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Applied Optics

Applied 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)

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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

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

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)

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