Open AccessApproximations for the arctangent function in efficient fringe pattern analysis
Author(s) -
Hongwei Guo,
Guoqing Liu
Publication year - 2007
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.15.003053
Subject(s) - inverse trigonometric functions , function (biology) , phase (matter) , mathematics , phase function , sequence (biology) , algorithm , mathematical analysis , optics , physics , genetics , quantum mechanics , evolutionary biology , scattering , biology
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.