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Abstarct: S-Transform, as a time-frequency analysis approach, has been successfully introduced into fringe pattern demodulation in recent years. The paper presents a thorough discussion on the application of this technique in analyzing fringe pattern. A brief review of the S transform profilometry is followed by the comparison between the one-dimensional S-Transform method and the two-dimensional S-Transform method, including one-dimensional S-Transform ridge method, one-dimensional S-Transform filtering method, two-dimensional S-Transform ridge method and two-dimensional S-Transform filtering method in the application of the phase retrieval from the fringe patterns with different noise, contrast, nonlinearity and fringe breaking. Numerical computer simulations and experiments were carried out to show the 1DST method is sensitive to the noise but suitable to detect detail of the measured object, while 2DST method with capability of smooth processing for the surface of the measured object is adapt to demodulate the fringe pattern with serious noise. [Copyright &y& Elsevier]

Abstract: An improved method is proposed to optimize the discrete wavelet decomposition, which can be used to decompose a deformed fringe by easily applying “ridge” information of continuous wavelet transform. With this method the zero component of a deformed fringe pattern can be extracted and eliminated automatically instead of using traditional repetitious tentative experiments. Computer simulations and experiments are carried out to verify our analysis by comparing the results from the correct level selection with that from the adjacent level selection. [Copyright &y& Elsevier]

Abstract: A Hilbert assisted wavelet transform (HWT) method is presented for phase reconstruction of 3D profilometry and interferometry. A rigorous mathematical demonstration about this HWT method is given in this paper. An important conclusion that the phase of the optical fringe pattern is equal to the phase of its HWT coefficients on the ridge is theoretically clarified. The strict relation between the scale parameter and the phase gradient (also called the angular frequency) of the fringe pattern is also given. Computer simulations and experiments reveal the validity of the method and the correctness of the mathematical demonstration. Since the filtering process is avoided in this method, it can deal with the frequency overlapping problem to a certain extent. Applications of this method in both optical profilometry and interferometry are shown and discussed in the experiment section. [Copyright &y& Elsevier]