基于S变换的改进窗口傅里叶三维测量法

讨论了一维S变换在处理条纹图中的应用,推导了S变换表达式,提出一种基于S变换脊的自适应窗口傅里叶三维测量法。利用S变换对于频率的敏感性以及S变换脊思想,求得任意点的瞬时频率。推导了在相位跳变剧烈区域相位二阶导φ″(b)对S变换脊的影响,并求得去除此影响后更为准确的瞬时频率。然后将瞬时频率倒数作为经典窗口傅里叶变换(WFT)的窗口大小,解出条纹图的精确相位。最后对去除相位二阶导影响前后基于S脊的WFT进行对比仿真;实验验证其与传统基于小波脊的WFT在抗噪声、解相位精度上的优势。

Windowed Fourier Transform Profilometry Based on Advanced S-Transform

An adaptive windowed Fourier transform (WFT) profilometry based on the ridge algorithm of S-transform is presented. The practical use of one-dimensional S-transform in processing fringe pattern is discussed, and the S-transform expression is derived. Every point′s instantaneous frequency is calculated by taking advantages of S-transform′s frequency sensitivity and its ridge idea. The influence of φ″(b) on the ridge of S-transform is derived in the sharp phase transition region, and a more accuracy instantaneous frequency is calculated after removing this deviation. Then an accurate phase map of fringe pattern is calculated by using the windowed Fourier transform based on the window which is the reciprocal of instantaneous frequency. Finally, the simulation which compares the accuracy of phase map calculated by WFT based on S-transform (SWFT) before and after removing the influence from deviation of φ″(b) is carried out. Experiments show its advantages in anti-noise and accuracy of the wrapped phase comparing to WFT based on wavelet-transform (WWFT).