Abstract

An algorithm for dynamic phase retrieval in temporal speckle pattern interferometry using least squares method and windowed Fourier filtering is proposed. The least squares method is used to evaluate the phase change between two speckle patterns provided that the phase of either one speckle pattern has been estimated. The windowed Fourier filtering is used to eliminate the noise in the phase change. Based on these two techniques, the proposed algorithm determines the phase of the initial speckle pattern by phase shifting method at first, then the phase of the rest speckle patterns are retrieved by sequentially evaluating the phase changes between every two consecutive speckle patterns. The algorithm solves the problem of speckle decorrelation by refreshing the reference image frame by frame, and also avoids the problem of error accumulation during the reference image refreshing process by the windowed Fourier filtering. Two experimental results are presented to demonstrate the effectiveness and robustness of the proposed algorithm.

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  1. R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993).
  2. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University Press, London, 1983).
  3. D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for Optical Testing, 2th ed. (Marcel Dekker, 2003).
  4. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24(18), 3053–3058 (1985).
    [CrossRef] [PubMed]
  5. J. M. Huntley, G. H. Kaufmann, and D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38(31), 6556–6563 (1999).
    [CrossRef] [PubMed]
  6. A. J. Haasteren and H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33(19), 4137–4142 (1994).
    [CrossRef] [PubMed]
  7. J. Millerd, N. Brock, J. Hayes, M. North-Morries, B. Kimbrough, and J. Wyant, “Pixelated phase-mask dynamic interferometers,” in Fringe 2005. The 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2006), Session 5, pp. 640–647.
  8. 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(1), 156–160 (1982).
    [CrossRef]
  9. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997).
    [CrossRef] [PubMed]
  10. H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).
    [CrossRef] [PubMed]
  11. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37(13), 2608–2614 (1998).
    [CrossRef] [PubMed]
  12. G. H. Kaufmann and G. E. Galizzi, “Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods,” Appl. Opt. 41(34), 7254–7263 (2002).
    [CrossRef] [PubMed]
  13. V. D. Madjarova, H. Kadono, and S. Toyooka, “Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11(6), 617–623 (2003).
    [CrossRef] [PubMed]
  14. F. A. Marengo Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47(9), 1310–1316 (2008).
    [CrossRef] [PubMed]
  15. X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Ph.D. dissertation 1666 (Swiss Federal Institute of Technology, 1997).
  16. A. Federico and G. H. Kaufmann, “Robust phase recovery in temporal speckle pattern interferometry using a 3D directional wavelet transform,” Opt. Lett. 34(15), 2336–2338 (2009).
    [CrossRef] [PubMed]
  17. Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46(36), 8645–8655 (2007).
    [CrossRef] [PubMed]
  18. T. E. Carlsson and A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39(16), 2628–2637 (2000).
    [CrossRef] [PubMed]
  19. W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40(5-6), 529–541 (2003).
    [CrossRef]
  20. L. Bruno and A. Poggialini, “Phase shifting speckle interferometry for dynamic phenomena,” Opt. Express 16(7), 4665–4670 (2008).
    [CrossRef] [PubMed]
  21. Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
    [CrossRef]
  22. Y. H. Huang, F. Janabi-Sharifi, Y. Liu, and Y. Y. Hung, “Dynamic phase measurement in shearography by clustering method and Fourier filtering,” Opt. Express 19(2), 606–615 (2011).
    [CrossRef] [PubMed]
  23. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29(14), 1671–1673 (2004).
    [CrossRef] [PubMed]
  24. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
    [CrossRef] [PubMed]
  25. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
    [CrossRef]
  26. Q. Kemao, H. X. Wang, and W. J. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47(29), 5408–5419 (2008).
    [CrossRef] [PubMed]
  27. C. Joenathan, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera,” Appl. Opt. 38(7), 1169–1178 (1999).
    [CrossRef] [PubMed]
  28. A. Svanbro, J. M. Huntley, and A. Davila, “Optimal re-referencing rate for in-plane dynamic speckle interferometry,” Appl. Opt. 42(2), 251–258 (2003).
    [CrossRef] [PubMed]
  29. A. Davila, J. M. Huntley, G. H. Kaufmann, and D. Kerr, “High-speed dynamic speckle interferometry: phase errors due to intensity, velocity, and speckle decorrelation,” Appl. Opt. 44(19), 3954–3962 (2005).
    [CrossRef] [PubMed]
  30. Q. Kemao, “Windowed Fourier transform (WFT) for fringe pattern analysis,” http://www3.ntu.edu.sg/home/mkmqian/ .
  31. W. J. Gao, N. T. T. Huyen, H. S. Loi, and Q. Kemao, “Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit,” Opt. Express 17(25), 23147–23152 (2009).
    [CrossRef] [PubMed]

2011

2009

2008

2007

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[CrossRef]

Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46(36), 8645–8655 (2007).
[CrossRef] [PubMed]

2005

2004

2003

2002

2000

1999

1998

1997

1994

1985

1982

An, W.

