Abstract

We propose a novel approach to retrieving the phase map coded by a single closed-fringe pattern in digital speckle pattern interferometry, which is based on the estimation of the local sign of the quadrature component. We obtain the estimate by calculating the local orientation of the fringes that have previously been denoised by a weighted smoothing spline method. We carry out the procedure of sign estimation by determining the local abrupt jumps of size π in the orientation field of the fringes and by segmenting the regions defined by these jumps. The segmentation method is based on the application of two-dimensional active contours (snakes), with which one can also estimate absent jumps, i.e., those that cannot be detected from the local orientation of the fringes. The performance of the proposed phase-retrieval technique is evaluated for synthetic and experimental fringes and compared with the results obtained with the spiral-phase- and Fourier-transform methods.

© 2006 Optical Society of America

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    [CrossRef]
  2. J. M. Huntley, "Automated analysis of speckle interferograms," in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59-139.
  3. T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996).
  4. 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 Publishing, Bristol, 1996), pp. 261-267.
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    [CrossRef]
  6. C. A. Sciammarella and T. Kim, "Determination of strains from fringe patterns using space-frequency representations," Opt. Eng. 42, 3182-3193 (2003).
    [CrossRef]
  7. A. Federico and G. H. Kaufmann. "Phase retrieval in digital speckle pattern interferometry using a chirped Gaussian wavelet transform and a smoothed time-frequency distribution," in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, and S. Winther, eds., Proc. SPIE 4933, 200-205 (2003).
    [CrossRef]
  8. A. Federico and G. H. Kaufmann, "Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution," Appl. Opt. 42, 7066-7071 (2003).
    [CrossRef] [PubMed]
  9. C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
    [CrossRef]
  10. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Am. A 18, 1862-1870 (2001).
    [CrossRef]
  11. M. Servín, J. A. Quiroga, and J. L. Marroquín, "General n-dimensional quadrature transform and its application to interferogram demodulation," J. Opt. Soc. Am. A 20, 925-934 (2003).
    [CrossRef]
  12. M. Servín, J. L. Marroquín, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18, 689-695 (2001).
    [CrossRef]
  13. A. Federico and G. H. Kaufmann, "Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines," Appl. Opt. 44, 2728-2735 (2005).
    [CrossRef] [PubMed]
  14. J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
    [CrossRef] [PubMed]
  15. M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
    [CrossRef]
  16. C. Xu and J. L. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process. 7, 359-369 (1998).
    [CrossRef]
  17. P. Soille, Morphological Image Analysis: Principles and Applications (Springer-Verlag, 2002).
  18. J. L. Marroquín, R. Rodríguez-Vera, and M. Servín, "Local phase from local orientation by solution of a sequence of linear systems," J. Opt. Soc. Am. A 15, 1536-1544 (1998).
    [CrossRef]
  19. M. D. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping (Wiley, 1998).
  20. S. Krinidis and I. Pitas, "Fast free-vibration modal analysis of 2-D physics-based deformable objects," IEEE Trans. Image Process. 14, 281-293 (2005).
    [CrossRef] [PubMed]
  21. G. H. Kaufmann, "Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry," Opt. Eng. 42, 2010-2014 (2003).
    [CrossRef]

2005 (2)

2004 (1)

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[CrossRef]

2003 (6)

N. K. Mohan and P. K. Rastogi, "Recent developments in digital speckle pattern interferometry," Opt. Lasers Eng. 40, 439-445 (2003).
[CrossRef]

C. A. Sciammarella and T. Kim, "Determination of strains from fringe patterns using space-frequency representations," Opt. Eng. 42, 3182-3193 (2003).
[CrossRef]

A. Federico and G. H. Kaufmann. "Phase retrieval in digital speckle pattern interferometry using a chirped Gaussian wavelet transform and a smoothed time-frequency distribution," in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, and S. Winther, eds., Proc. SPIE 4933, 200-205 (2003).
[CrossRef]

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

M. Servín, J. A. Quiroga, and J. L. Marroquín, "General n-dimensional quadrature transform and its application to interferogram demodulation," J. Opt. Soc. Am. A 20, 925-934 (2003).
[CrossRef]

A. Federico and G. H. Kaufmann, "Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution," Appl. Opt. 42, 7066-7071 (2003).
[CrossRef] [PubMed]

2001 (2)

1999 (1)

1998 (2)

1987 (1)

M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
[CrossRef]

1986 (1)

J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Barnes, T.

