Abstract

In this study, we propose the Hilbert transform (HT) method for phase analysis of a Dynamic ESPI signal. The data processing is performed in the temporal domain, using the temporal history of the interference signal at every single pixel. The final results give a temporal development of the two-dimensional deformation field. To reduce the influence of the fluctuations of bias intensity on the calculated phase, it was removed prior to performing the HT. This method was demonstrated for defects distinction and the determination of the sign change in the deformation field in two different experiments. The range of measurement lies between submicrons and tens of microns and the spatial resolution is better when compared to the fringe analysis method and the spatial carrier method.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. P. K. Rastogi (Ed.), Photomechanics (Springer-Verlag, Berlin, 1999).
  2. P.K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (John and Wiley and Sons Ltd., Chichester, 2001).
  3. D. W. Robinson, C. R. Raed (Ed.), Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, Bristol, 1993).
  4. Wolfgang Osten, �??Digital Processing and Evaluation of Fringe Patterns in Optical Metrology and Non-Destructive Testing,�?? D-28359 (Bremer Institut fur Angenwandte Strahltechnik, Bremen, 1998).
  5. V. Madjarova, S. Toyooka, R. Widiastuti, H. Kadono, �??Dynamic ESPI with subtraction-addition method for obtaining the phase,�?? Opt. Commun. 212, 35 (2002)
    [CrossRef]
  6. Xavier Colonna de Lega, Pierre Jacquot, �??Deformation measurement with object-induced dynamic phase shifting,�?? Appl. Opt. 35, 5115-5121 (1994).
    [CrossRef]
  7. X. Colonna de Lega, �??Continuous deformation measurement using dynamic phase shifting and wavelet transforms,�?? Applied Optics and Optoelectronics, ed. K.T.V. Gratten (Institute of Physics Publishing 1996)
  8. J. M. Huntly, G. H. Kaufmann, D. Kerr, �??Phase-shifted dynamic speckle pattern interferometry at 1kHz,�?? Appl. Opt. 38, 6556-6563 (1999).
    [CrossRef]
  9. T. E. Carlsson, A. Wei, �??Phase Evaluation of Speckle Patterns During Continuous Deformation by use of Phase-Shifting Speckle Interferometry,�?? Appl. Opt. 39, 2628-2637 (2000).
    [CrossRef]
  10. C. Joenathan, B. Franze, P. Haible, H.J. Tiziani, �??Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement,�?? J. Mod. Opt. 44, 1975-1984 (1998).
    [CrossRef]
  11. C. Joenathan., P. Haible, H. Tiziani, �??Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera,�?? Appl. Opt. 38, 1169-1178 (1999).
    [CrossRef]
  12. D. Benitez, P. A. Gaydecki, A. Zaidi, A. P. Fitzpatrick, �??The use of Hilbert transform in ECG signal analysis,�?? Computers in Biology and Medicine 31, 399-406 (2001)
    [CrossRef] [PubMed]
  13. Yuuki Watanabe, Ichirou Yamaguchi, �??Digital Hilbert transformation for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope,�?? Appl. Opt. 41, 4497-4502 (2002)
    [CrossRef] [PubMed]
  14. V. A. Grechikhin, B.S. Rinkevichius, �??Hilbert transform for processing of laser Doppler vibrometer signals,�?? Opt. Laser Eng. 30, 151-161 (1998).
    [CrossRef]
  15. Yanghua Zhao, Zhongping Chen, Christopher Saxer, Shaohua Xiang, Johannes F. de Boer, J. Stuart Nelson, �??Phase resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity,�?? Opt. Lett. 25, 14-16 (2000)
    [CrossRef]
  16. Stefan L. Hahn, Hilbert Transforms in Signal Processing (Artech House: Boston, 1996)
  17. G. Cloude, Speckle interferometry made simple and cheap, Proc. Int. Conf. Theoretical, Experimental and Computational Mechanics 2000, 796.
  18. Ronald N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Companies, Inc., 2000)
  19. Max Born, Emil Wolf, Principle of Optics: Electromagnetic theory of propagation, Interference and Diffraction of light (Cambridge University Press, Edinburg, 1999: 7th extended edition)
  20. E.C. Titchmarsh, Introduction to the theory of Fourier integrals (Chelsea Publishing Company, New York, 1986)
  21. Sanjit K. Mitra, Digital Signal Processing: A computer based approach (McGraw-Hill Companies, Inc., 2002)
  22. The Math Works, MATLAB Signal Processing Toolbox: User�??s guide (December 1996), <a href="http://www.mathworks.com">www.mathworks.com</a>
  23. Dennis C. Ghiglia, Mark D Pritt, Two-Dimensional Phase Unwrapping (John Wiley and Sons, Inc., New York, 1998)

