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Structured-lighting projection methods are the important parts of the optical three-dimensional (3D) measurement. Phase-shifting profilometry has a higher accuracy,however it requires multiple phase-shifting sinusoidal patterns’ projection,it can only be used for static measurement. The 3D shape measurement of dynamic objects is a challenging issue and attracts many scholars’ attention. The single frame 3D reconstruction technique (such as the Fourier transform, color-encoded or composite coded grating method and single frame Moiré retrieval method) can meet the requirements of dynamic measurement well since only one-frame deformed pattern is required to obtain the 3D information of the object, but there are still issues in the stability and accuracy when using these methods. Recently, Wang et. al. [26] presented a high-speed Moiré-based phase retrieval method. However, it is used only to measure the thin objects. Inspired by reference 27, we combined phase-shifting, moire algorithm and reconstruction algorithm of complex Fast Fourier Transform (FFT), proposed a dynamic three-dimensional (3D) measurement based on four-step phase-shifting Moiré algorithm. Only one fringe pattern of the object was required to reconstruct the 3D shape of the tested object after the four fringe patterns with a π /2 phase shift of the reference plane were captured in advance. Only a single Fourier transform of a complex fringe composed of two multiplexed fringe patterns is calculated,the calculation time of the inverse 2D FFT is decreased due to the smaller calculated data matrix. First, four sinusoidal fringe patterns with a π/2 phase-shift are projected on the reference plane and acquired four deformed fringe patterns of the reference plane. Then single-shot deformed fringe pattern of the tested object is captured in measurement process. Four Moiré fringe patterns can be obtained by numerical multiplication between the the AC component of the object pattern and the alternating components(AC) of the reference patterns respectively. The four low-frequency components corresponding to the Moiré fringe patterns are calculated by the complex encoding FT (Fourier transform) ,spectrum filtering and inverse FT. Thus the four phase-shifting Moiré fringe patterns can be retrieved. Then the wrapped phase of the object can be determined in the tangent form from the four phase shifting Moiré fringe patterns using the four-step phase shifting algorithm.The continuous phase distribution can be obtained by the phase unwrapping algorithm.The 3D shape distribution can be reconstructed according to the phase-to height mapping relation after the calibration of the system. Finally, experiments are conducted to prove the validity of the proposed method. The results demonstrate that our method not only can expand the measurement scope, but also can improve accuracy and speed.
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