光学学报, 2011, 31 (4): 0412001, 网络出版: 2011-03-24   

基于S变换的解相技术研究

Research of phase demodulation technique based on S-Transform
作者单位
四川大学电子信息学院光电系, 四川 成都 610064
摘要
S变换结合了窗口傅里叶变换和小波变换的优点,是一种很有应用前景的时频信号分析技术。相比窗口傅里叶变换,S变换的窗口大小随频率调整,具良好的时频分辨能力;与小波变换相比,它的时频表示形式更加直观,且与傅里叶频谱保持联系。在空间/时间方向上,所有位置S变换谱的叠加构成完整的傅里叶谱,而小波变换并不具备频谱的概念。讨论了一维S变换在基于条纹投影的光学三维测量中的应用,研究了基于滤波方式的S变换轮廓术;严格推导了条纹图的S变换表达式,完善了基于“脊”处理思想的S变换轮廓术,利用表达式中的调制度信息,研究了基于调制度排序的可靠度相位展开算法在S变换轮廓术的应用;讨论了一维广义S变换对条纹处理的影响。
Abstract
S-transform is one of the time-frequency analysis techniques, which combines the advantage of windowed Fourier transforma and wavelet transform. Compared with the windowed Fourier transform, S-transform has the perfect time-frequency resolution because its window size is adjusted by the variation of the frequency. Compared with the wavelet transform, the frequency concept of S-transform is clear because it relates to Fourier frequency of the signal. The complete Fourier spectrum can be constituted by superimposing S-transform coefficients along the direction of space/time, while the wavelet transform just calculates the similitude between the local fringe and the stretched wavelet function instead of obtaining the frequency distribution. The paper focuses on the application of S-transform in three dimensional optical measurement based on the structured light projection, and S-transform profilometry (STP) based on the filtering way is studied. The "ridge" theory of S-transforma profilometry is completed. A strict expression of the S-transform of the deformed fringe pattern is given. The modulation map can be used to guide phase unwrapping algorithm, the application of which to S-transform profilometry is studied. We also discuss the effect of one-dimensional generalized S-transform on the fringe processing.

蒋模华, 陈文静, 郑志平. 基于S变换的解相技术研究[J]. 光学学报, 2011, 31(4): 0412001. Jiang Mohua, Chen Wenjing, Zheng Zhiping. Research of phase demodulation technique based on S-Transform[J]. Acta Optica Sinica, 2011, 31(4): 0412001.

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