Abstract

Fast frequency-guided sequential demodulation (FFSD) for demodulating a single closed-fringe pattern is proposed as an improvement of frequency-guided sequential demodulation (FSD). Instead of using optimization to estimate the local frequencies for determining the sign of the phase, the FFSD estimates the local frequencies by directly calculating the gradient of the obtained phase with an undetermined sign. This improvement considerably reduces the computational complexity of the FSD and leads to a faster and simpler method. Simulated and experimental fringe patterns are used to test the proposed method and show that the demodulation speed of FFSD is about 150 times faster than that of the FSD, while the robustness and accuracy remain almost the same.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (1)

2008 (1)

L. T. H. Nam and Q. Kemao, Proc. SPIE 7155, 71550T(2008).
[CrossRef]

2007 (2)

2005 (1)

2004 (1)

2003 (1)

1987 (1)

M. Kass and A. Witkin, Comput. Vis. Graph. Image Process. 37, 362 (1987).
[CrossRef]

De la Rosa, I.

Kass, M.

M. Kass and A. Witkin, Comput. Vis. Graph. Image Process. 37, 362 (1987).
[CrossRef]

Kemao, Q.

H. Wang and Q. Kemao, Opt. Express 17, 15118 (2009).
[CrossRef] [PubMed]

L. T. H. Nam and Q. Kemao, Proc. SPIE 7155, 71550T(2008).
[CrossRef]

Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Q. Kemao and S. H. Soon, Opt. Lett. 32, 127 (2007).
[CrossRef]

H. Wang, K. Li, and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching,” (submitted to Opt. Express).

Li, K.

H. Wang, K. Li, and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching,” (submitted to Opt. Express).

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Marroquin, J. L.

Miramontes, G.

Nam, L. T. H.

L. T. H. Nam and Q. Kemao, Proc. SPIE 7155, 71550T(2008).
[CrossRef]

Quiroga, J. A.

Servin, M.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Soon, S. H.

Villa, J.

Wang, H.

H. Wang and Q. Kemao, Opt. Express 17, 15118 (2009).
[CrossRef] [PubMed]

H. Wang, K. Li, and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching,” (submitted to Opt. Express).

Witkin, A.

M. Kass and A. Witkin, Comput. Vis. Graph. Image Process. 37, 362 (1987).
[CrossRef]

Comput. Vis. Graph. Image Process. (1)

M. Kass and A. Witkin, Comput. Vis. Graph. Image Process. 37, 362 (1987).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Express (1)

Opt. Lasers Eng. (1)

Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

L. T. H. Nam and Q. Kemao, Proc. SPIE 7155, 71550T(2008).
[CrossRef]

Other (2)

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

H. Wang, K. Li, and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching,” (submitted to Opt. Express).

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Figures (2)

Fig. 1
Fig. 1

Demodulation of a simulated fringe pattern: (a) noisy simulated fringe pattern, (b) normalized fringe pattern, (c) phase with undetermined sign, (d) angle distribution of the phase gradient φ 0 ( x , y ) , (e) angle distribution of the smoothed phase gradient φ ˜ 0 ( x , y ) , (f) smoothed frequency, (g) angle distribution of the recovered phase gradient φ ( x , y ) , (h) phase with determined sign, (i) refined phase.

Fig. 2
Fig. 2

Demodulation of an experimental fringe pattern from speckle shearography: (a) original fringe pattern, (b) normalized fringe pattern, (c) smoothed frequency, (d) angle distribution of the recovered phase gradient φ ( x , y ) , (e) phase with determined sign, (f) refined phase.

Tables (1)

Tables Icon

Table 1 Demodulation Results of the Simulated Fringe Pattern

Equations (11)

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f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ] ,
f ( x , y ) cos [ φ ( x , y ) ] .
φ 0 ( x , y ) = arccos [ f ( x , y ) ] ,
U ( x , y ) = ( ε , η ) N x , y { f ( ε , η ) cos [ φ ( x , y ; ε , η ) ] } 2 ,
φ ( x , y ; ε , η ) = φ 0 ( x , y ) + ω x ( x , y ) ( ε x ) + ω y ( x , y ) ( η y ) .
f ( x , y ) · φ ( x , y ) = sin [ φ ( x , y ) ] | φ ( x , y ) | 2 ,
sign [ φ ( x , y ) ] = sign [ f ( x , y ) · φ ( x , y ) ] ,
φ 0 x ( x , y ) + j φ 0 y ( x , y ) = ω ( x , y ) e j θ ( x , y ) ,
ω ˜ 2 ( x , y ) e j 2 θ ˜ ( x , y ) = 1 N ( ε , η ) N x , y ω 2 ( ε , η ) e j 2 θ ( ε , η ) ,
φ ˜ 0 ( x , y ) = { ω ˜ ( x , y ) cos [ θ ˜ ( x , y ) ] , ω ˜ ( x , y ) sin [ θ ˜ ( x , y ) ] } .
φ ( x a , y a ) = { φ ˜ 0 ( x a , y a ) if φ ( x s , y s ) · φ ˜ 0 ( x a , y a ) 0 φ ˜ 0 ( x a , y a ) if φ ( x s , y s ) · φ ˜ 0 ( x a , y a ) < 0 ,

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