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.
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.
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 .
Phase unwrapping is one of the key steps of optical interferogram analysis.However,implementing phase-unwrapping algorithm(PUA) can be challenging,and the accuracy may be low when it is used to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. When weighted least-squares unwrapping approach is adopted to unwrap the phase,the weighting coefficients are designed and defined to distinguish the singularities regions and normal regions in wrapped phase patterns.The weighting coefficients corresponding to the singularities are given zero-weighted, the singularities will not affect the unwrapping.But weighted least-squares unwrapping approach has the smooth effect on the final phase map.In view of this problem, a Robust Weighted leastsquares phase-unwrapping algorithm is proposed in this paper, which is based on combining the phase correction operation and weighted least-squares(WLS) method.In our method, Two partial derivatives of the wrapped phase are obtained from the fringe patterns. The phase singularities are determined using reliability, and the weighting coefficient is obtained from the binary mask from the reliability mask generated by thresholding method. The Weighted leastsquares phase-unwrapping was solved using the preconditioned conjugate gradient (PCG) method,The result of WLS is used to estimate the fringe order directly.The spatial phase unwrapping algorithm is applied to correct the phase with residual wraps by. Experiments are conducted to prove the validity of the proposed method. Results are analyzed and compared with the other least-squares methods, The experimental results demonstrate that the performance of proposed method.
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.
In order to avoid frequency aliasing,improve the spatial resolution of the phase map in Fourier transform Profilometry(FTP),an approach based on the digital time-multiplexing technique is proposed to remove the background component from the deformed fringe pattern. Firstly, a sinusoidal fringe pattern is projected onto the tested object by digital-light-processing( DLP) projector, the fringe pattern modulated by the object’s surface is captured by a CCD camera.Secondly, apply Fourier transform to the captured fringe pattern to obtain the spectrum. Thirdly, rotate the specimen’s fringe pattern 90-deg to obtain the rotated fringe pattern , then obtain the new spectrum corresponding to the rotated fringe pattern.Fourthly,the new spectrum is subtracted from the original spectrum ,clip the negative going values in the resultant spectrum by digital manipulation.Fifthly, filter out the first-order spectrum from the resultant spectrum by the band filter,apply inverse Fourier transform to the selected spectrum to obtain complex fields,then retrieve the phase, unwrap the wrapped phase map by the phase unwrapping algorithm.Finally, the simulation and experimental evaluations are conducted to prove the validity and performance of the proposed method. The results are analyzed and compared with those of the conventional method.The effectiveness and superiority of the proposed method have been demonstrated and verified.
Digital Speckle correlation method (DSCM) is a computer-vision- based, non-contact, whole-field surface strain measuring method. It is becoming increasingly important as experimental mechanics tool. Its working principle is to compare one digital image of the displaced/deformed surface with the original one using a mathematically well-defined correlation function based on some subset of pixels. In the evolution of DSCM, several methods and techniques have been developed to raise the search speed and precision of DSCM. Typical methods include the coarse-fine search, Newton-Raphson and quasi-Newton method based on optimization theory. However, the coarse-fine search method considers only the rigid body translation displacement, New-Raphson and quasi-Newton is sensitive to the initial values and local extremum. It is possible for Quasi-Newton method to find a local extremum instead of global extremum, even impossible to obtain the extremum because bad initial estimate in iterative computation leads to divergence. The genetic algorithm can be used to optimize the subset correlation globally. But it has large computational workload if it is applied to complete all search procedures for whole speckle pattern. Its convergence velocity becomes the slower and slower along with searching near optimum solution. We present an improved DSCM by hybrid method, which combines the genetic algorithm, quasi-Newton with adjacent point initial estimate. Genetic algorithm is used to obtain the initial estimate for Quasi-Newton iterative method, which be performed only in preliminary search window. Initial estimate for the succedent search subset is obtained by corresponding adjacent point. The simulation experiments have proved the efficiency of the new method.
According to image correlation and stereoscopic vision theory, an improved digital image correlation is proposed, which is called as three dimensional digital marker method. The stereoscopic vision and image correlation techniques are integrated, the symbol point before and after deformation is tracked and registered by image correlation algorithm, three dimensional displacement is restored by the two dimensional displacement component in image plane of both cameras. The new method is an improved version of previous two dimensional digital marker method, which not only has the advantages such as experimental procedure simpleness, wide range of deformation measurement, but also extends the applicable scope. Finally, the proposed method is used to the foam specimen rigid translation. The results show that the new method is capable of measuring three dimensional displacement simply and quickly.
The phase unwrapping is a very difficult problem for profilometry of object containing depth discontinuities. The problem can be resolved with dual-frequency measurement technique. Two measurements with dual different frequencies cannot be contented with real-time demand. A novel profilometry is based on compound grating, generated by computer software, projected by liquid crystal projector, so that the grating with different precision is easily created, conveniently changed. The same purpose is attained as successively capturing two deforming gratings with different frequency. Two phase maps are estimated simultaneously, whose sensitivity to height variation is correlated with the pattern grating frequency. The phase uncertainty of the fine grating can be revised by the phase information coming from the coarse one. Finally, satisfactory experimental results are demonstrated. Meanwhile, it is verified that the new method has such advantages as high speed, accurate unwrapping and extensive measure range.
The shift step must be an accurate value in the traditional algorithm of phase-measuring profilometry technology, the result error is found in unequal step-shifting in which one or more step is not the accurate value. So the phase shifter is expensive to meet the high precision. In this paper, the software is made to give a chart of error phase in any unequal step phase-shifting, and a calibration algorithm is presented to give the correct phase based on this error-phase chart. With the help of computer emulator written by us, the calibration algorihtm based on checking proved to be correct. So the precise request of phase shifter is reduced greatly.
The surface profile is presented various, that forming cause of the specific trace is different. The specific trace is distributed as two types, from its criterion. First, the criterion of the specific trace is large, surpass a millimeter, is called grand specific trace; Second, the criterion is small, more or less the same length micron, is called micron specific trace. Using projection, contracting beam micrography, two-dimensions adusting image mode exchange, low-pass filter off noise, wavelet, and intelligent mode phase reconstruction, the surface profile of recognizing specific trace is given exactly and rapidly, that is a new optical image processing technology in recognition and diagnosis. This paper introduces the speciality above the technology and gave typical examples.
This paper described principle of some projection technologies, attached importance to some measurement technologies in engineering and measurement in complicated profile of fine-micro body. The optoelectronical system and the image processing system are supplied. The typical measurement result are obtained. It is proven that the projection technology is a composite technology, which has extensive applications in many ways.