Abstract

A new method that extracts phase directly from randomly phase-shifted interferograms is proposed. In this method, the background intensity and the modulation amplitude are determined by a temporal method and used as the system parameters and then the phase is extracted from one single interferogram by arc cosine function with range of (0, π). By partitioning the extracted phase distribution into watershed regions and determining the sign of phase in each region, the extracted phase is recovered to its principle phase with range of (–π, π). Numerical simulation and experiment are implemented to verify the effectiveness of this method. The method has applications in both static and dynamic phase measurement.

© 2010 OSA

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References

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    [CrossRef]

2010

2009

2008

2007

C. J. Stolz, “The National Ignition Facility: The world’s largest optical system,” Proc. SPIE 6834, 683402 (2007).
[CrossRef]

2005

2004

1991

K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991).
[CrossRef]

L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991).
[CrossRef]

1984

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Brock, N.

Cai, L. Z.

Cheng, X. C.

Dong, G. Y.

Gao, P.

Geist, E.

Han, B.

Hao, Q.

Harder, I.

Hayes, J.

Hu, Y.

Kim, S.-W.

Lindlein, N.

Mantel, K.

Meneses-Fabian, C.

Meng, X. F.

Millerd, J.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

North-Morris, M.

Novak, M.

Okada, K.

K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991).
[CrossRef]

Oliver, J.

Park, J.

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Sato, A.

K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991).
[CrossRef]

Schwider, J.

Shen, X. X.

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Soille, P.

L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991).
[CrossRef]

Stolz, C. J.

C. J. Stolz, “The National Ignition Facility: The world’s largest optical system,” Proc. SPIE 6834, 683402 (2007).
[CrossRef]

Su, X.

Sun, W. J.

Toto-Arellano, N.-I.

Tsujiuchi, J.

K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991).
[CrossRef]

Van Der Weide, D.

Vázquez-Castillo, J. F.

Vincent, L.

L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991).
[CrossRef]

Wang, Y. R.

Wang, Z.

Wyant, J.

Xu, X. F.

Yao, B.

Zhang, H.

Zhang, Q.

Zhang, S.

Zhu, Q.

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991).
[CrossRef]

Opt. Commun.

K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991).
[CrossRef]

Opt. Eng.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Opt. Express

Opt. Lett.

Proc. SPIE

C. J. Stolz, “The National Ignition Facility: The world’s largest optical system,” Proc. SPIE 6834, 683402 (2007).
[CrossRef]

Other

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometers, ” in Optical Shop Testing, D. Malacara, ed., John Wiley and Sons, 1992, pp. 501–598.

K. Creath, “Temporal phase measurement method,” in Interferogram Analysis, D.W. Robinson and G. T. Reid, eds. Institute of Physics, Bristol, UK, 1993, pp. 94–140.

Supplementary Material (4)

» Media 1: MOV (233 KB)     
» Media 2: MOV (847 KB)     
» Media 3: MOV (807 KB)     
» Media 4: MOV (413 KB)     

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Figures (3)

Fig. 1
Fig. 1

The process of recovering the extracted phase to its principle phase. (a) The extracted phase by Eq. (4) with range of (0, π); (b) the watershed regions of (a), (c) the phase difference between two adjacent frames, and (d) the recovered principle phase of (a) with range of (–π, π)

Fig. 2
Fig. 2

Simulation results. (a) interferogram (Media 1), (b) the calculated phase by Eq. (4) with range of (0, π), (c) the watershed regions of (b), (d) the recovered phase with range of (0, 2π) (Media 2), (e) the unwrapped phase and (f) the residual phase error.

Fig. 3
Fig. 3

Experiment results. (a) interferogram (Media 3), (b) the principle phase of (a) by our method (Media 4), (c) the unwrapped phase of (b) after tilt subtraction, and (d) the principle phase of (a) by Wang’s iterative method.

Tables (2)

Tables Icon

Table 1 The relation between the residual phase error and the number of fringe patterns used. (The number of pixels is (200 × 200), ε = 0.2, and unit is rad)

Tables Icon

Table 2 The relation between the residual phase error and the number of pixels (M × M) and the preset small value of ε. (N is 40 and unit is rad)

Metrics