Abstract

Quantitative phase extraction is a key step in optical measurement. While phase shifting technique is widely employed for static or semi-static phase measurement, it requires several images with known phase shifts at each deformed stage, thus is not suitable for dynamic phase measurement. Fourier transform offer a solution to extract phase information from a single fringe pattern. However, a high frequency spatial carrier which is sometimes not easy to generate is required to solve the phase ambiguity problem. In this paper, we aim to propose an ideal solution for dynamic phase measurement. Four images with known phase shift are captured at the reference stage to analyze the initial phase information. After the object starts continuous deformation, only one image is captured at each deformed stage. A clustering phase extraction method is then applied for deformation phase extraction utilizing the phase clustering effect within a small region. This method works well for speckle image with low and medium fringe density. When the fringe density is high, especially in the case of shearographic fringe, information insufficiency inherent with merely one deformed speckle image often results in poor quality wrapped phase map with plenty of phase residues, which make phase unwrapping a difficult task. In the light of this limitation, a Fourier transform based phase filtering method is proposed for fringe frequency analysis and adaptive filtering, and effectively removes most of the phase residues to reconstruct a high quality wrapped phase map. Several real experiments based on shearography are presented. Comparison between the proposed solution and standard phase evaluation methods is also given. The results demonstrate the effectiveness of the proposed integrated dynamic phase extraction method.

© 2011 OSA

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References

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  1. P. K. Rastogi, ed., Photomechanics (Springer, Berlin, 2000).
  2. Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
    [Crossref]
  3. L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
    [Crossref]
  4. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010).
    [Crossref] [PubMed]
  5. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [Crossref] [PubMed]
  6. C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
    [Crossref]
  7. C. J. Tay, C. Quan, Y. Fu, and Y. H. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43(21), 4164–4171 (2004).
    [Crossref] [PubMed]
  8. K. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18(3), 689–695 (2001).
    [Crossref]
  9. Q. F. Yu, S. H. Fu, X. Yang, X. Y. Sun, and X. L. Liu, “Extraction of phase field from a single contoured correlation fringe pattern of ESPI,” Opt. Express 12(1), 75–83 (2004).
    [Crossref] [PubMed]
  10. Q. F. Yu, S. H. Fu, X. L. Liu, X. Yang, and X. Y. Sun, “Single-phase-step method with contoured correlation fringe patterns for ESPI,” Opt. Express 12(20), 4980–4985 (2004).
    [Crossref] [PubMed]
  11. K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005).
    [Crossref] [PubMed]
  12. J. C. Estrada, M. Servin, and J. L. Marroquín, “Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes,” Opt. Express 15(5), 2288–2298 (2007).
    [Crossref] [PubMed]
  13. O. Dalmau-Cedeño, M. Rivera, and R. Legarda-Saenz, “Fast phase recovery from a single close-fring pattern,” J. Opt. Soc. Am. A 25(6), 1361–1370 (2008).
    [Crossref]
  14. H. X. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).
    [Crossref] [PubMed]
  15. 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]
  16. Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
    [Crossref]
  17. C. G. Dennis, and D. P. Mark, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, (Wiley, New York, 1998).
  18. L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
    [Crossref]
  19. Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
    [Crossref]
  20. K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
    [Crossref]
  21. A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
    [Crossref]
  22. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
    [Crossref]
  23. K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44(7), 075601 (2005).
    [Crossref]
  24. 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]

2010 (1)

2009 (4)

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

H. X. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).
[Crossref] [PubMed]

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

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]

2008 (2)

O. Dalmau-Cedeño, M. Rivera, and R. Legarda-Saenz, “Fast phase recovery from a single close-fring pattern,” J. Opt. Soc. Am. A 25(6), 1361–1370 (2008).
[Crossref]

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]

2007 (2)

J. C. Estrada, M. Servin, and J. L. Marroquín, “Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes,” Opt. Express 15(5), 2288–2298 (2007).
[Crossref] [PubMed]

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

2005 (3)

K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44(7), 075601 (2005).
[Crossref]

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005).
[Crossref] [PubMed]

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

2004 (4)

2003 (2)

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
[Crossref]

2001 (1)

1998 (1)

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

1997 (1)

1996 (1)

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[Crossref]

Asundi, A.

K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Chen, L. J.

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

Chen, Y. S.

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

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]

Chung, P. S.

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Cuevas, F. J.

Dalmau-Cedeño, O.

Dávila, A.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[Crossref]

Estrada, J. C.

Fu, S. H.

Fu, Y.

Gao, W. J.

Huang, Y. H.

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

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]

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

C. J. Tay, C. Quan, Y. Fu, and Y. H. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43(21), 4164–4171 (2004).
[Crossref] [PubMed]

C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

Hung, Y. Y.

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

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]

Huyen, N. T. T.

Ip, R. W. L.

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Kaufmann, G. H.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[Crossref]

Kemao, Q.

H. X. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).
[Crossref] [PubMed]

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]

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

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Kerr, D.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[Crossref]

Kupfer, G.

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Larkin, K. G.

Legarda-Saenz, R.

Li, C. L.

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

Liu, L.

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

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, X. L.

Loi, H. S.

Luk, B. L.

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Mackel, P.

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Marroquin, J. L.

Marroquín, J. L.

Ng, S. P.

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[Crossref]

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]

Oliver, J.

