Abstract

Fringe patterns produced by various optical interferometric techniques encode information such as shape, deformation, and refractive index. Denoising and demodulation are two important procedures to retrieve information from a single closed fringe pattern. Various existing denoising and demodulation techniques require fringe direction/orientation during the processing. Fringe orientation is often easier to obtain but fringe direction is needed in some demodulation techniques. A quality-guided orientation unwrapping scheme is proposed to estimate direction from orientation. Two techniques, one based on windowed Fourier ridges and the other based on fringe gradient, are proposed for the quality-guided orientation unwrapping scheme. The direction qualities are compared for both simulated and experimental fringe patterns. Their application to demodulation technique is also given.

© 2012 Optical Society of America

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References

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2011 (1)

2010 (1)

2009 (4)

2008 (3)

2007 (4)

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317(2007).
[CrossRef]

Q. Kemao and S. H. Soon, “Sequential demodulation of a single fringe pattern guided by local frequencies,” Opt. Lett. 32, 127–129 (2007).
[CrossRef]

2006 (1)

J. A. Quiroga, D. Crespo, J. A. G. Pedrero, and J. C. Martinez-Antón, “Recent advances in automatic demodulation of single fringe patterns,” FRINGE 2005 1, 90–97 (2006).

2005 (1)

2004 (1)

2003 (1)

2002 (2)

2001 (2)

1999 (2)

1998 (1)

Amold, J. F.

Asundi, A.

Baird, J. P.

Bone, D. J.

Chang, Y.

Chee, O. C.

Crespo, D.

J. A. Quiroga, D. Crespo, J. A. G. Pedrero, and J. C. Martinez-Antón, “Recent advances in automatic demodulation of single fringe patterns,” FRINGE 2005 1, 90–97 (2006).

Cuevas, F.

Cuevas, F. J.

Cui, X.

D’ Acquisto, L.

A. M. Siddiolo and L. D’ Acquisto, “A direction/orientation-based method for shape measurement by shadow Moire,” IEEE Trans. Instrum. Meas. 57, 843–849 (2008).
[CrossRef]

Dalmau-Cedeño, O. S.

Davies, E.

E. Davies, Machine Vision: Theory, Algorithms and Practicalities (Academic, 1990).

Fu, S.

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Gao, T.

Gao, W.

Ghiglia, D.

D. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

Han, L.

Huyen, N. T. H.

Jahne, B.

B. Jahne, Practical Handbook on Image Processing for Scientific Applications (CRC, 1997).

Kemao, Q.

Larkin, K. G.

Legarda-Saenz, R.

Lin, F.

Lindeberg, T.

T. Lindeberg, Scale_Space Theory in Computer Vision (Kluwer, 1994).

Liu, X.

Loi, H. S.

Marroquin, J. L.

Martinez-Antón, J. C.

J. A. Quiroga, D. Crespo, J. A. G. Pedrero, and J. C. Martinez-Antón, “Recent advances in automatic demodulation of single fringe patterns,” FRINGE 2005 1, 90–97 (2006).

Oldfield, M. A.

Pedrero, J. A. G.

J. A. Quiroga, D. Crespo, J. A. G. Pedrero, and J. C. Martinez-Antón, “Recent advances in automatic demodulation of single fringe patterns,” FRINGE 2005 1, 90–97 (2006).

Pritt, M. D.

D. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

Qiu, Z.

Qu, W.

Quiroga, J. A.

Ren, H.

Rivera, M.

Rodriquez-Vera, R.

Rosa, I.

Servin, M.

Siddiolo, A. M.

A. M. Siddiolo and L. D’ Acquisto, “A direction/orientation-based method for shape measurement by shadow Moire,” IEEE Trans. Instrum. Meas. 57, 843–849 (2008).
[CrossRef]

Soon, S. H.

Sun, X.

Tang, C.

Villa, J.

Wang, H.

Wang, L.

Wang, X.

Wang, Z.

Weickert, J.

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

Wu, J.

Yan, S.

Yang, X.

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66 (2007).
[CrossRef]

Yu, Q.

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef]

Yu, Y.

Zhou, D.

Zhou, X.

Appl. Opt. (5)

FRINGE 2005 (1)

J. A. Quiroga, D. Crespo, J. A. G. Pedrero, and J. C. Martinez-Antón, “Recent advances in automatic demodulation of single fringe patterns,” FRINGE 2005 1, 90–97 (2006).

IEEE Trans. Instrum. Meas. (1)

A. M. Siddiolo and L. D’ Acquisto, “A direction/orientation-based method for shape measurement by shadow Moire,” IEEE Trans. Instrum. Meas. 57, 843–849 (2008).
[CrossRef]

Int. J. Comput. Vis. (1)

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (2)

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317(2007).
[CrossRef]

Opt. Lett. (4)

Other (5)

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

B. Jahne, Practical Handbook on Image Processing for Scientific Applications (CRC, 1997).

D. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, 1998).