Appl. Opt. (5)

Computers in Biology and Medicine (1)

D. Benitez, P. A. Gaydecki, A. Zaidi, A. P. Fitzpatrick, �??The use of Hilbert transform in ECG signal analysis,�?? Computers in Biology and Medicine 31, 399-406 (2001)
[CrossRef] [PubMed]

J. Mod. Opt. (1)

C. Joenathan, B. Franze, P. Haible, H.J. Tiziani, �??Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement,�?? J. Mod. Opt. 44, 1975-1984 (1998).
[CrossRef]

Opt. Commun. (1)

V. Madjarova, S. Toyooka, R. Widiastuti, H. Kadono, �??Dynamic ESPI with subtraction-addition method for obtaining the phase,�?? Opt. Commun. 212, 35 (2002)
[CrossRef]

Opt. Laser Eng. (1)

V. A. Grechikhin, B.S. Rinkevichius, �??Hilbert transform for processing of laser Doppler vibrometer signals,�?? Opt. Laser Eng. 30, 151-161 (1998).
[CrossRef]

Opt. Lett. (1)

Yanghua Zhao, Zhongping Chen, Christopher Saxer, Shaohua Xiang, Johannes F. de Boer, J. Stuart Nelson, �??Phase resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity,�?? Opt. Lett. 25, 14-16 (2000)
[CrossRef]

Other (13)

Stefan L. Hahn, Hilbert Transforms in Signal Processing (Artech House: Boston, 1996)

G. Cloude, Speckle interferometry made simple and cheap, Proc. Int. Conf. Theoretical, Experimental and Computational Mechanics 2000, 796.

Ronald N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Companies, Inc., 2000)

Max Born, Emil Wolf, Principle of Optics: Electromagnetic theory of propagation, Interference and Diffraction of light (Cambridge University Press, Edinburg, 1999: 7th extended edition)

E.C. Titchmarsh, Introduction to the theory of Fourier integrals (Chelsea Publishing Company, New York, 1986)

Sanjit K. Mitra, Digital Signal Processing: A computer based approach (McGraw-Hill Companies, Inc., 2002)

The Math Works, MATLAB Signal Processing Toolbox: User�??s guide (December 1996), <a href="http://www.mathworks.com">www.mathworks.com</a>

Dennis C. Ghiglia, Mark D Pritt, Two-Dimensional Phase Unwrapping (John Wiley and Sons, Inc., New York, 1998)

X. Colonna de Lega, �??Continuous deformation measurement using dynamic phase shifting and wavelet transforms,�?? Applied Optics and Optoelectronics, ed. K.T.V. Gratten (Institute of Physics Publishing 1996)

P. K. Rastogi (Ed.), Photomechanics (Springer-Verlag, Berlin, 1999).

P.K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (John and Wiley and Sons Ltd., Chichester, 2001).

D. W. Robinson, C. R. Raed (Ed.), Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, Bristol, 1993).

Wolfgang Osten, �??Digital Processing and Evaluation of Fringe Patterns in Optical Metrology and Non-Destructive Testing,�?? D-28359 (Bremer Institut fur Angenwandte Strahltechnik, Bremen, 1998).

Supplementary Material (1)

» Media 1: AVI (2475 KB)     

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 (6)

Fig. 1.
Fig. 1.

Temporal history of the interference signal at single point

Fig. 2.
Fig. 2.

Out-of plane sensitive optical set-up for dynamic deformation simulations. L1, L2 and L3 - lenses, α-observation angle

Fig. 3.
Fig. 3.

Schematic of the front of the objects used in the experiments

Fig. 4.
Fig. 4.

Experiments of the plastic plate with the cutting in the middle of the specimen

Fig. 5
Fig. 5

(a) Spatio-temporal distribution obtained from the experiment with two directional deformation, (b) (2.5 MB) Movie of the temporal distribution of the two-dimensional deformation field

Fig. 6
Fig. 6

Cross-sections of the deformation at different points in space

Equations (5)

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

I ( x , y , t i ) = I 0 ( x , y , t i ) + I m ( x , y , t i ) cos { ϕ ( x , y , t i ) } , i = 1 , 2 , 3 , ,
v ( t ) = H i { u ( t ) } = 1 π + u ( t ) t t d t .
H i { u ( t ) } = 1 π t u ( t ) .
ϕ ( t ) = tan 1 ( H i { f ( ϕ ( t ) ) } f ( ϕ ( t ) ) ) .
Δ φ ( x , y , t i ) = { θ ( x , y , t i ) + φ ( x , y , t i ) } { θ ( x , y , t p ) + φ ( x , y , t p ) } ,

Metrics