Abstract

Phase demodulation from a single fringe pattern is a challenging task but of interest. A frequency-guided regularized phase tracker and a frequency-guided sequential demodulation method with Levenberg-Marquardt optimization are proposed to demodulate a single fringe pattern. Demodulation path guided by the local frequency from the highest to the lowest is applied in both methods. Since critical points have low local frequency values, they are processed last so that the spurious sign problem caused by these points is avoided. These two methods can be considered as alternatives to the effective fringe follower regularized phase tracker. Demodulation results from one computer-simulated and two experimental fringe patterns using the proposed methods will be demonstrated.

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References

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  1. D. W. Robinson, and G. T. Reid, eds., in Interferogram analysis: digital fringe pattern measurement techniques, (Bristol, England: Institute of Physics1993).
  2. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997).
    [CrossRef] [PubMed]
  3. 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]
  4. J. A. Quiroga and J. A. Gomez-Pedrero, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
    [CrossRef]
  5. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
    [CrossRef]
  6. J. Weickert, “Coherence-Enhancing Diffusion Filtering,” Int. J. Comput. Vis. 31(2/3), 111–127 (1999).
    [CrossRef]
  7. H. Wang, Q. Kemao, W. Gao, F. Lin, and H. S. Seah, “Fringe pattern denoising using coherence-enhancing diffusion,” Opt. Lett. 34(8), 1141–1143 (2009).
    [CrossRef] [PubMed]
  8. J. L. Marroquin, M. Servin, and R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14(8), 1742–1753 (1997).
    [CrossRef]
  9. J. L. Marroquin, R. Rodriguez-Vera, and M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15(6), 1536–1544 (1998).
    [CrossRef]
  10. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2288 .
    [CrossRef] [PubMed]
  11. M. Rivera, “Robust phase demodulation of interferograms with open or closed fringes,” J. Opt. Soc. Am. A 22(6), 1170–1172 (2005).
    [CrossRef]
  12. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns: I. general background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
    [CrossRef]
  13. M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20(5), 925–934 (2003).
    [CrossRef]
  14. Q. Kemao and S. Hock Soon, “Sequential demodulation of a single fringe pattern guided by local frequencies,” Opt. Lett. 32(2), 127–129 (2007).
    [CrossRef]
  15. O. Dalmau-Cedeño, M. Rivera, and R. Legarda-Saenz, “Fast phase recovery from a single close-fringe pattern,” J. Opt. Soc. Am. A 25(6), 1361–1370 (2008).
    [CrossRef]
  16. W. H. Press, S. A. Teukolsky, and W. T. Vetterling, B. P. Flannery, in Numerical Recipes in C: The Art of Scientific Computing (Second Edition), (Cambridge University Press, 2002), pp. 683–685.
  17. D. C. Ghiglia, and M. D. Pritt, in Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software, (John Wiley & Sons, Inc, 1998).

2009 (1)

2008 (1)

2007 (3)

2005 (1)

2003 (1)

2001 (3)

1999 (1)

J. Weickert, “Coherence-Enhancing Diffusion Filtering,” Int. J. Comput. Vis. 31(2/3), 111–127 (1999).
[CrossRef]

1998 (1)

1997 (2)

Bone, D. J.

Cuevas, F. J.

Dalmau-Cedeño, O.

Estrada, J. C.

Gao, W.

Gomez-Pedrero, J. A.

J. A. Quiroga and J. A. Gomez-Pedrero, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[CrossRef]

Hock Soon, S.

Kemao, Q.

Larkin, K. G.

Legarda-Saenz, R.

Lin, F.

Marroquin, J. L.

Marroquín, J. L.

Oldfield, M. A.

Quiroga, J. A.

Rivera, M.

Rodriguez-Vera, R.

Seah, H. S.

Servin, M.

Wang, H.

Weickert, J.