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40(5-6), 529–541 (2003).
[CrossRef]

Bruno, L.

Carlsson, T. E.

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40(5-6), 529–541 (2003).
[CrossRef]

T. E. Carlsson and A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39(16), 2628–2637 (2000).
[CrossRef] [PubMed]

Chen, Y. S.

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Creath, K.

Cuevas, F. J.

Davila, A.

Federico, A.

Frankena, H. J.

Franze, B.

Fu, Y.

Galizzi, G. E.

Gao, W. J.

Groves, R. M.

Haasteren, A. J.

Haible, P.

Han, B.

Huang, Y. H.

Y. H. Huang, F. Janabi-Sharifi, Y. Liu, and Y. Y. Hung, “Dynamic phase measurement in shearography by clustering method and Fourier filtering,” Opt. Express 19(2), 606–615 (2011).
[CrossRef] [PubMed]

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Hung, Y. Y.

Y. H. Huang, F. Janabi-Sharifi, Y. Liu, and Y. Y. Hung, “Dynamic phase measurement in shearography by clustering method and Fourier filtering,” Opt. Express 19(2), 606–615 (2011).
[CrossRef] [PubMed]

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Huntley, J. M.

Huyen, N. T. T.

Ina, H.

Janabi-Sharifi, F.

Joenathan, C.

Kadono, H.

Kaufmann, G. H.

Kemao, Q.

Kerr, D.

Kobayashi, S.

Liu, L.

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Liu, Y.

Loi, H. S.

Madjarova, V. D.

Marengo Rodriguez, F. A.

Marroquin, J. L.

Ng, S. P.

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Osten, W.

Pedrini, G.

Poggialini, A.

Servin, M.

Svanbro, A.

Takeda, M.

Tiziani, H. J.

Toyooka, S.

Wang, H.

Wang, H. X.

Wang, Z.

Wei, A.

Appl. Opt.

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24(18), 3053–3058 (1985).
[CrossRef] [PubMed]

A. J. Haasteren and H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33(19), 4137–4142 (1994).
[CrossRef] [PubMed]

M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997).
[CrossRef] [PubMed]

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37(13), 2608–2614 (1998).
[CrossRef] [PubMed]

C. Joenathan, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera,” Appl. Opt. 38(7), 1169–1178 (1999).
[CrossRef] [PubMed]

J. M. Huntley, G. H. Kaufmann, and D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38(31), 6556–6563 (1999).
[CrossRef] [PubMed]

T. E. Carlsson and A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39(16), 2628–2637 (2000).
[CrossRef] [PubMed]

G. H. Kaufmann and G. E. Galizzi, “Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods,” Appl. Opt. 41(34), 7254–7263 (2002).
[CrossRef] [PubMed]

A. Svanbro, J. M. Huntley, and A. Davila, “Optimal re-referencing rate for in-plane dynamic speckle interferometry,” Appl. Opt. 42(2), 251–258 (2003).
[CrossRef] [PubMed]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[CrossRef] [PubMed]

A. Davila, J. M. Huntley, G. H. Kaufmann, and D. Kerr, “High-speed dynamic speckle interferometry: phase errors due to intensity, velocity, and speckle decorrelation,” Appl. Opt. 44(19), 3954–3962 (2005).
[CrossRef] [PubMed]

Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46(36), 8645–8655 (2007).
[CrossRef] [PubMed]

F. A. Marengo Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47(9), 1310–1316 (2008).
[CrossRef] [PubMed]

Q. Kemao, H. X. Wang, and W. J. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47(29), 5408–5419 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Opt. Eng.

Y. H. Huang, S. P. Ng, L. Liu, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

W. An and T. E. Carlsson, “Speckle interferometry for measurement of continuous deformations,” Opt. Lasers Eng. 40(5-6), 529–541 (2003).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[CrossRef]

Opt. Lett.

Other

Q. Kemao, “Windowed Fourier transform (WFT) for fringe pattern analysis,” http://www3.ntu.edu.sg/home/mkmqian/ .

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993).

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University Press, London, 1983).

D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for Optical Testing, 2th ed. (Marcel Dekker, 2003).