Bone, D. J.

Canny, J.

J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Cuevas, F. J.

de Lega, X. Colonna

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 Publishing, Bristol, 1996), pp. 261-267.

Federico, A.

A. Federico and G. H. Kaufmann, "Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines," Appl. Opt. 44, 2728-2735 (2005).
[CrossRef] [PubMed]

A. Federico and G. H. Kaufmann, "Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution," Appl. Opt. 42, 7066-7071 (2003).
[CrossRef] [PubMed]

A. Federico and G. H. Kaufmann. "Phase retrieval in digital speckle pattern interferometry using a chirped Gaussian wavelet transform and a smoothed time-frequency distribution," in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, and S. Winther, eds., Proc. SPIE 4933, 200-205 (2003).
[CrossRef]

Ghiglia, M. D.

M. D. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping (Wiley, 1998).

He, X. Y.

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[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, 2001), pp. 59-139.

Kass, M.

M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
[CrossRef]

Kaufmann, G. H.

A. Federico and G. H. Kaufmann, "Local denoising of digital speckle pattern interferometry fringes using multiplicative correlation and weighted smoothing splines," Appl. Opt. 44, 2728-2735 (2005).
[CrossRef] [PubMed]

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

A. Federico and G. H. Kaufmann, "Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution," Appl. Opt. 42, 7066-7071 (2003).
[CrossRef] [PubMed]

A. Federico and G. H. Kaufmann. "Phase retrieval in digital speckle pattern interferometry using a chirped Gaussian wavelet transform and a smoothed time-frequency distribution," in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, and S. Winther, eds., Proc. SPIE 4933, 200-205 (2003).
[CrossRef]

Kim, T.

C. A. Sciammarella and T. Kim, "Determination of strains from fringe patterns using space-frequency representations," Opt. Eng. 42, 3182-3193 (2003).
[CrossRef]

Kreis, T.

T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996).

Krinidis, S.

S. Krinidis and I. Pitas, "Fast free-vibration modal analysis of 2-D physics-based deformable objects," IEEE Trans. Image Process. 14, 281-293 (2005).
[CrossRef] [PubMed]

Larkin, K. G.

Marroquín, J. L.

Mohan, N. K.

N. K. Mohan and P. K. Rastogi, "Recent developments in digital speckle pattern interferometry," Opt. Lasers Eng. 40, 439-445 (2003).
[CrossRef]

Oldfield, M. A.

Pitas, I.

S. Krinidis and I. Pitas, "Fast free-vibration modal analysis of 2-D physics-based deformable objects," IEEE Trans. Image Process. 14, 281-293 (2005).
[CrossRef] [PubMed]

Prince, J. L.

C. Xu and J. L. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process. 7, 359-369 (1998).
[CrossRef]

Pritt, M. D.

M. D. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping (Wiley, 1998).

Quan, C.

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[CrossRef]

Quiroga, J. A.

Rastogi, P. K.

N. K. Mohan and P. K. Rastogi, "Recent developments in digital speckle pattern interferometry," Opt. Lasers Eng. 40, 439-445 (2003).
[CrossRef]

Rodríguez-Vera, R.

Sciammarella, C. A.

C. A. Sciammarella and T. Kim, "Determination of strains from fringe patterns using space-frequency representations," Opt. Eng. 42, 3182-3193 (2003).
[CrossRef]

Servín, M.

Soille, P.

P. Soille, Morphological Image Analysis: Principles and Applications (Springer-Verlag, 2002).

Tan, S.

Tay, C. J.

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[CrossRef]

Terzopoulos, D.

M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
[CrossRef]

Watkins, L.

Witkin, A.

M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
[CrossRef]

Xu, C.

C. Xu and J. L. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process. 7, 359-369 (1998).
[CrossRef]

Yang, F. J.

