Abstract

For optical interferometry, a new quality-guided phase unwrapping algorithm based on the reliability evaluation of each pixel of the wrapped phase is proposed. First, the parameters used as quality measures in the past quality-guided algorithms are classified into the reliability measure and the quality measure, and the intensity of the object image belongs to the reliability measure. Then, by computing and applying a threshold to the intensity of the object image, the valid region (i.e., the interference region) is distinguished into the reliable region and the doubtful region. The wrapped phase in the reliable region is subsequently unwrapped by the way of multipaths integration, and different paths are guided by separate quality measures. Finally, starting from the reliable region, the doubtful region is unwrapped by the way that each path takes in the reliable region. Experimental results have shown that the proposed algorithm not only performs well, but also computes efficiently.

© 2011 Optical Society of America

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References

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  1. C. R. Mercer and G. Beheim, “Fiber-optic projected-fringe digital interferometry,” presented at the 1990 Fall Conference on Hologram Interferometry and Speckle Metrology, Baltimore, MD, 5–8 Nov. 1990.
  2. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).
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    [CrossRef]
  4. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
    [CrossRef] [PubMed]
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  6. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
    [CrossRef]
  7. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
    [CrossRef]
  8. A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).
  12. Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
    [CrossRef]
  13. H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
    [CrossRef]
  14. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7444 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. S. Fang, L. Wang, P. Yang, L. Meng, and M. Komori, “Object-image-based method to construct an unweighted quality map for phase extraction and phase unwrapping,” Appl. Opt. 50, 1482–1487 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. W. Xu and I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
    [CrossRef]
  21. S. Fang, L. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2011).
    [CrossRef]

2011 (3)

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

S. Fang, L. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2011).
[CrossRef]

S. Fang, L. Wang, P. Yang, L. Meng, and M. Komori, “Object-image-based method to construct an unweighted quality map for phase extraction and phase unwrapping,” Appl. Opt. 50, 1482–1487 (2011).
[CrossRef] [PubMed]

2010 (1)

2007 (1)

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

2004 (2)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).

2002 (1)

1999 (2)

J. Strand and T. Taxt, “Performance evaluation of two-dimensional phase unwrapping algorithms,” Appl. Opt. 38, 4333–4344 (1999).
[CrossRef]

W. Xu and I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (2)

1991 (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]

1982 (1)

Asundi, A.

Beheim, G.

C. R. Mercer and G. Beheim, “Fiber-optic projected-fringe digital interferometry,” presented at the 1990 Fall Conference on Hologram Interferometry and Speckle Metrology, Baltimore, MD, 5–8 Nov. 1990.

Bernabeu, E.

Bone, D. J.

Burton, D. R.

Chen, M.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Cumming, I.

W. Xu and I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

Cusack, R.

Fang, S.

Flynn, T. J.

T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
[CrossRef]

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 1996), pp. 2057–2059.

Gdeisat, M. A.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

Goldrein, H. T.

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]

González-Cano, A.

He, G.

Herráez, M. A.

Huntley, J. M.

Komori, M.

Kubo, A.

S. Fang, L. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2011).
[CrossRef]

S. Fang, L. Wang, M. Komori, and A. Kubo, “Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry,” Appl. Opt. 49, 6409–6415(2010).
[CrossRef] [PubMed]

Lalor, M. J.

Li, D.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

Liu, L.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

Liu, Y.

Lu, W.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

Lu, Y.

Meng, L.

Mercer, C. R.

C. R. Mercer and G. Beheim, “Fiber-optic projected-fringe digital interferometry,” presented at the 1990 Fall Conference on Hologram Interferometry and Speckle Metrology, Baltimore, MD, 5–8 Nov. 1990.

Morgan, C. J.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

Quiroga, J. A.

Strand, J.

Su, X.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Tang, J.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

Taxt, T.

Wang, L.

Wang, X.

Wensen, Z.

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]

Wyant, J. C.

J. C. Wyant, “Phase-shifting interferometry,” http://www.optics.arizona.edu/jcwyant/optics513/ChapterNotes/Chapter05/3.PrintedVersionPhaseShiftingInterferometry.pdf.

Xu, W.

W. Xu and I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

Yang, P.

Yang, Q.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[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]

Zhang, S.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

Zheng, D.

