Abstract

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].

© 2011 Optical Society of America

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References

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  1. D. Malacara and M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, Inc, 1998).
  2. M. Servin, J. C. Estrada, and J. A. Quiroga, Opt. Express 17, 21867 (2009).
    [PubMed]
  3. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72156 (1982).
  4. T. M. Kreis and W. P. O. Jueptner, Proc. SPIE 1553, 263(1992).
  5. J. Vargas, J. A. Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, Opt. Express 19, 638 (2011).
    [PubMed]
  6. B. K. P. Horn and B. G. Schunck, Artif. Intell. 17, 185 (1981).
  7. K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A 18, 1862 (2001).
  8. J. A. Quiroga and M. Servín, Opt. Commun. 224, 221 (2003).
  9. Z. Y. Wang and B. T. Han, Opt. Lett. 29, 1671 (2004).
    [PubMed]
  10. http://goo.gl/Snnz7.

2011 (1)

2009 (1)

2004 (1)

2003 (1)

J. A. Quiroga and M. Servín, Opt. Commun. 224, 221 (2003).

2001 (1)

1992 (1)

T. M. Kreis and W. P. O. Jueptner, Proc. SPIE 1553, 263(1992).

1982 (1)

1981 (1)

B. K. P. Horn and B. G. Schunck, Artif. Intell. 17, 185 (1981).

Belenguer, T.

Bone, D. J.

Estrada, J. C.

Han, B. T.

Horn, B. K. P.

B. K. P. Horn and B. G. Schunck, Artif. Intell. 17, 185 (1981).

Ina, H.

Jueptner, W. P. O.

T. M. Kreis and W. P. O. Jueptner, Proc. SPIE 1553, 263(1992).

Kobayashi, S.

Kreis, T. M.

T. M. Kreis and W. P. O. Jueptner, Proc. SPIE 1553, 263(1992).

Larkin, K. G.

Malacara, D.

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

Malacara, Z.

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

Oldfield, M. A.

Quiroga, J. A.

Schunck, B. G.

B. K. P. Horn and B. G. Schunck, Artif. Intell. 17, 185 (1981).

Servin, M.

Servín, M.

J. Vargas, J. A. Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, Opt. Express 19, 638 (2011).
[PubMed]

J. A. Quiroga and M. Servín, Opt. Commun. 224, 221 (2003).

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

Takeda, M.

Vargas, J.

Wang, Z. Y.

Artif. Intell. (1)

B. K. P. Horn and B. G. Schunck, Artif. Intell. 17, 185 (1981).

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

J. A. Quiroga and M. Servín, Opt. Commun. 224, 221 (2003).

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

T. M. Kreis and W. P. O. Jueptner, Proc. SPIE 1553, 263(1992).

Other (2)

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

http://goo.gl/Snnz7.

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Figures (6)

Fig. 1
Fig. 1

Two fringe patterns used in the first simulation.

Fig. 2
Fig. 2

Theoretical phase map of the simulated fringe patterns.

Fig. 3
Fig. 3

Reconstructed wrapped phases by the proposed OF (a) by the Kreis, (b) by the self-tuning, and (c) methods.

Fig. 4
Fig. 4

Obtained rms errors by the proposed OF, Kreis, and self-tuning method for different temporal frequencies.

Fig. 5
Fig. 5

Two real phase-shifted interferograms.

Fig. 6
Fig. 6

Reconstructed wrapped phases by the proposed OF (a) by the Kreis and (b) by the least-squares method using nine interferograms (reference phase).

Equations (10)

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I ( x + Δ x , y + Δ y , t + Δ t ) I ( x , y , t ) + I x Δ x + I y Δ y + I t Δ t ,
I x u + I y v + I t = 0 ,
E 2 = ( I x u + I y v + I t ) 2 + λ ( u x 2 + u y 2 + v x 2 + v y 2 ) ,
u k + 1 = u ¯ k I x [ I x u ¯ k + I y v ¯ k + I t ] / ( λ 2 + I x 2 + I y 2 ) , v k + 1 = v ¯ k I y [ I x u ¯ k + I y v ¯ k + I t ] / ( λ 2 + I x 2 + I y 2 ) ,
η = arctan ( v u ) .
I t = a + b cos ( Φ + ω 0 t ) , t = 0 , 1 ,
SPT { I ˜ t } = i exp ( i η ) b sin ( Φ + ω 0 t ) , t = 0 , 1 ,
SPT { · } = FT 1 { ( ω x + i ω y ω x 2 + ω y 2 ) FT { · } } ,
b sin ( Φ + ω 0 t ) = i exp ( i η ) SPT { I ˜ t } t = 0 , 1 ,
Φ = arctan ( i exp ( i η ) SPT { I ˜ t } I ˜ t ) t = 0 , 1.

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