Abstract

We present a simple and fast regularized frequency-stabilizing method for single open- or closed-fringe interferogram demodulation. The proposed method recovers the phase maps of interferograms by establishing a cost function, according to prior knowledge. Because only the phase field to be estimated is employed in the cost function, the optimization process is fast. Moreover, the recovered phase is continuous, and no further phase unwrapping is necessary. Computer simulation and experimental results have demonstrated both the rapidity and the efficiency of the method.

© 2010 Optical Society of America

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References

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2001

1997

Cuevas, F.

Cuevas, F. J.

Estrada, J. C.

Gao, W.

Guerrero, J. A.

Hock Soon, S.

Kemao, Q.

Lin, F.

Liu, D.

Luo, Y.

Marroquin, J. L.

Quiroga, J. A.

Rivera, M.

Seah, H. S.

Servin, M.

Tian, C.

Wang, H.

Yang, Y.

Zhuo, Y.

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Figures (3)

Fig. 1
Fig. 1

Typical character of the cost functions U i , j and U i , j . The magnitude of the U i , j is computed using the logarithm base 10 function for the purpose of comparison.

Fig. 2
Fig. 2

Demodulation experiments: (a) and (e) simulated ( 128 × 128 ) and real ( 256 × 256 ) interferograms, (b) and (f) normalized intensities for (a) and (e), (c) and (g) recovered coarse phases, and (d) and (h) refined phases.

Fig. 3
Fig. 3

Demodulation of a real interferogram using the RFS and the RPT: (a) original interferogram, (b) normalized intensity, (c) recovered coarse phase by the RFS, (d) refined phase by the RFS (rewrapped), (e) refined phase by the RFS (continuous), and (f) finally retrieved phase by the RPT.

Tables (1)

Tables Icon

Table 1 Time Employed for Regularized Frequency-Stabilizing and Regularized Phase-Tracking Methods in Presented Experiments

Equations (8)

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I i , j = a i , j + b i , j cos ϕ i , j + n i , j ,
I i , j = cos ϕ i , j .
U i , j = ( I i , j cos ϕ i , j ) 2 .
U i , j ( ϕ i , j ) = ( ε , η ) N i , j { ( I ε , η cos ϕ i , j ) 2 + [ I ε , η cos ( ϕ i , j + α ) ] 2 } + Ω ε , η , i , j ,
Ω ε , η , i , j = β ( ε , η ) N Ω θ = { 0 , 45 , 90 , 135 } { [ ( ϕ i , j ρ ) ε , η θ + ( ϕ i , j ρ ) i , j θ + ] 2 M ε , η , i , j θ + + [ ( ϕ i , j ρ ) ε , η θ ( ϕ i , j ρ ) i , j θ ] 2 M ε , η , i , j θ } ,
( ϕ i , j ρ ) i , j 0 ± = ϕ i , j ϕ i ± 1 , j , ( ϕ i , j ρ ) i , j 45 ± = ϕ i , j ϕ i ± 1 , j ± 1 , ( ϕ i , j ρ ) i , j 90 ± = ϕ i , j ϕ i , j ± 1 , ( ϕ i , j ρ ) i , j 135 ± = ϕ i , j ϕ i 1 , j ± 1 ,
M ε , η , i , j 0 ± = m ε , η m ε ± 1 , η m i ± 1 , j , M ε , η , i , j 45 ± = m ε , η m ε ± 1 , η ± 1 m i ± 1 , j ± 1 , M ε , η , i , j 90 ± = m ε , η m ε , η ± 1 m i , j ± 1 , M ε , η , i , j 135 ± = m ε , η m ε 1 , η ± 1 m i 1 , j ± 1 ,
ϕ ^ i , j = argmin [ U i , j ( ϕ i , j ) ] .

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