基于傅里叶变换的高精度条纹细分方法

针对传统傅里叶变换法在提取条纹图相位中存在的能量泄漏问题,提出了条纹图整周期裁剪的方法,可有效抑制能量泄漏对检相精度的影响,提高傅里叶变换法相位计算的精度。在此基础上,提出了一种基于傅里叶变换时移特性的叠栅条纹细分新方法。与传统傅里叶变换法相比,该方法求取相邻两帧条纹图间的相移,只需经过两次傅里叶变换,不需要截取条纹图的基频再逆变换回空域,因此计算量至少减少了一倍,计算速度大大提高。数值计算结果表明,对两束单色平面波形成的条纹,理想条件下细分精度高达10-12量级;对高斯包络调制的条纹,细分精度至少可达10-3量级。

Investigation of High Precision Subdivision Method for Fringes Based on Fast Fourier Transform

Aiming at the problem of energy leakage that occurs during the course of phase-extraction by using conventional fast Fourier transform (FFT) algorithm, an novel method that acquisition interferogram is firstly tailored to a few full-period of fringes is proposed to suppress the influence of energy leakage on the precision of phase-extraction. The precision of fast Fourier transform phase-extraction algorithm can be efficiently improved by tailoring the interferogram. Furthermore, a new subdivision method, which is based on the time-shift property of fast Fourier transform, for moiré interference fringes is developed. Compared with conventional fast Fourier transform phase-extraction algorithm, this new method pioneers a larruping means for fringes subdivision and can achieve high precision. It needs only to run fast Fourier transform algorithm twice to obtain the phase-shift between two sequential interferograms. The corresponding calculating time can then be greatly saved because it does not need to intersect the fundamental frequency of interferogram from spectral domain and inversely transform it into time domain again. Numerical results show that subdivision precision can reach 10-12 level for ideal situation that the interferogram is formed by two coherent plane waves and can be tailored to a few full-period of fringes. It can reach 10-3 level when the inteferogram is formed by two Gaussian waves.