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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 33 — Nov. 20, 2011
  • pp: 6225–6233

Reliable phase unwrapping algorithm based on rotational and direct compensators

Samia Heshmat, Satoshi Tomioka, and Shusuke Nishiyama  »View Author Affiliations

Applied Optics, Vol. 50, Issue 33, pp. 6225-6233 (2011)

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Phase unwrapping still plays an important role in many data-processing chains based on phase information. Here, we introduce a new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrapping using a rotational compensator (RC) method. The proposed algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensation for adjoining singular point (SP) pairs and uses RC for other SP pairs. The performance of the proposed method is tested through both simulated and real wrapped phase data. The proposed algorithm is faster than the original algorithm with the RC and has proved efficiency compared to other phase unwrapping methods.

© 2011 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(100.3175) Image processing : Interferometric imaging
(110.5086) Imaging systems : Phase unwrapping
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

Original Manuscript: August 5, 2011
Revised Manuscript: October 2, 2011
Manuscript Accepted: October 3, 2011
Published: November 16, 2011

Samia Heshmat, Satoshi Tomioka, and Shusuke Nishiyama, "Reliable phase unwrapping algorithm based on rotational and direct compensators," Appl. Opt. 50, 6225-6233 (2011)

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  1. D. C. Ghiglia and L. A. Romero, “Direct phase estimation from phase differences using fast elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989). [CrossRef] [PubMed]
  2. S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995). [CrossRef]
  3. S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002). [CrossRef] [PubMed]
  4. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  5. I. Lyuboshenko and H. Maitre, “Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the first green’s identity,” J. Opt. Soc. Am. A 16, 378–395 (1999). [CrossRef]
  6. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160(1982). [CrossRef]
  7. K. E. Perry, Jr., and J. McKelvie, “A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns,” Opt. Lasers Eng. 19, 269–284 (1993). [CrossRef]
  8. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000). [CrossRef]
  9. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  10. B. Breuckmann and W. Thieme, “Computer-aided analysis of holographic interferograms using the phase-shift method,” Appl. Opt. 24, 2145–2149 (1985). [CrossRef] [PubMed]
  11. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef] [PubMed]
  12. J. R. Buckland, J. M. Huntley, and S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995). [CrossRef] [PubMed]
  13. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995). [CrossRef] [PubMed]
  14. M. Costantine, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998). [CrossRef]
  15. B. Gutmann and H. Weber, “Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing,” Appl. Opt. 38, 5577–5593 (1999). [CrossRef]
  16. S. A. Karout, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Two-dimensional phase unwrapping using a hybrid genetic algorithm,” Appl. Opt. 46, 730–743 (2007). [CrossRef] [PubMed]
  17. D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  18. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  19. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399(1979). [CrossRef]
  20. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425(1988). [CrossRef]
  21. H. Takajo and T. Takahashi, “Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 1818–1827 (1988). [CrossRef]
  22. 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]
  23. S. Tomioka, S. Heshmat, N. Miyamoto, and S. Nishiyama, “Phase unwrapping for noisy phase maps using rotational compensator with virtual singular points,” Appl. Opt. 49, 4735–4745 (2010). [CrossRef] [PubMed]
  24. R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251(2007). [CrossRef]
  25. C. L. Martinez and X. Fabergas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domain,” IEEE Trans. Geosci. Remote Sens. 40, 2553–2566(2002). [CrossRef]
  26. M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25, 4035–4038 (1998). [CrossRef]
  27. J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998). [CrossRef]
  28. C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001). [CrossRef]
  29. Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005). [CrossRef]
  30. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007). [CrossRef]
  31. Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5408–5428 (2008). [CrossRef] [PubMed]
  32. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

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