid line and predictions in dashed line.

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Fig. 5. A simulated temporal SI signal.

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Fig. 6. Histograms of criterion defined in Eq. (10) for 4096 simulated SI temporal signals with 1, 5 and 10 iterations of sifting process.

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Fig. 7. (a) Pseudo-IMF obtained after fast EMD with areas identified as invalid (1) or valid (0) (gray levels in ordinate and sample number in abscissa), and (b) its discrete extracted IF.

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Fig. 8. In-plane SI experiment.

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Fig. 9. Phase extraction results: (a) (Media 1) of the raw phase, (b) (Media 2) the raw phase filtered with a 5×5 median filter and (c) (Media 3) the phase resulting from the 3DPP.

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Fig. 10. Cross-sections of the total computed displacement in each case depicted in Fig. 9.

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Equations (14)

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s (x, y, t) = α + β (x, y, t) \cdot \cos (ψ_{s} (x, y, t) + ψ_{opd} (x, y, t)),

s (t) = Σ_{k = 1}^{K} d_{k} (t) + m_{k} (t),

x_{f_{s}, φ} [k] = \cos (2 π \cdot f_{s} \cdot k + φ),

{〈 σ_{ϕ} 〉}_{φ} = {〈 \sqrt{\frac{1}{N} \sum_{k = 1}^{N} {((ϕ_{imf} (k) - 2 π f_{s} k - φ) - {〈 ϕ_{imf} (k) - 2 π f_{s} k - φ 〉}_{N})}^{2}} 〉}_{φ},

x (t) = \cos (2 πt) + α \cdot \cos (2 πνt + φ),

δ_{1}^{i} (α, ν, φ) = \frac{{∥ d_{1}^{i} (α, ν) - \cos (2 πt) ∥}_{1_{2}}}{{∥ α \cdot \cos (2 πνt + φ) ∥}_{1_{2}}},

δ_{1}^{i} = \frac{∥ d_{1}^{i} - 2 \sqrt{I_{1} \cdot I_{2} \cdot \cos (φ_{sp} - φ_{ref})} ∥}{∥ I_{1} + I_{2} ∥}

HT [u (t)] = \frac{1}{π} \int_{- \infty}^{\infty} \frac{u (x)}{t - x} dx = \frac{- 1}{πt} \otimes u (t), FT {HT [u (t)]} = {\begin{array}{c} i \cdot U (ν), ν > 0 \\ - i \cdot U (ν), ν < 0 \end{array},

φ_{as} (t) = \arctan (\frac{- HT [u (t)]}{u (t)})

f_{as} (t) = \frac{d}{dt} φ_{as} (t)

f_{as} [n] = \frac{1}{2 π} (φ_{as} [n] - φ_{as} [n - 1])

\bar{f} = \frac{1}{2 τ}

Δφ = \frac{2 π}{λ} (S_{1} - S_{2}) \cdot L = S \cdot L_{x},

S = \frac{4 π}{λ} \cdot \sin θ

Abstract

References

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