窗口傅里叶变换轮廓术中窗口尺度选取的改进

Improved algorithm to choose the window scale for windowed Fourier transform profilometry

多尺度窗口傅里叶变换法根据条纹信号的瞬时频率梯度来确定信号的局域平稳长度,再由局域平稳长度来控制窗口的尺度,即窗口的尺度和局域平稳长度成正比。使用多尺度窗口傅里叶变换法来使条纹信号的频谱局域化,可以在条纹信号的频率分辨率和空间分辨率之间达到一种较佳的调和。针对多尺度窗口傅里叶变换三维形貌测量技术中局域平稳长度提取算法的不足进行了改进,使窗口尺度的选取更具合理性,对变形光栅基频提取更精确,进一步减小了位相测量的误差。给出了理论分析、计算机模拟以及实验结果。

In the multi-scale windowed Fourier transform method,the local stationary length of a fringe signal is determined according to its instantaneous frequency gradient.The window scale is controlled by local stationary length,that is,the window scale is proportional to the local stationary length.There is a better harmonization between the frequency resolution and time resolution of a fringe signal as the spectrum is localized by multi-scale windowed Fourier transform method.The local stationary length extraction algorithm in multi-scale windowed Fourier transform three-dimensional shape measurement is improved,which make it more reasonable to the window scale selection and more accurate to the fundamental frequency spectrum extraction.The phase measurement error is reduced.The theoretical analysis,simulation and experimental results demonstrate the validity of the principle.