S变换轮廓术测量范围的研究

Study of the Measurement Range of S-Transform Profilometry

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, combining the advantages of both the windowed Fourier transform and the wavelet transform, is suitable for the demodulation of non-stationary signal such as the deformed fringe pattern. The fringe patterns analyzed by S-transform are discrete in application. During the calculation of the S-stransform coefficients, the Fourier spectrum of the signal is translated, which means that the frequency information of the adjacent island is used. The frequency overlapping caused by sampling, nonlinearity or height variation of the measured object affects the three-dimensional reconstruction result. The effects from the above factors in calculating S-transform coefficients are exhaustively studied from the point of view of the frequency analysis. The frequency-domain description and the measurement range of S-transform coefficients of digital signal are deduced when the nonlinearity from both the projector and CCD exists. The sampling condition and the structure condition are given as well. Both computer simulation and experimental results verify the analysis.