基于结构光投影的二维S变换轮廓术

S变换是一种集合了窗口傅里叶变换和小波变换优点的时频分析技术，目前一维S变换已成功应用于结构光投影的条纹相位解调中。由于二维S变换可以对图像在两个方向上进行时频分析，具有更优于一维S变换的分析和处理能力。为了完善S变换的条纹相位解调理论，将二维S变换方法引入到基于结构光投影的三维光学测量中，研究了二维S变换在条纹相位解调中的原理及应用，给出了详尽的理论分析,并同一维S变换结果进行了比较。模拟和实验都表明，在条纹图解相中，二维S变换比一维S变换提取的相位精度更高，即使在存在较严重噪声污染的情况下也表现出良好的可靠性，体现出二维S变换提取相位的优势。

2D S-Transform Profilometry Based on the Structured Light ProjectionWang Tao

The S transform is one of the time-frequency analysis techniques which combines the advantages of both the short-time Fourier transform and wavelet transform. The one-dimensional S transform has been successfully used in fringe phase demodulation based on structured light projection. The two-dimensional (2D) S transform is able to carry out the time-frequency analysis for images in two directions, which is better than one-dimensional (1D) S transform. The 2D S transform based on the structured light projection method is introduced to the three-dimensional (3D) optical measurement for completing S transform fringe phase demodulation theory. This work studies the theory and application of the 2D S transform in fringe phase demodulation and gives a detailed theoretical analysis. Furthermore, a comparison between the 2D S transform and the 1D S transform is carried out in fringe phase demodulation. The comparison result shows that the 2D S transform will achieve a higher accuracy than 1D S transform in extracting the phase distribution of the fringe patterns, even when the fringe patterns are seriously polluted by noises. Both the computer simulations and experiments verify that the 2D S transform outperforms the 1D S transform in the fringe analysis.