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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 3 — Jan. 20, 2012
  • pp: 328–337

Statistical analysis for windowed Fourier ridge algorithm in fringe pattern analysis

Wenjing Gao and Qian Kemao  »View Author Affiliations

Applied Optics, Vol. 51, Issue 3, pp. 328-337 (2012)

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Based on the windowed Fourier transform, the windowed Fourier ridges (WFR) algorithm and the windowed Fourier filtering algorithm (WFF) have been developed and proven effective for fringe pattern analysis. The WFR algorithm is able to estimate local frequency and phase by assuming the phase distribution in a local area to be a quadratic polynomial. In this paper, a general and detailed statistical analysis is carried out for the WFR algorithm when an exponential phase field is disturbed by additive white Gaussian noise. Because of the bias introduced by the WFR algorithm for phase estimation, a phase compensation method is proposed for the WFR algorithm followed by statistical analysis. The mean squared errors are derived for both local frequency and phase estimates using a first-order perturbation technique. These mean square errors are compared with Cramer–Rao bounds, which shows that the WFR algorithm with phase compensation is a suboptimal estimator. The above theoretical analysis and comparison are verified by Monte Carlo simulations. Furthermore, the WFR algorithm is shown to be slightly better than the WFF algorithm for quadratic phase.

© 2012 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(110.7410) Imaging systems : Wavelets

ToC Category:
Image Processing

Original Manuscript: July 1, 2011
Revised Manuscript: October 7, 2011
Manuscript Accepted: October 27, 2011
Published: January 18, 2012

Wenjing Gao and Qian Kemao, "Statistical analysis for windowed Fourier ridge algorithm in fringe pattern analysis," Appl. Opt. 51, 328-337 (2012)

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