Liu Fengwei, Wu Yongqian, Wu Fan
Opt Express. 2015 Apr 20;23(8):10794-807. doi: 10.1364/OE.23.010794.
The accuracy of phase-shifting interferometers (PSI) is crippled by nonlinearity of the phase shifter and instability of the environment such as vibration and air turbulence. A general algorithm, utilizing Lissajous figures and ellipse fitting, of correcting the phase extraction error in the phase shifting interferometry is described in this paper. By plotting N against D, where N and D represent the numerator and denominator terms of the phase extraction function (i.e. an arctangent function) respectively, a Lissajous ellipse is created. Once the parameters of the ellipse are determined by ellipse fitting, one can transform the ellipse to a unit circle (ETC). Through this process the phase extraction error caused by random phase shift errors can be corrected successfully. Proposed method is non-iterated, adapts to all phase shifting algorithms (PSAs), and has high accuracy. Some factors that may affect the performance of proposed method are discussed in numerical simulations. Optical experiments are implemented to validate the effectiveness of proposed algorithm.
相移干涉仪（PSI）的精度会受到相移器的非线性以及环境不稳定因素（如振动和空气湍流）的影响。本文描述了一种利用李萨如图形和椭圆拟合来校正相移干涉术中相位提取误差的通用算法。通过绘制N与D的关系图，其中N和D分别表示相位提取函数（即反正切函数）的分子项和分母项，从而创建一个李萨如图形椭圆。一旦通过椭圆拟合确定了椭圆的参数，就可以将椭圆转换为单位圆（ETC）。通过这个过程，可以成功校正由随机相移误差引起的相位提取误差。所提出的方法是非迭代的，适用于所有相移算法（PSA），并且具有较高的精度。在数值模拟中讨论了一些可能影响所提出方法性能的因素。进行了光学实验以验证所提出算法的有效性。
