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A two-dimensional continuous wavelet transform employing a real mother wavelet is applied to phase analysis of spatial carrier fringe patterns. In this method, a Hilbert transform is first performed on a carrier fringe pattern to get an analytic signal. Then a two-dimensional wavelet transform is calculated for the signal that is yielded by the first transform. Finally, the height-demodulated phase information can be gotten from the wavelet transform coefficients at the wavelet ridge position. The performance of the proposed method has been evaluated by using computer-generated and real fringe patterns. The result performed better than that of one-dimensional real wavelet transform algorithms in the area with phase discontinuous points and high phase variation, especially when there is much noise in the fringe patterns. Computer simulations and experiments verified the validity of the proposed method. [c] 2009 Optical Society of America OCIS codes: 100.2650, 100.5070, 100.7410.

The phase unwrapping algorithm plays a very important role in many noncontact optical profilometries based on triangular measurement theory. Here we focus on discussing how to diminish the phase error caused by incorrect unwrapping path in wavelet transform profilometry. We employ the amplitude value map of wavelet transform coefficients at the wavelet-ridge position to identify the reliability of the phase data and the path of phase unwrapping. This means that the wrapped phase located at the pixel with the highest amplitude value will be selected as the starting point of the phase unwrapping, and that pixels with higher amplitude value will be unwrapped earlier. So the path of phase unwrapping is always in the direction of the pixel with highest amplitude value to the one with lowest amplitude value. Making full use of the amplitude information of wavelet coefficients at the wavelet-ridge position keeps the phase unwrapping error limited to local minimum areas even in the worst case. Computer simulations and experiments verify our theory. OCIS codes: 100.5088, 100.2650, 100.7410, 120.3180.

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-feld fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object. OCIS codes: 120.0120, 120.2650, 120.2830.