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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 6 — Mar. 19, 2007
  • pp: 3053–3066

Approximations for the arctangent function in efficient fringe pattern analysis

Hongwei Guo and Guoqing Liu  »View Author Affiliations

Optics Express, Vol. 15, Issue 6, pp. 3053-3066 (2007)

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In fringe pattern analyses, the computational burden of implementing the arctangent function over an entire phase map is not trivial, hindering it from being used in real-time measurements. For overcoming this problem, this paper presents a general method for approximating the arctangent function. The domain of the arctangent function is split into a sequence of intervals. For each interval, approximation polynomials are determined in the maximum-norm sense. By applying these polynomials instead of the standard arctangent function to the fringe analyses, the efficiencies of phase evaluations are improved significantly. The accuracies and simplicities of the approximations have been analyzed numerically, and their validities have also been verified by using experimental results.

© 2007 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

Original Manuscript: November 21, 2006
Revised Manuscript: March 7, 2007
Manuscript Accepted: March 7, 2007
Published: March 19, 2007

Hongwei Guo and Guoqing Liu, "Approximations for the arctangent function in efficient fringe pattern analysis," Opt. Express 15, 3053-3066 (2007)

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