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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]

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]