Abstract

Novel approaches based on windowed Fourier transform for demodulation of fringe patterns were previously presented [Appl. Opt. 43, 2695–2702 (2004)], where extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single-carrier fringe pattern was the main focus. I show that the same methods can be applied to process a single closed-fringe pattern in either noise reduction or phase approximation, which adds to the versatility of the windowed Fourier-transform method for fringe pattern analysis.

© 2004 Optical Society of America

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References

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  1. K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef]
  2. M. Servin, J. L. Marroguin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997).
    [CrossRef] [PubMed]
  3. 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]
  4. G. H. Kaufmann, G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
    [CrossRef]
  5. Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
    [CrossRef]
  6. M. Servin, J. L. Marroguin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
    [CrossRef]
  7. M. Servin, M. Kujawinska, “Modern fringe analysis in interferometry,” in Handbook of Optical Engineering, D. Malacara, B. J. Thompson, eds. (Marcel Dekker, New York, 2001).

2004 (1)

2003 (1)

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[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]

M. Servin, J. L. Marroguin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
[CrossRef]

1997 (1)

1996 (1)

G. H. Kaufmann, G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Cuevas, F. J.

Ding, X.

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Federico, A.

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]

Galizzi, G. E.

G. H. Kaufmann, G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Kaufmann, G. H.

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]

G. H. Kaufmann, G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Kujawinska, M.

M. Servin, M. Kujawinska, “Modern fringe analysis in interferometry,” in Handbook of Optical Engineering, D. Malacara, B. J. Thompson, eds. (Marcel Dekker, New York, 2001).

Liu, X.

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Marroguin, J. L.

Qian, K.

Qiu, Z.

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Servin, M.

Sun, X.

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Yu, Q.

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Eng. (3)

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]

G. H. Kaufmann, G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Q. Yu, X. Sun, X. Liu, X. Ding, Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Other (1)

M. Servin, M. Kujawinska, “Modern fringe analysis in interferometry,” in Handbook of Optical Engineering, D. Malacara, B. J. Thompson, eds. (Marcel Dekker, New York, 2001).

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Figures (2)

Fig. 1
Fig. 1

Filtering a real speckle fringe pattern by WFF: (a) original pattern (courtesy of Chen Lujie, National University of Singapore); (b) filtered pattern; (c) combination of the upper half of (a) and the lower half of (b) for a comparison; (d) peaks (white lines) and valleys (black lines) of (b).

Fig. 2
Fig. 2

Phase approximation by WFR: (a) phase with sign ambiguity; (b) horizontal frequency by WFR; (c) phase without sign ambiguity; (d) combination of the upper half of Fig. 1(a) and the lower half of (c) for a comparison; (e) combination of the upper half of Fig. 1(a) and the cosine of the lower half of (c) for a comparison.

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