数字全息相位解包裹方法的适用性分析  

Analysis on the Application Range of the Phase Unwrapped Method in Digital Holography

作　　者：李建素 党长营 LI Jian-su;DANG Chang-ying(School of Mechanical Engineering,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学机械工程学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2020年第2期161-169,187,共10页Journal of North University of China(Natural Science Edition)

基　　金：山西省青年科技研究基金资助项目(201701D221167)。

摘　　要：相位解包裹是数字全息测量中必不可少的一环,为了更好地应用数字全息测量技术,对常用的三种相位解包裹方法(基于离散余弦变换(DCT法)、四次快速傅里叶变换(4-FFT法)以及两次快速傅里叶变换(2-FFT法)的相位解包裹方法)的适用性进行分析和验证.首先从理论上,分别以三种方法成立的前提为依据,推导得出了三种方法基本公式各自成立的范围和精度,并指出这三种解包裹方法均不适用于解相位跳变大于π的包裹相位.通过peaks函数仿真模拟真实相位,进行包裹和解包裹运算.实验结果证明了当相位跳变小于π时,上述三种相位解包裹方法均适用,其中DCT法和4-FFT法精度较高,DCT法仅存在一个常数相位误差,4-FFT法的均方差为1.3×10^-16 rad,2-FFT法的均方差为2.494 rad.反之,当相位跳变大于π时,上述三种方法均不适用,解包裹失败.总之,三种常用的解包裹方法中,DCT法可靠性更高,精度更高.该分析结果将为数字全息技术中相位解包裹技术发展提供理论支撑.The phase unwrapping is an indispensable procedure in digital holography.To employ this measurement technology preferably,the application ranges of the three phase unwrapped methods based on the fast cosine transform(DCT),four times fast Fourier transforms(4-FFT)and two times fast Fourier transforms(2-FFT)were analyzed.Firstly,the application ranges and the accuracies of the three unwrapped methods were deduced by the fundamental formulas of the three methods.The analysis indicates that the three unwrapped methods are not fit for the wrapped phase whose phase gradient is greater thanπ.Subsequently,the simulation experiments of phase unwrapping were carried out by the peaks function.The results point out that the three unwrapped methods are fit for the wrapped phase whose phase gradient is smaller thanπ,and the accuracies of the DCT and 4-FFT are much higher in three methods.There is a constant error of the DCT,and the mean-square deviation of 4-FFT and 2-FFT are as low as 1.3×10^-16 rad and as high as 2.494 rad,respectively.But the three methods are failed when the phase gradient is greater thanπ.In all,the DCT method is higher reliability and precision comparing to other two methods.The analysis results will provide a theoretical basis for the development of digital holographic phase unwrapping technology.

关 键 词：数字全息术 相位解包裹 相位跳变 解包裹相位 包裹相位 

分 类 号：O438.1[机械工程—光学工程]