伸缩窗口傅里叶变换在三维形貌测量中的应用

Application of Dilating Gabor Transform to Three-Dimensional Shape Analysis

为了克服窗口傅里叶变换在分析非平稳信号所存在的缺陷 ,基于窗口傅里叶变换技术提出了伸缩傅里叶变换法并应用于三维形貌测量中。通过对窗函数在空间尺度上引入伸缩变换 ,得到一个可调宽度的空间 频率窗 ,实现空间频率分辨率随光栅图像条纹频率变化自动可调的实时快速测量。该方法克服了窗口傅里叶变换分析中所有频率窗口的大小形状固定不变的缺点 ,适合复杂物体形貌的测量。给出了理论分析、计算机模拟以及实验研究结果。

In order to overcome the disadvantage of Gabor transform analyzing nonstationary signals, dilating Gabor transform is applied to analyze the optical fringes of three-dimensional shape measurement. A changeable window is obtained by introducing dilating transformation to the window function on the space scale, and it is realized automatic measurement adjusting the space-frequency solution with the changes of the fringe's frequency. This technique overcomes the limitation of the Gabor transform gird method (GTGM) that utilizes all the same size and shape window, and it is fit for complex object shape measurement. The theoretical analysis, simulation and experimental results presented demonstrate the validity of the principle.