傅里叶变换轮廓术中频谱泄漏的讨论

Discussion on Phase Errors Caused by Frequency Leakage in FTP

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响。由于用傅里叶变换轮廓术进行三维面形测量时 ,测得的变形光场是空间有限函数 ,故离散傅里叶变换时先要进行周期拓展 ,如果拓展周期选择不当 ,拓展后的条纹将不连续 ,对之进行傅里叶变换会产生频谱泄漏。文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系 ,给出了由泄漏引起的视场边缘误差的计算模型和定量分析。提出采用条纹外插以减小泄漏误差的方法 ,计算机模拟及初步实验证实了该方法的有效性。

The phase error caused by leakage in a 3- D object measurement Fourier transform profilometry (FTP) method is discussed. Because the deformed fringe pattern captured by CCD camera is a function with limited extension in space,itmustbe extended to infinite space before discrete Fourier transform is computed.If the extended period is notintegertimes of the grating period,the smooth fringes can not be obtained through extending. When Fourier transform of the discontinuous fringe is calculated,phase error will occur,which is called leakage error.In this paper,the relationship between extended period and frequency leakage is analyzed,the calculation model of phase errors caused by leakage is proposed,quantitative analysis of phase error is presented. A fringe extrapolation method is put forward to decrease the leakage errors.Computer simulations and primary experiments have confirmed the analysis.