针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。

There are noticeable errors at the border of the pattern when the traditional Fourier transform method (FTM) is used to evaluate the carrier intefergram fringe pattern. A new extrapolation of fringe prolongation method for interferogram fringe pattern analysis based on FTM is proposed to eliminate boundary effects. This extrapolation algorithm is derived mathematically. And numerical simulations are performed to evaluate the performance of the method for one-dimensional digital signal and two-dimensional spatial carrier fringe pattern. The source of error is analyzed, and a comprehensive comparison is made between results from traditional FTM and this new extrapolation. The results show, the rather large error caused by the boundary effect in the course of carrier interferogram fringe pattern treatment with traditional FTM, is reduced effectively. In the wave surface measurement based on spatial phase modulation, the calculating precision for phase reaches 3.3 mrad by treating the spatial carrier fringe pattern with the new method.