三角函数逼近算法及其在光学条纹图像分析中的应用

摘要

三角函数与反三角函数作为基本初等函数,在光学条纹图像分析中有着广泛的应用.在某些特定情况下,如硬件计算或要求快速计算时,可以通过逼近函数来计算其近似值.现讨论三角函数及反三角函数的最佳逼近方法.基于∞范数,选择特定区间推导函数的最佳逼近多项式,给出了多项式的系数与最大逼近误差；再利用三角恒等式将其推广至函数的整个定义区间,得到了各三角函数与反三角函数的分段逼近多项式.并且将其结果用于条纹图像的分析,以实验证明了所述方法的有效性.%Trigonometric and inverse trigonometric functions, as the basic elementary functions, are widely used in optical measurement. In some cases, however, it is necessary to calculate their approximations in order to meet the need in hardware calculation or fast calculation. For this purpose, a method is presented in which the best approximation polynomial for a trigonometric or inverse trigonometric function, in a certain interval, is deduced based on the ∞-norm, and then the sectional approximation polynomials are obtained by use of trigonometric equations so that the values of the function in its whole domain of definition can be calculated. The coefficients and accuracies of the approximation polynomials for some typical trigonometric and inverse trigonometric functions are also provided. These results are used in optical fringe analysis, thus experimentally demonstrating the validity of the presented approach.