J. Weickert, “Coherence-Enhancing Diffusion Filtering,” Int. J. Comput. Vis. 31(2/3), 111–127 (1999).
[CrossRef]

Appl. Opt. (1)

Int. J. Comput. Vis. (1)

J. Weickert, “Coherence-Enhancing Diffusion Filtering,” Int. J. Comput. Vis. 31(2/3), 111–127 (1999).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

J. A. Quiroga and J. A. Gomez-Pedrero, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

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. (2)

Other (3)

D. W. Robinson, and G. T. Reid, eds., in Interferogram analysis: digital fringe pattern measurement techniques, (Bristol, England: Institute of Physics1993).

W. H. Press, S. A. Teukolsky, and W. T. Vetterling, B. P. Flannery, in Numerical Recipes in C: The Art of Scientific Computing (Second Edition), (Cambridge University Press, 2002), pp. 683–685.

D. C. Ghiglia, and M. D. Pritt, in Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software, (John Wiley & Sons, Inc, 1998).

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Figures (4)

Fig. 1
Fig. 1

Computer-simulated fringe pattern demodulated by FFRPT. (a) Noisy Computer-simulated fringe pattern. (b) True phase of the fringe pattern. (c) Normalized fringe pattern to be demodulated. (d) Binarized fringe pattern for fringe follower. (e) Rewrapped phase result demodulated following (d). (f) Rewrapped phase result demodulated following inverse of (d).

Fig. 2
Fig. 2

Computer-simulated fringe pattern demodulated by FGRPT and FSD-LM. (a) Frequency estimated by FGRPT from fringe pattern in Fig. 1(a). (b) Snapshot 1 of demodulation guided by the frequency in (a). (c) Snapshot 2 of demodulation guided by the frequency in (a). (d) Rewrapped phase result demodulated by FGRPT. (e) Frequency estimated by FSD-LM from fringe pattern in Fig. 1(a). (f) Rewrapped phase result demodulated by FSD-LM.

Fig. 3
Fig. 3

Experimental fringe pattern demodulated by FGRPT and FSD-LM. (a) Noisy fringe pattern from speckle shearography. (b) Normalized fringe pattern to be demodulated. (c) Frequency estimated by FGRPT. (d) Rewrapped phase result demodulated by FGRPT. (e) Cosine value of (d). (f) Frequency estimated by FSD-LM. (g) Rewrapped phase result demodulated by FSD-LM. (h) Cosine value of (g).

Fig. 4
Fig. 4

Experimental fringe pattern demodulated by FGRPT and FSD-LM. (a) Noisy fringe pattern from electronic speckle pattern interferometry. (b) Normalized fringe pattern to be demodulated. (c) Frequency estimated by FGRPT. (d) Rewrapped phase result demodulated by FGRPT. (e) Cosine value of (d). (f) Frequency estimated by FSD-LM. (g) Rewrapped phase result demodulated by FSD-LM. (h) Cosine value of (g).

Tables (1)

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Table 1 Demodulation results

Equations (8)

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f(x,y)=a(x,y)+b(x,y)cos[φ(x,y)],
f(x,y)cos[φ(x,y)].
U(x,y)=(ε,η)Nx,y({f(ε,η)cos[φe(x,y,ε,η)]}2+λ[φ0(ε,η)φe(x,y,ε,η)]2m(ε,η)),
φe(x,y,ε,η)=φ0(x,y)+ωx(x,y)(εx)+ωy(x,y)(ηy),
φ0(x,y)=arccos[f(x,y)],
U(x,y)=(ε,η)Nx,y{f(ε,η)cos[φ0(x,y)+ωx(x,y)(εx)+ωy(x,y)(ηy)]}2,
ω(x,y)=ωx2(x,y)+ωy2(x,y).
φinitial(x,y)=(ε,η)N'x,y(φ(ε,η)U2(ε,η)+1m(ε,η))/(ε,η)N'x,y(m(ε,η)U2(ε,η)+1),

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