Qian, K.

K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
[Crossref]

Qian, K. M.

K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44(7), 075601 (2005).
[Crossref]

Quan, C.

C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

C. J. Tay, C. Quan, Y. Fu, and Y. H. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43(21), 4164–4171 (2004).
[Crossref] [PubMed]

Quan, C. G.

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

Rivera, M.

Seah, H. S.

K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
[Crossref]

Servin, K. M.

Servin, M.

Soon, S. H.

K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44(7), 075601 (2005).
[Crossref]

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Steinchen, W.

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Sun, X. Y.

Tay, C. J.

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

C. J. Tay, C. Quan, Y. Fu, and Y. H. Huang, “Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis,” Appl. Opt. 43(21), 4164–4171 (2004).
[Crossref] [PubMed]

Van Der Weide, D.

Vossing, F.

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Wang, H. X.

Wu, C. M. L.

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Yamaguchi, I.

Yang, L. X.

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Yang, X.

Yu, Q. F.

Zhang, S.

Zhang, T.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Mater. Sci. Eng. Rep. (1)

Y. Y. Hung, Y. S. Chen, S. P. Ng, L. Liu, Y. H. Huang, B. L. Luk, R. W. L. Ip, C. M. L. Wu, and P. S. Chung, “Review and comparison of shearography and active thermography for nondestructive evaluation,”, ” Mater. Sci. Eng. Rep. 64(5-6), 73–112 (2009).
[Crossref]

Opt. Eng. (4)

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]

K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42(10), 2792–2793 (2003).
[Crossref]

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[Crossref]

K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. 44(7), 075601 (2005).
[Crossref]

Opt. Express (7)

Opt. Laser Technol. (1)

Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. 35(8), 649–654 (2003).
[Crossref]

Opt. Lasers Eng. (3)

L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. 30(2), 199–212 (1998).
[Crossref]

Y. H. Huang, S. P. Ng, L. Liu, C. L. Li, Y. S. Chen, and Y. Y. Hung, “NDT&E using shearography with impulsive thermal stressing and clustering phase extraction,” Opt. Lasers Eng. 47(7-8), 774–781 (2009).
[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. (1)

Optik (Stuttg.) (2)

C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) 116(3), 123–128 (2005).
[Crossref]

Other (2)

P. K. Rastogi, ed., Photomechanics (Springer, Berlin, 2000).

C. G. Dennis, and D. P. Mark, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, (Wiley, New York, 1998).

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Figures (7)

Fig. 1
Fig. 1

Demonstration of clustering effect of wrapped phase values within an area of 3x3 pixels.

Fig. 2
Fig. 2

Typical shearographic fringe pattern of a central loaded rectangular plate (a) and the corresponding wrapped phase obtained by the clustering approach (b)

Fig. 3
Fig. 3

Comparison of unwrapped phase maps of the clustering method and four-step phase shifting at the horizontal mid-section.

Fig. 4
Fig. 4

(a) Initial wrapped phase map determined from the clustering method; (b) Wrapped phase map after 50 times fringe averaging; (c) The central area of (b) showing plenty of phase residues; (d) unwrapped phase map of (b) using Raster unwrapping algorithm.

Fig. 5
Fig. 5

(a) Cosine fringe map obtained from the wrapped phase map determined from clustering method; (b) Fourier spectrum of (a); (c) low-pass filter determined by thresholding; (d) reconstructed cosine fringe map after Fourier filtering; (e) reconstructed wrapped phase map after Fourier phase filtering; (f) unwrapped phase map by Raster unwrapping algorithm.

Fig. 6
Fig. 6

Reconstructed wrapped phase map by the proposed clustering method and Fourier phase filtering method.

Fig. 7
Fig. 7

Fringe pattern depicting a vertical crack of a steel tube subject to continuous pressurization at different time (a), (b), (c) and the corresponding wrapped phase map obtained from the clustering method and Fourier phase filtering method (d), (e), (f).

Equations (10)

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I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ]
I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) + Δ ( x , y ) ]
Δ = ± arccos [ ( I a ) / b ] φ + 2 n π
d ( x m , x n ) = { | x m x n | i f | x m x n | π 2 π | x m x n | i f | x m x n | > π } x m , x n [ π , π )
S u m D i s t ( x k ) = i = 4 4 d ( x k , x k + i ) k = 0 , 1 , 17
x c = { x k | S u m D i s t ( x k ) S u m D i s t ( x i ) ; i k }
f ( x , y ) = cos ( Δ ( x , y ) ) + r ( x , y ) g ( x , y ) = sin ( Δ ( x , y ) ) + r ( x , y )
F ( u , v ) = 1 2 δ ( u Δ x 2 π , v Δ y 2 π ) + 1 2 δ ( u + Δ x 2 π , v + Δ y 2 π ) + R ( u , v ) G ( u , v ) = i 2 δ ( u + Δ x 2 π , v + Δ y 2 π ) i 2 δ ( u Δ x 2 π , v Δ y 2 π ) + R ( u , v )
f ^ ( x , y ) = i f f t { F ( u , v ) * f l t ( u , v ) } g ^ ( x , y ) = i f f t { G ( u , v ) * f l t ( u , v ) }
Δ ( x , y ) = arctan 2 ( g ^ ( x , y ) , f ^ ( x , y ) )

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