## Dynamic phase measurement in shearography by clustering method and Fourier filtering |

Optics Express, Vol. 19, Issue 2, pp. 606-615 (2011)

http://dx.doi.org/10.1364/OE.19.000606

Acrobat PDF (1245 KB)

### 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

## 1. Introduction

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]

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]

## 2. The clustering phase extraction method

### 2.1. Theoretical background

*a*,and

*φ*can be determined by four-step phase shifting technique before the object starts to deform, and

*n*is an integer.

*Δ*in Eq. (3) still has two uncertainties to determine. One is the phase ambiguity problem associated with the arccosine function. The other is the phase unwrapping problem associated with the

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]

*π*(if some phase values are out of this range, adjust

*n*in Eq. (3) to make them in range) as shown in Fig. 1 . Within these 18 phase values (represented by hollow dots), it can be observed that 9 correct phase data cluster together near the arrow position, while the other 9 wrong phase values distribute randomly. This observation inspires an algorithm to determine the clustering centre to represent the correct wrapped phase value for the specific pixel.

*π*indicates the periodic feature of sinusoidal functions and the phase distances are measured as the shortest arc length. In this specific definition, the distance between

*φ*without ambiguity is a necessity for the success of the clustering method. If

*φ*is subject to phase ambiguity problem (i.e.

*φ*is determined from arccosine function instead of phase shifting method), then the candidate phase values determined from Eq. (3) will have two clustering centers, making the resultant wrapped phase subject to phase ambiguity.

### 2.2. Comparison with phase shifting method

## 3. The Fourier phase filtering method

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]

## 4. Dynamic phase measurement experiment

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]

## 5. Conclusions

## Acknowledgments

## References and links

1. | P. K. Rastogi, ed., |

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. |

3. | L. X. Yang, W. Steinchen, G. Kupfer, P. Mackel, and F. Vossing, “Vibration analysis by means of digital shearography,” Opt. Lasers Eng. |

4. | S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express |

5. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

6. | C. Quan, C. J. Tay, and Y. H. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) |

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. |

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 |

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 |

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 |

11. | K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express |

12. | J. C. Estrada, M. Servin, and J. L. Marroquín, “Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes,” Opt. Express |

13. | O. Dalmau-Cedeño, M. Rivera, and R. Legarda-Saenz, “Fast phase recovery from a single close-fring pattern,” J. Opt. Soc. Am. A |

14. | H. X. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express |

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. |

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. |

17. | C. G. Dennis, and D. P. Mark, |

18. | L. J. Chen, C. G. Quan, C. J. Tay, and Y. H. Huang, “Fringe contrast-based 3D profilometry using fringe projection,” Optik (Stuttg.) |

19. | Q. Kemao, S. H. Soon, and A. Asundi, “Smoothing filters in phase-shifting interferometry,” Opt. Laser Technol. |

20. | K. Qian, H. S. Seah, and A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. |

21. | A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. |

22. | Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. |

23. | K. M. Qian and S. H. Soon, “Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis,” Opt. Eng. |

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 |

**OCIS Codes**

(090.2880) Holography : Holographic interferometry

(100.2650) Image processing : Fringe analysis

(100.3020) Image processing : Image reconstruction-restoration

(100.5070) Image processing : Phase retrieval

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

(070.2615) Fourier optics and signal processing : Frequency filtering

**ToC Category:**

Image Processing

**History**

Original Manuscript: December 3, 2010

Revised Manuscript: December 3, 2010

Manuscript Accepted: December 20, 2010

Published: January 5, 2011

**Citation**

Yuanhao Huang, Farrokh Janabi-Sharifi, Yusheng Liu, and Y. Y. Hung, "Dynamic phase measurement in shearography by clustering method and Fourier filtering," Opt. Express **19**, 606-615 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-606

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### References

- P. K. Rastogi, ed., Photomechanics (Springer, Berlin, 2000).
- 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]
- 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]
- 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]
- I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997). [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]
- 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]
- 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]
- 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]
- 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]
- K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005). [CrossRef] [PubMed]
- 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]
- 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]
- 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, Y. S. Chen, and Y. Y. Hung, “Shearographic phase retrieval using one single specklegram: a clustering approach,” Opt. Eng. 47(5), 054301 (2008). [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]
- C. G. Dennis, and D. P. Mark, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, (Wiley, New York, 1998).
- 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]
- 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]
- 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]
- Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007). [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]
- 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]

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