Abstract

This work describes a rapid-phase unwrapping algorithm that combines the rapidity and simplicity of a path-dependent algorithm and the robustness of a path-independent algorithm by rotating the phase map or the unwrapping direction 90° after a scan in one direction. It offers a solution for noise-contaminated phase data, which includes artifacts, complex-shaped borders, or regions of holes. The algorithm can be used in real-time processing. In addition, a phase-dislocation masking method is presented that can be used to detect and clean inconsistent data and improve the rms values of signal-to-noise ratio in unwrapped phase maps.

© 2007 Optical Society of America

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References

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  1. B. Wang, Y. Shi, T. Pfeifer, and H. Mischo, "Phase unwrapping by blocks," Measurement 25, 285-290 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. D. C. Ghiglia, G. A. Mastin, and L. A. Romero, "Cellular-automata method for phase unwrapping," J. Opt. Soc. Am. A 4, 267-280 (1987).
    [CrossRef]
  4. J. J. Gierloff, "Phase unwrapping by regions," Proc. SPIE 818, 2-9 (1987).
  5. K. Andresen and Q. Yu, "Robust phase unwrapping by spin filtering combined with a phase direction map," Optik 4, 145-149 (1994).
  6. J. M. Huntley, "Noise immune phase unwrapping algorithm," Appl. Opt. 28, 3268-3270 (1989).
    [CrossRef] [PubMed]
  7. D. C. Ghiglia and L. A. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107-117 (1994).
    [CrossRef]
  8. A. Spik and D. W. Robinson, "Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor," Opt. Lasers Eng. 14, 25-37 (1991).
    [CrossRef]
  9. R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Satellite radar interferometry: two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
    [CrossRef]

1999 (1)

B. Wang, Y. Shi, T. Pfeifer, and H. Mischo, "Phase unwrapping by blocks," Measurement 25, 285-290 (1999).
[CrossRef]

1994 (2)

1991 (1)

A. Spik and D. W. Robinson, "Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor," Opt. Lasers Eng. 14, 25-37 (1991).
[CrossRef]

1989 (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)

1982 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. A (2)

Measurement (1)

B. Wang, Y. Shi, T. Pfeifer, and H. Mischo, "Phase unwrapping by blocks," Measurement 25, 285-290 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

A. Spik and D. W. Robinson, "Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor," Opt. Lasers Eng. 14, 25-37 (1991).
[CrossRef]

Optik (1)

K. Andresen and Q. Yu, "Robust phase unwrapping by spin filtering combined with a phase direction map," Optik 4, 145-149 (1994).

Proc. SPIE (1)

J. J. Gierloff, "Phase unwrapping by regions," Proc. SPIE 818, 2-9 (1987).

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]

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Figures (5)

Fig. 1.
Fig. 1.

Unwrapping path: (a) Unwrapping path in a true phase map, (b) Three types of 2π phase jumps, showing the contradiction of unwrapping paths in Type III

Fig. 2.
Fig. 2.

Find out the two end points of inconsistent 2π phase jumps and mask the inconsistent data. (a) The different residues of the two end points of phase dislocation; (b) mask several inconsistent data by Goldstein's method and Wang's method.

Fig. 3.
Fig. 3.

Phase unwrapping by spinning iteration. (a) Unwrap from left to right; (b) unwrap from top to bottom; (c) unwrap from right to left; (d) unwrap from bottom to top; (e) unwrap from left to right.

Fig. 4.
Fig. 4.

A series of spinning iterations of the phase unwrapping algorithm. (a) Original wrapped phase map including complex borders; (b)-(e) unwrapping from left to right after rotating the phase map 90° counterclockwise each time, a round of spinning iteration been finished; (f) the whole phase map has been unwrapped by another spinning iteration.

Fig. 5.
Fig. 5.

(a). Original wrapped phase map including inconsistent data in top right corner; (b) enlarged portion of (a) with phase dislocation masked; (c) unwrapped same region, including the masking points.

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