Abstract

In speckle interferometry (SI), temporal signals are amplitude- and frequency-modulated signals and exhibit a fluctuating background. Prior to phase computation, this background intensity must be eliminated. Here our approach is to build a complex signal from the raw one and to fit a circle through the points cloud representing its sampled values in the complex plane. The circle fit is computed from a set of points whose length is locally adapted to the signal. This procedure—new to our knowledge in SI—yields the background and the modulation depth and leads to the determination of the instantaneous frequency. The method, applied to simulated and experimental signals, is compared to empirical mode decomposition (EMD). It shows great robustness in the computation of the sought quantities in SI, especially with signals close to the critical sampling or, on the contrary, highly oversampled, situations where the background elimination by EMD is the most prone to errors.

© 2011 Optical Society of America

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2010

P. F. Pai, Adv. Adapt. Data Anal. 2, 39 (2010).
[CrossRef]

S. Equis and P. Jacquot, Proc. SPIE 7387, 738709 (2010).
[CrossRef]

2009

1999

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

1998

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

1993

I. D. Coope, J. Optim. Theory Appl. 76, 381 (1993).
[CrossRef]

1985

1984

N. I. Chernov and G. A. Ososkov, Comput. Phys. Commun. 33, 329 (1984).
[CrossRef]

1976

I. Kåsa, IEEE Trans. Instrum. Meas. IM-25, 8 (1976).

Aboutajdine, D.

D. Aboutajdine, M. Najim, and J. G. Postaire, in Signal Processing, Theories and Applications, Proceedings of EUSIPCO-80, First European Signal Processing Conference, Lausanne, Switzerland, September 16–18, 1980, M.Kunt and F.De Coulon, eds. (North-Holland, 1980), p. 57.

Cherbuliez, M.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Chernov, N. I.

N. I. Chernov and G. A. Ososkov, Comput. Phys. Commun. 33, 329 (1984).
[CrossRef]

Colonna de Lega, X.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Coope, I. D.

I. D. Coope, J. Optim. Theory Appl. 76, 381 (1993).
[CrossRef]

Creath, K.

Equis, S.

S. Equis and P. Jacquot, Proc. SPIE 7387, 738709 (2010).
[CrossRef]

S. Equis and P. Jacquot, Opt. Express 17, 611 (2009).
[CrossRef] [PubMed]

Flandrin, P.

G. Rilling and P. Flandrin, in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2006), p. 444.

Huang, N. E.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Jacquot, P.

S. Equis and P. Jacquot, Proc. SPIE 7387, 738709 (2010).
[CrossRef]

S. Equis and P. Jacquot, Opt. Express 17, 611 (2009).
[CrossRef] [PubMed]

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Kåsa, I.

I. Kåsa, IEEE Trans. Instrum. Meas. IM-25, 8 (1976).

Liu, H. H.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Long, S. R.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Najim, M.

D. Aboutajdine, M. Najim, and J. G. Postaire, in Signal Processing, Theories and Applications, Proceedings of EUSIPCO-80, First European Signal Processing Conference, Lausanne, Switzerland, September 16–18, 1980, M.Kunt and F.De Coulon, eds. (North-Holland, 1980), p. 57.

Ososkov, G. A.

N. I. Chernov and G. A. Ososkov, Comput. Phys. Commun. 33, 329 (1984).
[CrossRef]

Pai, P. F.

P. F. Pai, Adv. Adapt. Data Anal. 2, 39 (2010).
[CrossRef]

Postaire, J. G.

D. Aboutajdine, M. Najim, and J. G. Postaire, in Signal Processing, Theories and Applications, Proceedings of EUSIPCO-80, First European Signal Processing Conference, Lausanne, Switzerland, September 16–18, 1980, M.Kunt and F.De Coulon, eds. (North-Holland, 1980), p. 57.

Rilling, G.

G. Rilling and P. Flandrin, in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2006), p. 444.

Shen, Z.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Shih, H. H.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Tung, C.-C.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Wu, M. C.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Yuen, N. C.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Zheng, Q.

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Adv. Adapt. Data Anal.

P. F. Pai, Adv. Adapt. Data Anal. 2, 39 (2010).
[CrossRef]

Appl. Opt.

Comput. Phys. Commun.

N. I. Chernov and G. A. Ososkov, Comput. Phys. Commun. 33, 329 (1984).
[CrossRef]

IEEE Trans. Instrum. Meas.

I. Kåsa, IEEE Trans. Instrum. Meas. IM-25, 8 (1976).

J. Optim. Theory Appl.

I. D. Coope, J. Optim. Theory Appl. 76, 381 (1993).
[CrossRef]

Opt. Express

Proc. R. Soc. A

N. E. Huang, N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yuen, C.-C. Tung, and H. H. Liu. Proc. R. Soc. A 454A, 903 (1998).
[CrossRef]

Proc. SPIE

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

S. Equis and P. Jacquot, Proc. SPIE 7387, 738709 (2010).
[CrossRef]

Other

G. Rilling and P. Flandrin, in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2006), p. 444.

D. Aboutajdine, M. Najim, and J. G. Postaire, in Signal Processing, Theories and Applications, Proceedings of EUSIPCO-80, First European Signal Processing Conference, Lausanne, Switzerland, September 16–18, 1980, M.Kunt and F.De Coulon, eds. (North-Holland, 1980), p. 57.

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Figures (5)

Fig. 1
Fig. 1

Principle of the method of the osculating circle to the signal trajectory in the complex plane.

Fig. 2
Fig. 2

CFIT procedure of phase extraction in SI.

Fig. 3
Fig. 3

Phase error as a function of the sampling frequency.

Fig. 4
Fig. 4

Leendertz SI setup with in-plane sensitivity vector S.

Fig. 5
Fig. 5

Phase maps corresponding to the total displacement (given in radians) and the cross sections (along dotted lines) shown with the theoretical phase.

Equations (7)

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

z [ k ] = s [ k ] + i HT { s [ k ] } .
min p = 1 N k { ( x p a k ) 2 + ( y p b k ) 2 R k } 2 ,
J k = p = 1 N k { ( x p a k ) 2 + ( y p b k ) 2 R k 2 } 2 .
θ p = arctan ( det ( v , v p + 1 ) / ( v · v p + 1 ) ) .
N k + 1 = 2 n π / ν k .
s [ k ] = cos ( 2 π k / 2 r + φ r ) + σ [ k ] ,
δ ϕ = ϕ ex 2 π k / 2 r φ r ,

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