Jiang Mohua, Chen Wenjing, Zheng Zhiping. Research of phase demodulation technique based on S-Transform[J]. Acta Optica Sinica, 2011, 31(4): 412001
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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.