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S变换结合了窗口傅里叶变换和小波变换的优点,适合于解调具有非平稳特性的变形条纹图。实际应用时,S变换处理的对象为离散条纹。计算S变换系数时,利用了信号的傅里叶谱的平移形式,即将相邻频域周期内的频谱信息用于系数计算。当抽样、非线性以及物体高度变化导致频谱出现混叠时,会影响S变换的重建效果。从离散信号频域分析角度,研究了上述原因对S变换的影响;推导了在考虑数字视频投影仪和CCD非线性影响时,离散变形条纹的S变换的频谱表达式以及S变换轮廓术的测量范围。给出了S变换轮廓术的抽样条件及结构条件。计算机模拟和实验验证了该结论。
S transform combines the advantages of windowed Fourier transform and wavelet transform and is suitable for demodulating deformed fringe patterns with non-stationary characteristics. Practical applications, S transform object for discrete stripes. When calculating the S-transform coefficients, the Fourier transform of the signal is utilized, that is, the spectral information of the adjacent frequency-domain period is used for the coefficient calculation. When sampling, non-linearity and object height changes lead to aliasing of the spectrum, the reconstruction effect of the S transform will be affected. From the perspective of frequency domain analysis of discrete signals, the influence of the above-mentioned reasons on S-transform is studied. The spectral expression of S-transform of discrete deformation fringes and the measurement of S-transform profiler are deduced when considering the nonlinear effect of digital video projectors and CCDs range. The sampling conditions and structural conditions of S-transform profilometry are given. Computer simulation and experiment verify the conclusion.