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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5126–5133

Noise robust linear dynamic system for phase unwrapping and smoothing

Julio C. Estrada, Manuel Servin, and Juan A. Quiroga  »View Author Affiliations

Optics Express, Vol. 19, Issue 6, pp. 5126-5133 (2011)

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Phase unwrapping techniques remove the modulus 2π ambiguities of wrapped phase maps. The present work shows a first-order feedback system for phase unwrapping and smoothing. This system is a fast phase unwrapping system which also allows filtering some noise since in deed it is an Infinite Impulse Response (IIR) low-pass filter. In other words, our system is capable of low-pass filtering the wrapped phase as the unwrapping process proceeds. We demonstrate the temporal stability of this unwrapping feedback system, as well as its low-pass filtering capabilities. Our system even outperforms the most common and used unwrapping methods that we tested, such as the Flynn’s method, the Goldstain’s method, and the Ghiglia least-squares method (weighted or unweighted). The comparisons with these methods show that our system filters-out some noise while preserving the dynamic range of the phase-data. Its application areas may cover: optical metrology, synthetic aperture radar systems, magnetic resonance, and those imaging systems where information is obtained as a demodulated wrapped phase map.

© 2011 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

Original Manuscript: November 11, 2010
Revised Manuscript: January 15, 2011
Manuscript Accepted: January 25, 2011
Published: March 3, 2011

Julio C. Estrada, Manuel Servin, and Juan A. Quiroga, "Noise robust linear dynamic system for phase unwrapping and smoothing," Opt. Express 19, 5126-5133 (2011)

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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 (1982). [CrossRef]
  2. 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 (1974). [CrossRef] [PubMed]
  3. Q. Kemao, “Two-dimensional windowed fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007). [CrossRef]
  4. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express 17, 21867–21881 (2009). [CrossRef] [PubMed]
  5. L. N. Mertz, “Speckle imaging, photon by photon,” Appl. Opt. 18, 611–614 (1979). [CrossRef] [PubMed]
  6. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  7. K. A. Stetson, J. Wahid, and P. Gauthier, “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36, 4830–4838 (1997). [CrossRef] [PubMed]
  8. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982). [CrossRef] [PubMed]
  9. T. R. Judge, and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994). [CrossRef]
  10. D. C. Ghiglia, and M. D. Pritt, Two-dimensional Phase Unwrapping; Theory, Algoritms, and Software (Wiley-Interscience, 1998). [PubMed]
  11. 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]
  12. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef] [PubMed]
  13. 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]
  14. J. L. Marroquin, and M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995). [CrossRef]
  15. J. L. Marroquin, M. Tapia, R. Rodriguez-Vera, and M. Servin, “Parallel algorithms for phase unwrapping based on markov random field models,” J. Opt. Soc. Am. A 12, 2578–2585 (1995). [CrossRef]
  16. K. M. Hung, and T. Yamada, “Phase unwrapping by regions using least-squares approach,” Opt. Eng. 37, 2965–2970 (1998). [CrossRef]
  17. V. V. Volkov, and Y. Zhu, “Deterministic phase unwrapping in the presence of noise,” Opt. Lett. 28, 2156–2158 (2003). [CrossRef] [PubMed]
  18. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroquin, and R. Rodriguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 38, 1934–1941 (1999). [CrossRef]
  19. . J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Principles, Algorothims, ans Applications (Prentice-Hall, October 5, 1995), 3rd ed.

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