Approximations for the arctangent function in efficient fringe pattern analysis.
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.
Guo
Hongwei
H
Liu
Guoqing
G