三维测量中一种新的自适应窗口傅里叶相位提取法

A Novel Adaptive Windowed Fourier Transform for Phase Retrieval in 3D Shape Measurement

针对多尺度窗口傅里叶变换中,窗口尺寸的自适应选取及提取基频时的频谱混叠等问题,提出基于希尔伯特-黄变换(HHT)的自适应窗口傅里叶相位提取法。对变形条纹信号进行HHT后,通过谱分析,自适应确定能够准确描述条纹信号变化情况的瞬时频率及条纹图的背景分量。根据所得的瞬时频率,给出自适应定位条纹信号局部平稳区域的步骤,进而确定窗口尺寸。不需额外计算,可有效去除背景分量以减少基频提取过程中零频频谱的干扰。与现有的用最大脊法确定窗口尺寸的方法相比,本方法不受被测相位必须线性逼近且变化缓慢的前提约束。实验证明本方法有效、可行,且对测量携带陡峭边缘或面形复杂的物体也能进行较为精确有效的测量。

Method of adaptive windowed Fourier transform based on Hilbert-Huang transform（HHT） is presented to address the issue of adaptive selection of window size and spectrum aliasing in multiscale windowed Fourier transform for phase retrieval of fringe pattern.Spectrum obtuined by HHT is analyzed to adaptively determine the background and instantaneous frequencies which can describe the change of signals in detail for fringe pattern.By using the presented steps,local stationary regions are located adaptively according to instantaneous frequencies,and then scale factors of window function are got.Before performing adaptive windowed Fourier transform,the background which has been determined is eliminated from fringe pattern to avoid spectrum aliasing caused by expansion of zero-spectrum especially without extra computation.Compared with the method such as the ridge of wavelet transform or the ridge of S transform,the presented method is not limited by hypothesis of linear approximation and changing slowly for measured phase.Experments illustrate the effectiveness and feasibility of this method which is accurate and robust even for measurement of object which carries with steep edge or complex surface.