Abstract

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.

© 2003 Optical Society of America

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References

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  1. D. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994).
    [CrossRef]
  2. D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).
  3. K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
    [CrossRef]
  4. L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
    [CrossRef]
  5. J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
    [CrossRef]
  6. S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998).
  7. V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
    [CrossRef]
  8. K. Qian, H. S. Seah, and A. Asundi, in International Conference on Advanced Technology in Experimental Mechanics (Materials and Mechanics Division, Japan Society of Mechanical Engineers, Nagoya, Japan, 2003).

2003 (1)

K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
[CrossRef]

2001 (1)

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

1998 (1)

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

1997 (1)

L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
[CrossRef]

Asundi, A.

K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
[CrossRef]

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

K. Qian, H. S. Seah, and A. Asundi, in International Conference on Advanced Technology in Experimental Mechanics (Materials and Mechanics Division, Japan Society of Mechanical Engineers, Nagoya, Japan, 2003).

Barnes, T. H.

L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
[CrossRef]

Fang, J.

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Han, B.

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994).
[CrossRef]

Ifju, P.

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994).
[CrossRef]

Li, H. J.

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998).

Murukeshan, V. M.

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Post, D.

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994).
[CrossRef]

Qian, K.

K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
[CrossRef]

K. Qian, H. S. Seah, and A. Asundi, in International Conference on Advanced Technology in Experimental Mechanics (Materials and Mechanics Division, Japan Society of Mechanical Engineers, Nagoya, Japan, 2003).

Reid, G. T.

D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

Robinson, D. W.

D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

Seah, H. S.

K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
[CrossRef]

K. Qian, H. S. Seah, and A. Asundi, in International Conference on Advanced Technology in Experimental Mechanics (Materials and Mechanics Division, Japan Society of Mechanical Engineers, Nagoya, Japan, 2003).

Seng, O. L.

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Tan, S. M.

L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
[CrossRef]

Watkins, L. R.

L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
[CrossRef]

Xiong, C. Y.

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Zhang, Z. L.

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Electron. Lett. (1)

L. R. Watkins, S. M. Tan, and T. H. Barnes, Electron. Lett. 33, 2116 (1997).
[CrossRef]

J. Mod. Opt. (1)

J. Fang, C. Y. Xiong, H. J. Li, and Z. L. Zhang, J. Mod. Opt. 48, 507 (2001).
[CrossRef]

Opt. Eng. (1)

K. Qian, H. S. Seah, and A. Asundi, Opt. Eng. 42, 1721 (2003).
[CrossRef]

Opt. Laser Technol. (1)

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Other (4)

K. Qian, H. S. Seah, and A. Asundi, in International Conference on Advanced Technology in Experimental Mechanics (Materials and Mechanics Division, Japan Society of Mechanical Engineers, Nagoya, Japan, 2003).

S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998).

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994).
[CrossRef]

D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

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Figures (3)

Fig. 1
Fig. 1

Four phase-shifted speckle fringe patterns with phase shifts of 0, π/2, 3π/2, and π.

Fig. 2
Fig. 2

Phase derivatives by use of the phase shift and digital shear (24-pixel shear) technique (a) before smoothing the speckle patterns and (b) after smoothing the speckle patterns.

Fig. 3
Fig. 3

Phase derivative by use of the proposed PSWFR: (a) phase derivative and (b) contours that correspond to a 24-pixel shear.

Equations (13)

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ft=at+btcosφt,
Wfu,ξ=-+ftgt-uexp-jξtdt,
Wfu,ξ=Ia+Iφ+I-φ,
Ia=auexp-jξugˆξ,
Iφ=12buexpjφu-ξugˆξ-φu,
I-φ=12buexp-jφu+ξugˆξ+φu,
Wfu,ξIφ=12bugˆξ-φu.
fit=at+btcosφt+i-1π/2, i=1,2,3,4.
Wf1u,ξ-Wf3u,ξ=2Iφ+2I-φ,
Wf4u,ξ-Wf2u,ξ=2jIφ+2jI-φ,
Iφ=14Wf1u,ξ-Wf3u,ξ+jWf4u,ξ-jWf2u,ξ.
ft=14f1t-f3t+jf4t-jf2t=12btexpφt,
Wfu,ν,ξ,η=-+fx,ygx-ugy-ν×exp-jξxexp-jηydxdy,

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