S变换轮廓术中消除条纹非线性影响的方法

Elimination of Nonlinear Error in Deformed Fringe Pattern by S-Transform Profilometry

S变换是短时傅里叶变换和小波变换的延伸和推广,是一种无损可逆的非平稳信号时频分析方法。它不仅具有线性、多分辨性和逆变换唯一性等特点,而且其反变换与傅里叶变换保持着直接的联系。在S变换中,以简谐波作为基波,以可以同时进行伸缩和平移的高斯函数作为窗函数。同短时傅里叶变换相比,S变换的时频分辨率可以同时达到最佳,同小波变换相比,S变换谱同傅里叶变换谱保持着直接联系。讨论了S变换在受到非线性因素影响下的变形条纹解相中的应用,推导了相应的条纹图的S变换公式;分别研究了S变换"脊"分析方法和S变换滤波分析方法在非线性因素影响下的变形条纹解相中的应用,完成了相应的计算机模拟和实验验证,并将S变换三维重建效果与傅里叶变换和小波变换的结果进行对比,由此表明了S变换具有更好的恢复效果。

S-Transform, a hybrid and extension of the short-time （or windowed） Fourier transform and the wavelet transform, is one of lossless and reversible time-frequency analysis methods, which is suitable to analyze non- stationary signals. It not only has advantages of linearity, multi-resolution and uniqueness of inverse, but also its inverse transform directly keeps in contact with the Fourier transform. In S-Transform, the harmonic wave is used as a basic element function, and the window function is a Gaussian function with the ability of both dilation and translation, which is controlled by a frequency parameter. Compared with the short-time （or windowed） Fourier transform, it has optimized the time-resolution and frequency resolution simultraneously. Compared with wavelet transform, it keeps in contact with the Fourier transform. S transform in the application of demodulation of fringe pattern with nonlinear parts has been deeply discussed, S-transform expression of the deformed fringe pattern considering by nonlinear effects is deduced and two ways, including S transform filtering method and S transform ridge method are proposed, which are used to eliminate the nonlinear error in three-dimensional optical measurement based on the structured light projection. Computer simulations and experiments have verified the proposed two methods. Compared with Fourier transform and wavelet transform, the proposed methods based on S transform have better reconstruction results.