Zhong, H.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

Zhong, X.

Zhu, L.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

Zhu, Y.

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[CrossRef]

Appl. Opt. (8)

Chin. Opt. Lett. (1)

IEEE Geosci. Remote Sens. Lett. (1)

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368 (2011).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

W. Xu and I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

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

Opt. Lasers Eng. (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Opt. Lett. (1)

Optik (2)

S. Fang, L. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2011).
[CrossRef]

Y. Zhu, L. Zhu, Q. Yang, D. Li, W. Lu, and L. Liu, “Improved reliability-guided phase unwrapping algorithm based on the fringe modulation and second-order phase difference,” Optik 118, 175–180 (2007).
[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 (4)

J. C. Wyant, “Phase-shifting interferometry,” http://www.optics.arizona.edu/jcwyant/optics513/ChapterNotes/Chapter05/3.PrintedVersionPhaseShiftingInterferometry.pdf.

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 1996), pp. 2057–2059.

C. R. Mercer and G. Beheim, “Fiber-optic projected-fringe digital interferometry,” presented at the 1990 Fall Conference on Hologram Interferometry and Speckle Metrology, Baltimore, MD, 5–8 Nov. 1990.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).

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Figures (13)

Fig. 1
Fig. 1

(a) Wrapped phase map and (b) the modulation map (low values are shown as dark pixels and high values by light pixels, and below is the same).

Fig. 2
Fig. 2

(a) Wrapped phase map and (b) the quality map (the pseudocorrelation map).

Fig. 3
Fig. 3

Part of an experimental object image.

Fig. 4
Fig. 4

Distribution of residues.

Fig. 5
Fig. 5

Sketch of quality-guided process: (a) The starting pixel a is selected, and its neighboring pixels are examined and placed in the “adjacent list”. (b) The highest-quality pixel b is unwrapped, and its wrapped neighbor g is placed into the list, while the invalid pixels h and f are rejected. (c) The process is proceeding. (d) All valid pixels are unwrapped at last.

Fig. 6
Fig. 6

Phase predictions from a 5 × 5 window centered at the current pixel.

Fig. 7
Fig. 7

(a) Object image ( 336 × 92 pixels), (b) the reliable region (white pixels), (c) the wrapped phase map.

Fig. 8
Fig. 8

Unwrapped results: (a) the proposed algorithm, (b) FMWDA, (c) TQGA.

Fig. 9
Fig. 9

Error map: (a) the region with discrepancy between Figs. 8a, 8b and (b) the region with difference between Figs. 8a, 8c.

Fig. 10
Fig. 10

(a) Wrapped phase map ( 1240 × 290 pixels), (b) the result of the proposed algorithm, (c) FMWDA, (d) TQGA.

Fig. 11
Fig. 11

Error map: (a) the region with discrepancy between Figs. 10a, 10b, (b) the region with difference between Figs. 10a, 10c.

Fig. 12
Fig. 12

Close examination of regions m, n, o: (a) the wrapped phase, (b) the unwrapped phase of the proposed algorithm, (c) the result of FMWDA.

Fig. 13
Fig. 13

Close examination of region p: (a) the wrapped phase, (b) the unwrapped phase of the proposed algorithm, (c) the result of TQGA.

Equations (10)

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I o ( x , y ) = I s n ( x , y ) + I s r ( x , y ) ,
Δ φ ( x , y ) = arctan n = 0 N 1 I n ( x , y ) sin ( 2 π n / N ) n = 0 N 1 I n ( x , y ) cos ( 2 π n / N ) ,
C R ( k ) = C R ( k 1 ) + Δ c r ,
{ C R ( k ) > 50 % G ( k + 1 ) G ( k ) > 5 .
{ ϕ k p = 2 ϕ [ k ] ϕ [ k ] w k = 1 ,
{ ϕ k p = ϕ [ k ] w k = 0.5 .
ϕ p = ( 1 N u w k ϕ k p ) / ( 1 N u w k ) ,
ϕ u = Δ φ + int ( ϕ p Δ φ 2 π ) * 2 π ,
{ d p = ( 1 N u w k | ϕ k p ϕ p | ) / ( 1 N u w k ) < t d u = | ϕ p ϕ u | < t ,
t = t 0 * a k ,

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