Abstract

We evaluate the use of smoothing splines with a weighted roughness measure for local denoising of the correlation fringes produced in digital speckle pattern interferometry. In particular, we also evaluate the performance of the multiplicative correlation operation between two speckle patterns that is proposed as an alternative procedure to generate the correlation fringes. It is shown that the application of a normalization algorithm to the smoothed correlation fringes reduces the excessive bias generated in the previous filtering stage. The evaluation is carried out by use of computer-simulated fringes that are generated for different average speckle sizes and intensities of the reference beam, including decorrelation effects. A comparison with filtering methods based on the continuous wavelet transform is also presented. Finally, the performance of the smoothing method in processing experimental data is illustrated.

© 2005 Optical Society of America

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References

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  1. O. J. Løkberg, “Recent developments in video speckle interferometry,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 157–194.
  2. N. K. Mohan, P. K. Rastogi, “Recent developments in digital speckle pattern interferometry,” Opt. Lasers Eng. 40, 439–445 (2003).
    [CrossRef]
  3. 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.
  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, UK, 1996), pp. 261–267.
  5. L. Watkins, S. Tan, T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
    [CrossRef]
  6. C. A. Sciammarella, T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (2003).
    [CrossRef]
  7. 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]
  8. A. Federico, 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. S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
    [CrossRef]
  10. S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
    [CrossRef]
  11. 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]
  12. Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
    [CrossRef]
  13. M. Unser, “Splines,” IEEE Signal Process Mag. 16, 22–38 (1999).
    [CrossRef]
  14. N. Alcalá Ochoa, F. M. Santoyo, C. P. López, B. Barrientos, “Multiplicative electronic speckle-pattern interferometry fringes,” Appl. Opt. 39, 5138–5141 (2000).
    [CrossRef]
  15. D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, D. Kerr, “Measurement of transient deformations using dual-pulse addition ESPI,” Appl. Opt. 37, 7259–7267 (1998).
    [CrossRef]
  16. C. de Boor, A Practical Guide to Splines (Springer-Verlag, Berlin, 1994).
  17. C. de Boor, Department of Computer Sciences, University of Wisconsin-Madison, 1210 West Dayton Street, Madison, Wis. 53706-1685, “Calculation of the smoothing spline with weighted roughness measure.” This paper can be downloaded at the Web site http://www.cs.wisc.edu .
  18. J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
    [CrossRef]
  19. Z. Wang, A. C. Bovik, “A universal quality index,” IEEE Signal Process Lett. 9, 81–84 (2002).
    [CrossRef]
  20. G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42, 2010–2014 (2003).
    [CrossRef]

2003 (5)

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

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

Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
[CrossRef]

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, “Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution,” Appl. Opt. 42, 7066–7071 (2003).
[CrossRef] [PubMed]

2002 (2)

Z. Wang, A. C. Bovik, “A universal quality index,” IEEE Signal Process Lett. 9, 81–84 (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 (2)

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]

J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
[CrossRef]

2000 (3)

S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
[CrossRef]

N. Alcalá Ochoa, F. M. Santoyo, C. P. López, B. Barrientos, “Multiplicative electronic speckle-pattern interferometry fringes,” Appl. Opt. 39, 5138–5141 (2000).
[CrossRef]

1999 (2)

1998 (1)

Alcalá Ochoa, N.

Barnes, T.

Barrientos, B.

Bovik, A. C.

Z. Wang, A. C. Bovik, “A universal quality index,” IEEE Signal Process Lett. 9, 81–84 (2002).
[CrossRef]

Chang, S. G.

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
[CrossRef]

S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
[CrossRef]

Chen, J.

Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
[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 Publishing, Bristol, UK, 1996), pp. 261–267.

de Boor, C.

C. de Boor, A Practical Guide to Splines (Springer-Verlag, Berlin, 1994).

Fan, H.

Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
[CrossRef]

Farrant, D. I.

Federico, A.

A. Federico, 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, 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]

García-Botella, A.

J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
[CrossRef]

Gómez-Pedrero, J.

J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
[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, “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, 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]

D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, D. Kerr, “Measurement of transient deformations using dual-pulse addition ESPI,” Appl. Opt. 37, 7259–7267 (1998).
[CrossRef]

Kerr, D.

Kim, T.

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

Løkberg, O. J.

O. J. Løkberg, “Recent developments in video speckle interferometry,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 157–194.

López, C. P.

Mohan, N. K.

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

Oreb, B. F.

Petzing, J. N.

Qin, Y.

Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
[CrossRef]

Quiroga, J. A.

J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
[CrossRef]

Rastogi, P. K.

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

Santoyo, F. M.

Sciammarella, C. A.

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

Tan, S.

Tyrer, J. R.

Unser, M.

M. Unser, “Splines,” IEEE Signal Process Mag. 16, 22–38 (1999).
[CrossRef]

Vetterli, M.

S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, “A universal quality index,” IEEE Signal Process Lett. 9, 81–84 (2002).
[CrossRef]

Watkins, L.

Yu, B.