E. Davies, Machine Vision: Theory, Algorithms and Practicalities (Academic, 1990).

T. Lindeberg, Scale_Space Theory in Computer Vision (Kluwer, 1994).

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Figures (10)

Fig. 1.
Fig. 1.

Orientation and direction.

Fig. 2.
Fig. 2.

Simulated fringe pattern. (a) Noiseless fringe pattern; (b) wrapped phase; (c) theoretical direction; (d) fringe pattern with speckle noise.

Fig. 3.
Fig. 3.

WFR-based orientation unwrapping of Fig. 2(d). (a) Orientation θ WFR ; (b) density D WFR ; (c) direction β WFR .

Fig. 4.
Fig. 4.

Gradient-based orientation unwrapping of Fig. 2(d). (a) Orientation θ GRA ; (b) density D GRA ; (c) direction β GRA .

Fig. 5.
Fig. 5.

Direction error plots. (a) Error plots of direction results in low frequency regions; (b) error plots of direction results in high frequency regions.

Fig. 6.
Fig. 6.

Demodulation results of Fig. 2(d). (a) Phase obtained using β T ; (b) phase obtained using β WFR ; (c) phase obtained using β GRA .

Fig. 7.
Fig. 7.

Filtered results of Fig. 6. (a) Filtered phase obtained using β T ; (b) filtered phase obtained using β WFR ; (c) filtered phase obtained using β GRA .

Fig. 8.
Fig. 8.

Demodulation error plots. (a) Error plots of demodulation results in low density regions; (b) error plots of demodulation results in high density regions.

Fig. 9.
Fig. 9.

Direction and phase obtained with WFR-based orientation unwrapping. (a) An experimental fringe pattern (image courtesy: Weijuan Qu, Ngee Ann Polytechnic); (b) orientation θ WFR ; (c) density D WFR ; (d) direction β WFR ; (e) phase obtained using β WFR ; (f) filtered phase of (e).

Fig. 10.
Fig. 10.

Direction and phase obtained with gradient-based orientation unwrapping. (a) Experimental fringe pattern; (b) orientation θ GRA ; (c) density D GRA ; (d) direction β GRA ; (e) phase obtained using β GRA ; (f) filtered phase of (e).

Equations (16)

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f ( x , y ) = b ( x , y ) cos [ φ ( x , y ) ] ,
[ cos β ( x , y ) , sin β ( x , y ) ] φ ( x , y ) = 0 ,
β ( x , y ) = arctan 2 [ φ x ( x , y ) , φ y ( x , y ) ] ,
f ( x , y ) = [ f x ( x , y ) , f y ( x , y ) ] T = b ( x , y ) sin [ φ ( x , y ) ] [ φ x ( x , y ) , φ y ( x , y ) ] T ,
θ ( x , y ) = arctan [ f x ( x , y ) / f y ( x , y ) ] .
θ ( x , y ) = { β ( x , y ) π / 2 < β ( x , y ) π / 2 M 2 π [ β ( x , y ) + π ] else ,
β ( x , y ) = { θ ( x , y ) cos [ θ ( x , y ) ] cos [ θ ( x 0 , y 0 ) ] + sin [ θ ( x , y ) ] sin [ θ ( x 0 , y 0 ) ] 0 M 2 π [ θ ( x , y ) + π ] else .
S f ( u , v ; ξ , η ) = f ( x , y ) g u , v ; ξ , η * ( x , y ) d x d y ,
g u , v ; ξ , η ( x , y ) = g ( x u , y v ) exp ( j ξ x + j η y ) ;
[ ω x ( u , v ) , ω y ( u , v ) ] = arg max ξ , η | S f ( u , v ; ξ , η ) | ,
θ WFR ( x , y ) = arctan [ ω x ( x , y ) / ω y ( x , y ) ] .
D WFR ( x , y ) = ω TLF ( x , y ) = ω x 2 ( x , y ) + ω y 2 ( x , y ) .
θ GRA ( x , y ) = 1 2 arctan 2 { u = x ε x + ε v = y ε y + ε 2 f x σ ( u , v ) f y σ ( u , v ) , u = x ε x + ε v = y ε y + ε [ f y σ 2 ( u , v ) f x σ 2 ( u , v ) ] } ,
| f ( x , y ) | = b ( x , y ) | sin [ φ ( x , y ) ] | ω TLF ( x , y ) ,
D GRA = K ρ | f σ ( x , y ) | ,
E β = y = 1 N x = 1 M | 2 sin [ β ( x , y ) β T ( x , y ) 2 ] | M × N ,

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