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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 21 — Jul. 20, 2012
  • pp: 4984–4994

Phase unwrapping for noisy phase map using localized compensator

Satoshi Tomioka and Shusuke Nishiyama  »View Author Affiliations

Applied Optics, Vol. 51, Issue 21, pp. 4984-4994 (2012)

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Phase unwrapping for a noisy image suffers from many singular points. Singularity-spreading methods are useful for the noisy image to regularize the singularity. However, the methods have a drawback of distorting phase distribution in a regular area that contains no singular points. When the singular points are confined in some local areas, the regular region is not distorted. This paper proposes a new phase unwrapping algorithm that uses a localized compensator obtained by clustering and by solving Poisson’s equation for the localized areas. The numerical results demonstrate that the proposed method can improve the accuracy compared with other singularity-spreading methods.

© 2012 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(090.2880) Holography : Holographic interferometry
(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: January 11, 2012
Revised Manuscript: May 21, 2012
Manuscript Accepted: May 28, 2012
Published: July 11, 2012

Satoshi Tomioka and Shusuke Nishiyama, "Phase unwrapping for noisy phase map using localized compensator," Appl. Opt. 51, 4984-4994 (2012)

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  1. 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]
  2. K. E. Perry 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]
  3. 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]
  4. 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]
  5. B. Breuckmann and W. Thieme, “Computer-aided analysis of holographic interferograms using the phase-shift method,” Appl. Opt. 24, 2145–2149 (1985). [CrossRef]
  6. J. Jiang, J. Cheng, Y. Zhou, and G. Chen, “Clustering-driven residue filter for profile measurement system,” J. Opt. Soc. Am. A 28, 214–221 (2011). [CrossRef]
  7. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  8. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef]
  9. 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]
  10. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995). [CrossRef]
  11. M. Costantine, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998). [CrossRef]
  12. 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]
  13. 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]
  14. 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]
  15. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  16. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  17. 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]
  18. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988). [CrossRef]
  19. 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]
  20. 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]
  21. R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007). [CrossRef]
  22. 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]
  23. S. Heshmat, S. Tomioka, and S. Nishiyama, “A reliable phase unwrapping algorithm based on rotational and direct compensators,” Appl. Opt. 50, 6225–6233 (2011). [CrossRef]
  24. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991). [CrossRef]
  25. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), pp. 52–54.
  26. C. A. Brebia and S. Walker, Boundary Element Techniques in Engineering (Newnes-Butterworths, 1980).
  27. S. Tomioka and S. Nisiyama, “Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method,” Eng. Anal. Bound. Elem. 34, 393–404 (2010). [CrossRef]
  28. M. Arai, T. Adachi, and H. Matsumoto, “Highly accurate analysis by boundary element method based on uniform gradient condition,” Trans. Jpn. Soc. Mech. Eng. A 61, 161–168 (1995), in Japanese. [CrossRef]
  29. M. Guiggiani, G. Krishinasamy, T. J. Rudolphi, and F. J. Rizz, “A general algorithm for the numerical solution of hypersingular boundary integral equations,” Trans. ASME 59, 604–614 (1992). [CrossRef]
  30. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users’ Guide(Society for Industrial and Applied Mathematics, 1992).
  31. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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