Wenjing Chen

Reliability-guided phase unwrapping in wavelet-transform profilometry

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.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

Wavelet ridge techniques in optical fringe pattern analysis

Wavelet ridge techniques utilizing daughter wavelets under two different kinds of definitions in the optical fringe pattern analysis are theoretically clarified. The clarification reveals that the phase of the optical fringe pattern is equal to that of its wavelet transform coefficients on the ridge using both of the two wavelet definitions. The differences between the two definitions in the performance of wavelet transform algorithms are verified in theory. The strict relations between the instantaneous frequency of the fringe pattern and the scale parameter at the wavelet ridge position are also theoretically clarified for the phase gradient method. A simple method for selecting the scale vector is introduced. Computer simulations and experiments reveal the correctness of the clarification and the validity of the proposed method.

Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet

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.

Fringe inverse videogrammetry based on global pose estimation

Fringe inverse videogrammetry based on global pose estimation is presented to measure a three-dimensional (3D) coordinate. The main components involve an LCD screen, a tactile probe equipped with a microcamera, and a portable personal computer. The LCD is utilized to display fringes, a microcamera is installed on the tactile probe, and the 3D coordinate of the center of the probe tip can be calculated through the microcameras pose. Fourier fringe analysis is exploited to complete subpixel location of reference points. A convex-relaxation optimization algorithm is employed to estimate the global camera pose, which guarantees global convergence compared with bundle adjustment, a local pose estimation algorithm. The experiments demonstrate that fringe inverse videogrammetry can measure the 3D coordinate precisely.

Study on wavelet transform profilometry based on fringe projection with two carrier frequencies

We focus on the discussion of Wavelet transform profilometry based on dual-frequency fringe projection in this work. Employing a deformed fringe pattern with dual-frequency components captured by a CCD camera, we can calculate two wavelet ridge-lines from its continuous wavelet transform coefficients. Then, two sets of wrapped phase maps with difference resolution can be extracted. The longer the equivalent wave length is, the lower the measurement accuracy is. However, the direct shape reconstruction is not accuracy from low frequency component even though the fringe order from the low frequency component is easier to obtain correctly than from the high frequency component. Therefore the fringe order from low frequency component is used to guide the calculation of the fringe order of the high frequency component in dual-frequency fringe projection technique. Employing the relationship between the two carriers f2 and f1 (supposing f1<f2). we discuss the structure condition and sampling condition of wavelet transform profilometry based on dual-frequency fringe projection from the aspect of frequency analysis, which guarantee the correct shape reconstruction from the dual-frequency fringe. We finished the theoretical derivation and computer simulations to verify the correction of the theory.