Abstract

In this work, we show a windowed phase-unwrapping technique that uses a first-order dynamic system and scans the phase following its iso-phase contours. In previous works, we have shown that low-pass first-order dynamic systems are very robust and useful in phase-unwrapping problems. However, it is well known that all phase-unwrapping methods have a minimum signal-to-noise ratio that they tolerate. This paper shows that scanning the phase within local windows and using a path following strategy, the first-order unwrapping method increases its tolerance to noise. In this way, using the improved approach, we can unwrap phase maps where the basic dynamic phase-unwrapping system fails. Tests and results are given, as well as the source code in order to show the performance of the proposed method.

© 2012 Optical Society of America

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References

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2012 (2)

J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: A review and comparison,” Opt. Lasers Eng. 50, 1026–1029 (2012).
[CrossRef]

M. A. Navarro, J. C. Estrada, M. Servin, J. A. Quiroga, and J. Vargas, “Fast two-dimensional simultaneous phase unwrapping and low-pass filtering,” Opt. Express 20, 2556–2561 (2012).
[CrossRef]

2011 (1)

2009 (1)

2007 (1)

1999 (1)

1998 (1)

1997 (1)

1996 (1)

1995 (3)

1994 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

1987 (2)

K. A. Stenson and W. R. Brohinsky, “Electro-optic holography system for vibration analysis and nondestructive testing,” Opt. Eng. 26, 1234–1239 (1987).

P. Hariharan, B. F. Oreb, and C. H. Freund, “Stroboscopic holographic interferometry: measurements of vector components of vibration,” Appl. Opt. 26, 3899–3903 (1987).
[CrossRef]

1983 (1)

1982 (2)

Brohinsky, W. R.

K. A. Stenson and W. R. Brohinsky, “Electro-optic holography system for vibration analysis and nondestructive testing,” Opt. Eng. 26, 1234–1239 (1987).

Buckland, J. R.

Cuevas, F. J.

Estrada, J. C.

Flynn, T. J.

Freund, C. H.

Ghiglia, D. C.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Hariharan, P.

Huntley, J. M.

Ina, H.

Itoh, K.

Kobayashi, S.

Macy, W. W.

Malacara, D.

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

Marroquin, J. L.

Marroquín, J. L.

Navarro, M. A.

Oreb, B. F.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping; Theory, Algorithms, and Software (Wiley-Interscience, 1998).

Quiroga, J. A.

Rivera, M.

Rodriguez-Vera, R.

Romero, L. A.

Servin, M.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

Stenson, K. A.

K. A. Stenson and W. R. Brohinsky, “Electro-optic holography system for vibration analysis and nondestructive testing,” Opt. Eng. 26, 1234–1239 (1987).

Strobel, B.

Takeda, M.

Tapia, M.

Turner, S. R. E.

Vargas, J.

J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: A review and comparison,” Opt. Lasers Eng. 50, 1026–1029 (2012).
[CrossRef]

M. A. Navarro, J. C. Estrada, M. Servin, J. A. Quiroga, and J. Vargas, “Fast two-dimensional simultaneous phase unwrapping and low-pass filtering,” Opt. Express 20, 2556–2561 (2012).
[CrossRef]

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Eng. (1)

K. A. Stenson and W. R. Brohinsky, “Electro-optic holography system for vibration analysis and nondestructive testing,” Opt. Eng. 26, 1234–1239 (1987).

Opt. Express (4)

Opt. Lasers Eng. (1)

J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: A review and comparison,” Opt. Lasers Eng. 50, 1026–1029 (2012).
[CrossRef]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Other (3)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping; Theory, Algorithms, and Software (Wiley-Interscience, 1998).

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

J. C. Estrada, “Phase unwrapping software,” http://goo.gl/RW2nQ .

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Figures (4)

Fig. 1.
Fig. 1.

Scanning the phase following its iso-phase contours. In (a) is the wrapped phase and in (b)–(h) are the snapshots of the scanning sequence applying the windowed phase-unwrapping algorithm. In (h) we see the global unwrapped phase as expected.

Fig. 2.
Fig. 2.

Two experimentally obtained wrapped phase maps. These are vibration modes obtained from a cadaveric chinchilla tympanic membrane using a digital holography technique. The phase maps were obtained using a stroboscopic double-exposure method.

Fig. 3.
Fig. 3.

Unwrapped phase from the phase map of Fig. 2(a). Panel (a) shows the unwrapped phase obtained with the branch-cut method of [17], panel (b) shows the unwrapped phase obtained with the windowed phase-unwrapped method proposed here. For illustration purposes, panels (c) and (d) show the unwrapped phase rewrapped.

Fig. 4.
Fig. 4.

Unwrapped phase from the phase map of Fig. 2(a). Panel (a) shows the unwrapped phase obtained with the branch-cut method of [17], panel (b) shows the unwrapped phase obtained with the windowed phase unwrapped method proposed here. For illustration purposes, panels (c) and (d) show the unwrapped phase rewrapped.

Equations (2)

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ϕ^(x,y)=m=x1x+1n=y1y+1{ϕ^(m,n)τW[ϕ(x,y)ϕ^(m,n)]}s(m,n),
p(x,y)=ϕ(x,y)*h(x,y),

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