S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
[CrossRef]

Appl. Opt. (3)

IEEE Signal Process Lett. (1)

Z. Wang, A. C. Bovik, “A universal quality index,” IEEE Signal Process Lett. 9, 81–84 (2002).
[CrossRef]

IEEE Signal Process Mag. (1)

M. Unser, “Splines,” IEEE Signal Process Mag. 16, 22–38 (1999).
[CrossRef]

IEEE Trans. Image Proc. (2)

S. G. Chang, B. Yu, M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Proc. 9, 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Proc. 9, 1532–1546 (2000).
[CrossRef]

Opt. Commun. (1)

J. A. Quiroga, J. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001).
[CrossRef]

Opt. Eng. (4)

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

C. A. Sciammarella, T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (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]

Opt. Lasers Eng. (2)

Y. Qin, J. Chen, H. Fan, “The study and application of a new filtering method on electronic speckle pattern interferometric fringes,” Opt. Lasers Eng. 39, 449–456 (2003).
[CrossRef]

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

Opt. Lett. (1)

Other (5)

O. J. Løkberg, “Recent developments in video speckle interferometry,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 157–194.

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.

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, UK, 1996), pp. 261–267.

C. de Boor, A Practical Guide to Splines (Springer-Verlag, Berlin, 1994).

C. de Boor, Department of Computer Sciences, University of Wisconsin-Madison, 1210 West Dayton Street, Madison, Wis. 53706-1685, “Calculation of the smoothing spline with weighted roughness measure.” This paper can be downloaded at the Web site http://www.cs.wisc.edu .

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Figures (8)

Fig. 1
Fig. 1

Schematic view of quadrature filters Ĥ(wx, wy) (a) and V ̂ ( w x , w y ) (b). Row {wy = 0, wx < 0} and column {wy < 0, wx = 0} are excluded from the filtered region in ˆH and ˆV, respectively.

Fig. 2
Fig. 2

Computer-simulated phase distribution used for the numerical evaluation.

Fig. 3
Fig. 3

Multiplicative correlation fringes corresponding to the optical phase map given in Fig. 2.

Fig. 4
Fig. 4

Weight matrix λ used to minimize Eq. (8).

Fig. 5
Fig. 5

Filtered fringe pattern obtained by application of the weighted smoothing spline method and the normalization algorithm to Fig. 3.

Fig. 6
Fig. 6

(a) Intensity along a horizontal direction across the center of the fringe pattern shown in Fig. 3, and its oversmoothing; (b) normalization of the smoothed fringes obtained in (a); (c) comparison of the original (dashed curve) and the normalized (continuous curve) intensities.

Fig. 7
Fig. 7

Fringe pattern generated by a plate subjected to a thermal load.

Fig. 8
Fig. 8

Filtered image of Fig. 7.

Tables (2)

Tables Icon

Table 1 Quality Index Q Obtained for the Multiplicative, Subtractlve, and Additive Correlation Operations for an Average Speckle Size of 1 and 2 Pixels As a Function of Ratio α and When Decorrelation Effects Are and Are Not Present

Tables Icon

Table 2 Quality Index Q Obtained for the Weighted Smoothing Spline and the Wavelet Shrinkage Methods for an Average Speckle Size of 1 and 2 Pixels As a Function of the Ratio α and When Decorrelation Effects Are and Are Not Present

Equations (15)

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

I i ( x , y ) = I s ( x , y ) + I r ( x , y ) + 2 [ I s ( x , y ) I r ( x , y ) ] 1 / 2 cos [ ψ ( x , y ) ψ r ] ,
I f ( x , y ) = I s ( x , y ) + I r ( x , y ) + 2 [ I s ( x , y ) I r ( x , y ) ] 1 / 2 cos [ ψ f ( x , y ) ψ r ] ,
I D ( x , y ) I i I f = 2 I M ( x , y ) sin [ ψ ( x , y ) + ϕ ( x , y ) 2 ] sin [ ϕ ( x , y ) 2 ] ,
I A ( x , y ) I f + I i = 2 I 0 ( x , y ) + 2 I M ( x , y ) cos [ ψ ( x , y ) + ϕ ( x , y ) 2 ] cos [ ϕ ( x , y ) 2 ] ,
I P ( x , y ) I D ( HI ) ( x , y ) 2 + ( 1 ) I A ( HI ) ( x , y ) 2 2 = 2 I i ( HI ) ( x , y ) I f ( HI ) ( x , y ) ,
s ( x ) = k c ( k ) β n ( x k ) ,
s 2 = k [ g ( k ) s ( k ) ] 2 + λ d x [ n x n s ( x ) ] 2 ,
2 = ρ j w j [ g ( x j ) s ( x j ) ] 2 + a b d x λ ( x ) [ m x m s ( x ) ] 2 ,
cos ϕ ( x , y ) m H ( x , y ) cos ϕ H ( x , y ) + m V ( x , y ) cos ϕ V ( x , y ) m H ( x , y ) + m V ( x , y ) .
I i ( x , y ) = | A r + A s exp ( i ψ ) ( 1 d [ 0 , 1 ] ) + d [ 0 , 1 ] A s exp ( i ψ ) | 2 ,
Q 4 σ E O Ē Ō ( σ E 2 + σ O 2 ) [ Ē 2 + Ō 2 ] = σ E O σ E σ O 2 Ē Ō Ē 2 + Ō 2 2 σ E σ O σ E 2 σ O 2 ,
Ē = 1 N 2 x , y = 1 N E ( x , y ) , Ō = 1 N 2 x , y = 1 N O ( x , y ) ,
σ E 2 = 1 N 2 1 x , y = 1 N [ E ( x , y ) Ē ] 2 ,
σ O 2 = 1 N 2 1 x , y = 1 N [ O ( x , y ) Ō ] 2 ,
σ E O = 1 N 2 1 x , y = 1 N [ E ( x , y ) Ē ] [ O ( x , y ) Ō ]

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