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.

To determine the shape of a complex object with vertical measurement mode and higher accuracy, a novel modulation measuring profilometry realizing auto-synchronous phase shifting and vertical scanning is proposed. Coaxial optical system for projection and observation instead of triangulation system is adopted to avoid shadow and occlusion. In the projecting system, sinusoidal grating is perpendicular to optical axis. For moving the grating along a direction at a certain angle to optical axis, 1D precision translation platform is applied to achieve purposes of both phase-shifting and vertical scanning. A series of fringe patterns with different modulation variations are captured by a CCD camera while scanning. The profile of the tested object can be reconstructed by the relationship between the height values and the modulation distributions. Unlike the previous method based on Fourier transform for 2D fringe pattern, the modulation maps are calculated from the intensity curve formed by the points with definite pixel coordinates in the captured fringe patterns. The paper gives the principle of the proposed method, the set-up of measurement system and the method for system calibration. Computer simulation and experiment results proved its feasibility.

In this paper, a fast rotary mechanical projector (RMP) is designed and manufactured for high-speed 3D shape measurement. Compared with the common high-speed projectors, RMP has a good performance in high-speed projection, which can obtain high quality projected fringes with shorter camera exposure time by using the error diffusion binary coding method and chrome plating technology. The magnitude, acceptability of systemic projection error is analyzed and quantified in detail. For the quantified error, the probability distribution function (PDF) algorithm is introduced to correct the error. Corrected projection error is reduced to more than one third of the original error. Subsequently, a monocular measurement system composed of the RMP and a single camera is constructed. The combination of the RMP device and PDF algorithm ensure the accuracy of a corresponding 3D shape measurement system. Experiments have demonstrated that the proposed solution has a good performance for the 3D measurement of high-speed scenes.

The high-speed three-dimensional (3-D) shape measurement technique has become more and more popular recently, because of the strong demand for dynamic scene measurement. The single-shot nature of Fourier Transform Profilometry (FTP) makes it highly suitable for the 3-D shape measurement of dynamic scenes. However, due to the band-pass filter, FTP method has limitations for measuring objects with sharp edges, abrupt change or non-uniform reflectivity. In this paper, an improved Temporal Fourier Transform Profilometry (TFTP) algorithm combined with the 3-D phase unwrapping algorithm based on a reference plane is presented, and the measurement of one deformed fringe pattern producing a new 3-D shape of an isolated abrupt objects has been achieved. Improved TFTP method avoids band-pass filter in spatial domain and unwraps 3-D phase distribution along the temporal axis based on the reference plane. The high-frequency information of the measured object can be well preserved, and each pixel is processed separately. Experiments verify that our method can be well applied to a dynamic 3-D shape measurement with isolated, sharp edges or abrupt change. A high-speed and low-cost structured light pattern sequence projection has also been presented, it is capable of projection frequencies in the kHz level. Using the proposed 3-D shape measurement algorithm with the self-made mechanical projector, we demonstrated dynamic 3-D reconstruction with a rate of 297 Hz, which is mainly limited by the speed of the camera.

The S-transform, conceptually viewed as an extension of the short-time Fourier transform and the wavelet transform, features a time-frequency representation known for its local spectral property and multiresolution strategy. It has been introduced in optical three-dimensional shape measurement based on a fringe projection technique recently. In this paper, an application of S-transform for demodulating fringe patterns affected by the nonlinearity has been discussed. Two methods based on the S-transform, called S-transform ridge method and S-transform filtering method, are used to eliminate the phase errors caused by nonlinear factors of the projector and CCD camera. The theoretical representations of S-transform ridge method and S-transform filtering method in fringe analysis are given. The computer simulation and experiment are carried out to verify our research. Compared with the reconstructions of the windowed Fourier transform, the wavelet transform and the S-transform ridge method, the S-transform filtering method gives a better result under considering the influence of the fringe nonlinearity.