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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 off-axis Ronchi test based on the phase-shifting technique is presented to measure the aspheric mirror quantitatively. In this paper, slopes of deviations from the mirror''s ideal aspheric shape are derived when an off-axis point source is used. By integrating these slopes, the deviations of the shape are obtained and then the tested shape can be reconstructed. Compared with the coaxial Ronchi test, the measurement error caused by combination fringes can be avoided, and this system is more flexible. In the experiment, a marked point is used to guide the phase unwrapping procedure, which improves the accuracy of extracting corresponding phase points. In addition, the method has strong anti-noise ability. The validity of the method has been verified by both computer simulations and a preliminary experiment. [Copyright &y& Elsevier]

Abstract: The present study proposes a new method for measuring the surface shape of an object using elliptically pattern grating projection. Based on phase measuring profilometry (PMP), elliptically pattern grating is projected on the surface of the object to measure its shape in 3D. The computing formula for solving the phase by the phase-shifting fringe method is derived, and the 3D shape formula for the altitude is reestablished. The error-contrastive analysis of the object's surface shape is re-established based on the proposed method and traditional PMP. The proposed method was shown to have a strong anti-noise ability and able to measure objects under high noise. More accurate measurement results were obtained by computer simulation and experiment to verify the feasibility of the proposed method. [Copyright &y& Elsevier]