基于傅里叶变换的三维轮廓测量技术研究

Research on Three-Dimensional Topography Measurement Technology Based on Fourier Transform

摘要: 随着三维测量技术的不断发展，通过投影光栅条纹对三维物体进行测量已经成为近年以来的研究热点。本文主要研究了基于光栅条纹的相位展开方法，并详细阐述其工作原理，推导展开相位与实际物体高度之间的几何映射关系。傅里叶变换轮廓术(FIP)进行三维面形测量时，若无频谱混叠，可以得到很好的测量效果，但由于FIP是全局变换，频域内丢失了空间信息。当被测物体形状复杂或被噪声严重污染时，频域中频谱分布展宽，可能发生频谱混叠，导致基频分量提取不完整，从而不能精确地测量被测物体。因此，本文通过对传统FTP法以及两种改进FTP法的测量范围进行分析，并比较这两种改进方法间的异同。实验表明，π相移法的测量结果要优于灰度图法的测量结果，且随着物体高度梯度值的增加，π相移法的测量结果逐渐优于灰度图法的测量结果。

Abstract: With the continuous development of 3D measurement technology, the measurement of 3D objects by projecting and shooting structured optical stripes has become a hot research topic in recent years. This paper mainly studies the phase unfolding method based on grating stripes, elaborates its implementation principle, and derives the geometric mapping relationship between the unfolded phase and the actual object height. Fourier Transform Profilometry (FIP) for 3D surface shape measurement, if no spectral overlap, can get good measurement results, but because FIP is a global transform, the spatial information is lost in the frequency domain. When the measured object has a complex shape or is seriously polluted by noise, the spectrum distribution in the frequency domain is broadened and spectral overlap may occur, resulting in incomplete extraction of the fundamental frequency components, and the measured object can not be recovered correctly. Therefore, in this paper, a comparative study of the measurement range of the traditional FTP method and two improved FTP methods is conducted by combining experimental methods, and the similarities and differences between these two improved methods are analyzed by means of experiments. The experiments show that the measurement results of the π-phase shift method are better than those of the grayscale map method, and the measurement results of the π-phase shift method are gradually better than those of the grayscale map method as the value of the object height gradient increases.