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Image Process. (2)

C. Xu and J. L. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process. 7, 359-369 (1998).
[CrossRef]

S. Krinidis and I. Pitas, "Fast free-vibration modal analysis of 2-D physics-based deformable objects," IEEE Trans. Image Process. 14, 281-293 (2005).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Int. J. Comput. Vision (1)

M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: active contour models," Int. J. Comput. Vision 1, 321-331 (1987).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

C. J. Tay, C. Quan, F. J. Yang, and X. Y. He, "A new method for phase extraction from a single fringe pattern," Opt. Commun. 239, 251-258 (2004).
[CrossRef]

Opt. Eng. (2)

C. A. Sciammarella and T. Kim, "Determination of strains from fringe patterns using space-frequency representations," Opt. Eng. 42, 3182-3193 (2003).
[CrossRef]

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

Opt. Lasers Eng. (1)

N. K. Mohan and P. K. Rastogi, "Recent developments in digital speckle pattern interferometry," Opt. Lasers Eng. 40, 439-445 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

A. Federico and G. H. Kaufmann. "Phase retrieval in digital speckle pattern interferometry using a chirped Gaussian wavelet transform and a smoothed time-frequency distribution," in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, and S. Winther, eds., Proc. SPIE 4933, 200-205 (2003).
[CrossRef]

Other (5)

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

T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996).

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 Publishing, Bristol, 1996), pp. 261-267.

M. D. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping (Wiley, 1998).

P. Soille, Morphological Image Analysis: Principles and Applications (Springer-Verlag, 2002).

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Figures (6)

Fig. 1
Fig. 1

(a) Computer-simulated DSPI fringes, (b) filtering and normalization of (a), (c) orientation field βπ obtained from (b), (d) edge map f(x, y) obtained from (c), (e) evolution of snakes A and B; (f) sign map associated with the segmentation procedure; (g) quadrature component of the fringe pattern, and (h) three-dimensional plot of the continuous phase distribution.

Fig. 2
Fig. 2

(a) Computer-simulated DSPI fringes used to evaluate the performance of the phase-retrieval method, (b) filtering and normalization of (a), (c) orientation field βπ obtained from (b).

Fig. 3
Fig. 3

(a) Edge map f (x, y) obtained from Fig. 2(c), (b) evolution of snakes A and B, (c) details of the evolution of snakes A and B.

Fig. 4
Fig. 4

(a) Sign map associated with segmentation, (b) quadrature component of the fringe pattern, (c) phase map wrapped by use of the filtered quadrature component shown in (b).

Fig. 5
Fig. 5

Quadrature component determined from (a) the Fourier-transform method and (b) the spiral-phase-transform method. (c) Contour plot of the continuous phase distribution obtained by unwrapping Fig. 4(c).

Fig. 6
Fig. 6

(a) Experimental DSPI fringes generated by a flawed plate subjected to a thermal load, (b) denoised and normalized fringe pattern, (c) contour plot of the continuous phase distribution obtained from the proposed phase-retrieval method.

Equations (9)

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I S ( x , y ) = I 0 ( x , y ) + I M ( x , y ) cos [ ϕ ( x , y ) ] ,
I ( x , y ) = cos [ ϕ ( x , y ) ] .
β π ( x , y ) = arctan [ I ( x , y ) y / I ( x , y ) x ] ,
β 2 π ( x , y ) = arctan [ ϕ ( x , y ) y / ϕ ( x , y ) x ] .
β π ( x , y ) = β 2 π ( x , y ) + k π ,
sign [ I ( x , y ) y ] = sign { sin [ ϕ ( x , y ) ] } sign { sin [ β 2 π ( x , y ) ] } ,
x ( s , t ) t = α 2 x ( s , t ) s 2 β 3 x ( s , t ) s 3 + v ( x , y ) ,
μ 2 u ( x , y ) [ u ( x , y ) f ( x , y ) x ] { [ f ( x , y ) x ] 2 + [ f ( x , y ) y ] 2 } = 0 ,
μ 2 v ( x , y ) [ v ( x , y ) f ( x , y ) y ] { [ f ( x , y ) x ] 2 + [ f ( x , y ) y ] 2 } = 0 ,

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