J. Millerd, N. Brock, J. Hayes, M. North-Morries, B. Kimbrough, and J. Wyant, “Pixelated phase-mask dynamic interferometers,” in Fringe 2005. The 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2006), Session 5, pp. 640–647.

X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry,” Ph.D. dissertation 1666 (Swiss Federal Institute of Technology, 1997).

Supplementary Material (2)

» Media 1: AVI (3926 KB)     
» Media 2: AVI (4105 KB)     

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Figures (2)

Fig. 1
Fig. 1

Dynamic phase retrieval by the proposed algorithm for the deformation of a circular plate. (a-c) Fringe patterns at three different time instances; (d-f) the corresponding wrapped phase maps obtained by the proposed algorithm; Media 1 displays the animation of the fringe patterns and the obtained phase results; (g-i) phase results obtained by taking the initial speckle pattern as a fixed reference; (j-l) phase results obtained by refreshing the reference image frame by frame, but the windowed Fourier filtering is not employed.

Fig. 2
Fig. 2

Dynamic phase retrieval by the proposed algorithm for the deformation of a honeycomb aluminum panel. (a-c) Fringe patterns at three different time instances; (d-f) the corresponding wrapped phase maps obtained by the proposed algorithm; Media 2 displays the animation of the fringe patterns and the obtained phase results

Equations (18)

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f ( x , t i ) = a ( x , t i ) + b ( x , t i ) cos [ φ ( x , t i ) ] + n ( x , t i ) ,        i = 0 , 1 , 2 , , N 1 ,
f k ( x , t 0 ) = a ( x , t 0 ) + b ( x , t 0 ) cos [ φ ( x , t 0 ) + δ k ] + n ( x , t 0 ) ,        k = 0 , 1 , 2 , 3 ,
f ( x , t β ) = a ( x , t β ) + b ( x , t β ) cos [ φ ( x , t α ) + Δ φ β , α ( x ) ] ,
Δ φ β , α ( x ) = φ ( x , t β ) φ ( x , t α ) .
a ( x , t β ) a ( ζ , t β ) , b ( x , t β ) b ( ζ , t β ) , Δ φ β , α ( x ) Δ φ β , α ( ζ ) , f o r x N ζ .
f ( x , t β ) a ( ζ , t β ) + b ( ζ , t β ) cos [ φ ( x , t α ) + Δ φ β , α ( ζ ) ] = a ( ζ , t β ) + c ( ζ , t β ) cos [ φ ( x , t α ) ] + d ( ζ , t β ) sin [ φ ( x , t α ) ] ,
c ( ζ , t β ) = b ( ζ , t β ) cos [ Δ φ β , α ( ζ ) ] d ( ζ , t β ) = b ( ζ , t β ) sin [ Δ φ β , α ( ζ ) ] .
r = x N ζ ( f ( x , t β ) { a ( ζ , t β ) + c ( ζ , t β ) cos [ φ ( x , t α ) ] + d ( ζ , t β ) sin [ φ ( x , t α ) ] } ) 2 .
r a ( ζ , t β ) = 0 ,       r c ( ζ , t β ) = 0 ,       r d ( ζ , t β ) = 0 ,
X = A 1 B ,
A = [ M x N ζ cos [ φ ( x , t α ) ] x N ζ sin [ φ ( x , t α ) ] x N ζ cos [ φ ( x , t α ) ] x N ζ cos 2 [ φ ( x , t α ) ] x N ζ cos [ φ ( x , t α ) ] sin [ φ ( x , t α ) ] x N ζ sin [ φ ( x , t α ) ] x N ζ cos [ φ ( x , t α ) ] sin [ φ ( x , t α ) ] x N ζ sin 2 [ φ ( x , t α ) ] ] ,
B = { x N ζ f ( x , t β ) x N ζ f ( x , t β ) cos [ φ ( x , t α ) ] x N ζ f ( x , t β ) sin [ φ ( x , t α ) ] } T ,
X = [ a ( ζ , t β ) , c ( ζ , t β ) , d ( ζ , t β ) ] T .
Δ φ β , α ( ζ ) = tan 1 [ d ( ζ , t β ) / c ( ζ , t β ) ] ,
b ( ζ , t β ) = c 2 ( ζ , t β ) + d 2 ( ζ , t β ) .
Φ ( x ) = exp [ j Δ φ β , α ( x ) ] ,
Δ φ β , α ¯ ( x ) = angle [ Φ ¯ ( x ) ] .
Δ φ k , 0 ¯ ( x ) = n = 1 k Δ φ n , n 1 ¯ ( x ) ..

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