DEFORMATION MEASUREMENT USING DUAL-FREQUENCY PROJECTION GRATING PHASE-SHIFT PROFILOMETRY

2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to solve such an issue. In the measurement, two properchosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.

Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.

Measurement of a discontinuous object based on a dual-frequency grating

The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed： one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.

Automated Phase-measuring Profilometry of 3-D Diffuse Objects Using a Single Phase Step Method

The technique of phase measuring profilometry using a single phase step method is proposed.This method can automatically obtain phase value at each pixel by using a discret cosine transform algorithm.The method is able to automatically recognize any position between depression and elevation on an object surface.Theoretical analysis and experimental verification are presented.

Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry

This study describes a novel fringe-shaping technique developed to alleviate the fringe truncation problem engendered by the acquired saturated and/or weak fringe images from high-/low-reflectance surfaces of three-dimensional（3D） objects in phase-shifting profilometry. The particle swarm optimization algorithm is employed to perform the recovery of the truncated fringes with optimal fitting for compensation after single-trial acquisition. The results show that the proposed method improves phase recovery accuracy to accomplish 3 D surface reconstruction with only one set of phase-shifting fringes under different truncation sceneries.

Generic and flexible self-correction method for nonlinearity-induced phase error in three-dimensional imaging

In three-dimensional imaging employing phase-shifting profilometry(PSP), the nonlinear response of projector and camera makes the fringe gray distribution non-sinusoidal, which further leads to phase error. Although the double 3-step phaseshifting method is simple and effective, it needs to add an additional set of fringe sequences, which reduces the measurement efficiency. To this end, this paper introduces a generic and flexible self-correction method for nonlinearity-induced phase error.First, according to the nonlinearity-induced phase error model, we introduce an additional wrapped phase with a phase difference of π/3. The error waveform of the two wrapped phases is opposite but not coincident. Then, we introduce an estimation algorithm for the additional wrapped phase offset. Finally, we fuse the two wrapped phases to correct the phase error. Experiments confirm that the root mean squared error of the proposed method is 64.1% lower than that of the traditional method and 13.3% lower than that of the Hilbert transform method. The proposed method does not require any additional fringes or hardware assistance and can be easily extended to 4-step or 5-step PSP.