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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 49, Iss. 7 — Mar. 1, 2010
  • pp: 1075–1079

Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase

Qian Kemao, Wenjing Gao, and Haixia Wang  »View Author Affiliations


Applied Optics, Vol. 49, Issue 7, pp. 1075-1079 (2010)
http://dx.doi.org/10.1364/AO.49.001075


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Abstract

A windowed Fourier filtered and quality guided (WFF-QG) phase unwrapping algorithm was proposed recently [ Appl. Opt. 47, 5420–5428 (2008)], based on the windowed Fourier transform [ Appl. Opt. 47, 5408–5419 (2008)] where the phase is assumed to be locally quadric. We consider a locally higher order polynomial phase. After the phase is filtered and unwrapped by the WFF-QG, it is postprocessed by a congruence operation (CO), so that the unwrapped phase is congruent to the original wrapped phase. The unwrapped phase can now be assumed to be a locally high-order polynomial, and, consequently, least squares fitting (LSF) is proposed to suppress the noise. This postprocessing algorithm is abbreviated as CO-LSF. The CO-LSF is theoretically a reasonable choice to improve the WFF-QG results, especially when the noise is severe. This is because for severe noise, a large window is necessary for reliable phase extraction in the WFF-QG. However, this large window makes the quadric phase assumption less reasonable and leads to a large phase error. The CO-LSF thus helps to reduce the phase error by more reasonably assuming that the phase is a high-order polynomial. The polynomial order of 4 is suggested for the CO-LSF, as higher order polynomials do not give significant improvement to the WFF-QG. One disadvantage of the CO-LSF is that it is more sensitive to phase discontinuities than the WFF-QG.

© 2010 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(110.5086) Imaging systems : Phase unwrapping
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

History
Original Manuscript: December 9, 2009
Revised Manuscript: January 14, 2010
Manuscript Accepted: January 14, 2010
Published: February 22, 2010

Citation
Qian Kemao, Wenjing Gao, and Haixia Wang, "Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase," Appl. Opt. 49, 1075-1079 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-7-1075


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References

  1. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software (Wiley, 1998).
  2. Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650-2654 (2002). [CrossRef] [PubMed]
  3. Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sensing Lett. 4, 23-26 (2007). [CrossRef]
  4. M. Servin, J. L. Marroguin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540-4548(1997). [CrossRef] [PubMed]
  5. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroguin, and R. Rodriguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 38, 1934-1941 (1999). [CrossRef]
  6. Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408-5419 (2008). [CrossRef] [PubMed]
  7. Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5408 (2008). [CrossRef] [PubMed]
  8. B. Friedlander and J. M. Francos, “Model based phase unwrapping of 2-D signals,” IEEE Trans. Signal Process. 44, 2999-3007 (1996). [CrossRef]
  9. S. S. Gorthi and P. Rastogi, “Analysis of reconstructed interference fields in digital holographic interferometry using the polynomials phase transform,” Meas. Sci. Technol. 20, 075307 (2009). [CrossRef]
  10. S. S. Gorthi and P. Rastogi, “Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function,” J. Mod. Opt. 56, 949-954 (2009). [CrossRef]
  11. S. S. Gorthi and P. Rastogi, “Piecewise polynomial phase approximation approach for the analysis of reconstructed interference fields in digital holographic interferometry,” J. Opt. A: Pure Appl. Opt. 11, 065405 (2009). [CrossRef]
  12. S. S. Gorthi and P. Rastogi, “Windowed high-order ambiguity function method for fringe analysis,” Rev. Sci. Instrum. 80, 073109 (2009). [CrossRef] [PubMed]
  13. S. S. Gorthi and P. Rastogi, “Improved high-order ambiguity-function method for the estimation of phase from interferometric fringes,” Opt. Lett. 34, 2575-2577 (2009). [CrossRef] [PubMed]
  14. S. Peleg and B. Friedlander, “The discrete polynomial-phase transform,” IEEE Trans. Signal Process. 43, 1901-1914 (1995). [CrossRef]
  15. S. S. Gorthi, G. Rajshekhar, and P. Rastogi, “Strain estimation in digital holographic interferometry using piecewise polynomial phase approximation based method,” Opt. Express 18, 560-565 (2010). [CrossRef] [PubMed]
  16. P. O'Shea, “A fast algorithm for estimating the parameters of a quadratic FM signal,” IEEE Trans. Signal Process. 52, 385-393 (2004). [CrossRef]
  17. A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598-2604 (2001). [CrossRef]
  18. W. Gao, N. T. H. Huyen, H. S. Loi, and Q. Kemao, “Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit,” Opt. Express 17, 23147-23152 (2009). [CrossRef]

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