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.  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.
The phase-shifting method is widely used in fringe projection profilometry (FPP),The digital light projector (DLP) and charge coupled device (CCD) are generally nonlinear devices.The captured fringes do not have a good sinusoidal property,which leads to errors in the retrieved phase map.The methods to calibrate the nonlinear response of a FPP and compensate for the associated error can be classified into active methods(correction before pattern projection) and passive methods(correction after pattern projection).The basic idea of the active method to precisely obtain the input output relation function of the projector. The passive method compensates the error in phase domain by the post-processing algorithms. Huang et. al. presented the double three-step phase shifting algorithm to reduce the nonlinear phase error by projecting two groups of three-step phase-shifting fringe with an initial phase offset of 60 degree.Subsequently,some scholars improved this method. Zheng et.al. presented a method that combined the two wrapped phases to obtain the combination of the wrapped phase,it is simpler than Huang’s method because only one time phase unwrapping procedure is needed. Lei et. al. combined double-step phase-shifting method and multifrequency temporal phase unwrapping algorithm, proposed a multi-frequency inverse-phase method to realize the 3D shape measurement of the complicated objects. Mao proposed a similar approach.The main difference between Lei and Mao is that the operation order of double-step phase-shifting algorithm for error compensation is different. In Mao’s method,error compensation is performed in the wrapped phase map while it is done with the unwrapped phase map in Lei’s method.This paper compares double-step phase-shifting algorithm, its variational algorithm (Zheng's method, Lei’ s method, Mao's method) and phase shift algorithm with twice the number of steps for nonlinear error compensation, our study finds that these algorithms have similar effect in reducing nonlinear phase error. Phase shift algorithm with twice the number of steps is simpler and more direct than double-step phase-shifting algorithm.In variational algorithm, Zheng’s method reduces the number of phase unwrapping by half compared with traditional double-step phase shifting algorithm,Mao’s method is essentially the same as Lei’s method,it was by introducing multi-frequency temporal phase unwrapping algorithm that Lei and Mao's method can measure the complex object. Experimental results are presented to demonstrate the rationality of this analysis.
Digital holography is a powerful tool for noncontact quantitative phase imaging. According to the relative incident angle between the object beam and the reference beam, digital holography is grouped into on-axis and off-axis digital holography, The measurable area is narrow in off-axis digital holography, on-axis digital holography suffers from image blurring. Phase-shifting technique is usually used to obtain the high-quality object image. However, the phase shifting technique requires to record multiple phase-shifted holograms. The most conventional holography configuration requires a separately generated reference and object beams that result in a low stability. The paper presents an One-shot common-path phase-shifting holography based on micro polarizer camera and large-shearing Wollaston Prism. The system employs a commercial micro polarizer camera and a doubly-refractive prism with large shearing. The Wollaston prism separates the incoming beam into two orthogonally polarized components ,brings the reference and object from the two-windows to overlap at the lateral shearing region. The two light beams transmit through the quarter wave plate(QWP) and pixelated micro polarizer array(PMA) camera, QWP is used to transform the orthogonally polarized light into orthogonal circular components, The circular polarizations interfere at CCD after passing through the micro polarizer array. The data captured by PMA camera can be parsed into four phase shifting fringe images corresponding to each direction of the four polarizations. The interpolation method is used to obtain the same resolution as the original image. The phase distribution of the specimen can be retrieved using the four-step algorithm. Finally, experiments are conducted to prove the validity of the proposed method. The results demonstrate the capability and applicability of the system .
Digital holography is a powerful tool for non-contact quantitative phase imaging. Off-axis configuration remains a popular choice among the digital holography systems due to its ability to separate the dc and cross-terms in the recorded hologram in Fourier spectral space.However, compensating the off-axis tilt of the reference wave is one of the open challenges in the off-axis digital holography.Deng et al. proposed an off-axis tilt compensation method based on hologram rotation [DENG et.al. Opt. Let., 2017]. The off-axis tilt is removed by subtracting the phase of the digital reference hologram obtained by rotating the original specimen’s hologram from the retrieved phase corresponding to the original hologram. Nonetheless, Deng’s method is extremely time consuming due to the computation of Fourier transform,inverse Fourier transform and phase unwrapping for many times. In this paper, we propose a simple algorithm to compensate the off-axis tilt . Firstly, apply Fourier transform to the original off-axis hologram, filter out the first-order spectrum by band filter, then determine directly the spectrum of digital reference hologram from the spectrum of the original hologram, then filter out the first-order spectrum from the spectrum of digital reference hologram, apply inverse Fourier transform to the two first-order spectra to obtain two complex fields, then retrieve directly the phase difference from the two complex fields using the direct phase difference algorithm, then unwrap the wrapped phase map by the phase unwrapping algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Deng’s method, demonstrating that our method not only can speed up by more than 50% the calculation time, but also can improve measurement accuracy.