Abstract

We evaluate the use of a smoothed space-frequency distribution (SSFD) to retrieve optical phase maps in digital speckle pattern interferometry (DSPI). The performance of this method is tested by use of computer-simulated DSPI fringes. Phase gradients are found along a pixel path from a single DSPI image, and the phase map is finally determined by integration. This technique does not need the application of a phase unwrapping algorithm or the introduction of carrier fringes in the interferometer. It is shown that a Wigner-Ville distribution with a smoothing Gaussian kernel gives more-accurate results than methods based on the continuous wavelet transform. We also discuss the influence of filtering on smoothing of the DSPI fringes and some additional limitations that emerge when this technique is applied. The performance of the SSFD method for processing experimental data is then illustrated.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, UK, 2001), pp. 59–139.
  2. M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, D. Robinson, G. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 145–193.
  3. X. Colonna De Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.
  4. L. Watkins, S. Tan, T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
    [CrossRef]
  5. N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
    [CrossRef]
  6. M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
    [CrossRef]
  7. L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
    [CrossRef]
  8. A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
    [CrossRef]
  9. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. 1. Fundamentals,” Proc. IEEE 80, 520–538 (1992).
    [CrossRef]
  10. F. Hlawatsch, G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process Mag. 9, 21–67 (1992).
    [CrossRef]
  11. T. Claasen, W. Mecklenbräuker, “The Wigner distribution—a tool for time-frequency signal analysis. I. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).
  12. S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).
  13. A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
    [CrossRef]
  14. G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010–2014 (2003).
    [CrossRef]

2003 (1)

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010–2014 (2003).
[CrossRef]

2002 (2)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

2001 (1)

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

1999 (1)

1992 (3)

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. 1. Fundamentals,” Proc. IEEE 80, 520–538 (1992).
[CrossRef]

F. Hlawatsch, G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process Mag. 9, 21–67 (1992).
[CrossRef]

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

1989 (1)

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

1980 (1)

T. Claasen, W. Mecklenbräuker, “The Wigner distribution—a tool for time-frequency signal analysis. I. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

Afifi, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Barnes, T.

Boashash, B.

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. 1. Fundamentals,” Proc. IEEE 80, 520–538 (1992).
[CrossRef]

Boudreaux-Bartels, G.

F. Hlawatsch, G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process Mag. 9, 21–67 (1992).
[CrossRef]

Claasen, T.

T. Claasen, W. Mecklenbräuker, “The Wigner distribution—a tool for time-frequency signal analysis. I. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

Cohen, L.

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

Colonna De Lega, X.

X. Colonna De Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.

Delprat, N.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Escudié, B.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Fassi-Fihri, A.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Federico, A.

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Guillemain, P.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Hlawatsch, F.

F. Hlawatsch, G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process Mag. 9, 21–67 (1992).
[CrossRef]

Huntley, J. M.

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, UK, 2001), pp. 59–139.

Kaufmann, G. H.

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010–2014 (2003).
[CrossRef]

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Kronland-Martinet, R.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Kujawinska, M.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, D. Robinson, G. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 145–193.

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).

Marjane, M.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Mecklenbräuker, W.

T. Claasen, W. Mecklenbräuker, “The Wigner distribution—a tool for time-frequency signal analysis. I. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

Nassim, K.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Rachafi, S.

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Tan, S.

Tchamitchian, P.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Torrsani, B.

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Watkins, L.

IEEE Signal Process Mag. (1)

F. Hlawatsch, G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process Mag. 9, 21–67 (1992).
[CrossRef]

IEEE Trans. Inf. Theory (1)

N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrsani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992).
[CrossRef]

Opt. Commun. (1)

M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, S. Rachafi, “Paul wavelet-based algorithm for optical phase distribution evaluation,” Opt. Commun. 211, 47–51 (2002).
[CrossRef]

Opt. Eng. (3)

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

A. Federico, G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002).
[CrossRef]

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010–2014 (2003).
[CrossRef]

Opt. Lett. (1)

Philips J. Res. (1)

T. Claasen, W. Mecklenbräuker, “The Wigner distribution—a tool for time-frequency signal analysis. I. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

Proc. IEEE (2)

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. 1. Fundamentals,” Proc. IEEE 80, 520–538 (1992).
[CrossRef]

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

Other (4)

J. M. Huntley, “Automated analysis of speckle interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, Chichester, UK, 2001), pp. 59–139.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, D. Robinson, G. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 145–193.

X. Colonna De Lega, “Continuous deformation measurement using dynamic phase-shifting and wavelet transform,” in Applied Optics and Optoelectronics 1996, K. T. V. Grattan, ed. (Institute of Physics, Bristol, UK, 1996), pp. 261–267.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Computer-simulated DSPI fringes (a) containing speckle noise and (b) after speckle noise was reduced.

Fig. 2
Fig. 2

Phase gradient values obtained along the central row of the filtered image shown in Fig. 1(b) when the local maximum tracking procedure and the SSFD method were applied.

Fig. 3
Fig. 3

Phase gradient values obtained along the central row of Fig. 1(b) when the SSFD and CWT methods were applied: dashed curve, original phase gradients; triangles, values determined with the SSFD method; circles, results evaluated with the CWT approach.

Fig. 4
Fig. 4

Comparison of the phase distributions obtained by integration of the phase gradients shown in Fig. 3: dashed curve, original phase; triangles, values determined with the SSFD method; circles, results evaluated with the CWT method.

Fig. 5
Fig. 5

DSPI fringes recorded from the study of the deformation of a metal plate subjected to a thermal load.

Fig. 6
Fig. 6

Phase gradient values obtained along the row y = 115 of Fig. 5 when the SSFD method was applied.

Fig. 7
Fig. 7

Phase map determined from Fig. 5 by integration of the phase gradients evaluated with the SSFD method.

Tables (1)

Tables Icon

Table 1 Comparison of Figures of Merit Obtained with the SSFD and the CWT Methods for Different Speckle Sizes when a Speckle Noise Reduction Filter Was Applied

Equations (10)

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

Ix, y=I0x, y1+γx, ycos ϕx, y,
Qx, ω=- zx+u2z*x-u2exp-iuωdu,
SQx, ω=-- Qx, ωθx, x, ω, ωdxdω,
ϕxx=- ωSQx, ωdω- SQx, ωdω.
SQx, ω=Ãx, ωδω-ωx,
Qn, kp=-NN-1 zn+p2z*n-p2exp-2πikpN.
Qn, kp=02N-1 zint2n+p-Nzint*2n-p+N×exp-2πi2kp2N,
θν, τ=exp-ν2/ηνexp-τ2/ητ,
MSE= x,y=1512ϕox, y-ϕx, y2x,y=1512 ϕox, y,
σ= x,y=1512ϕox, y-ϕx, y-1/5122x,y=1512 ϕox, y-ϕx, y25122-11/2,

Metrics