Canlin Zhou

Enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm

Abstract Measuring objects with large reflectivity variations across their surface is one of the open challenges in phase measurement profilometry (PMP). Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to phase fluctuations and errors. Jiang et al. proposed a high dynamic range real-time three-dimensional (3D) shape measurement method (Jiang et al., 2016) [17] that does not require changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval whenever any of the regular fringe patterns are saturated. Nonetheless, Jiangs method has some drawbacks: (1) the phases of saturated pixels are estimated by different formulas on a case by case basis; in other words, the method lacks a universal formula; (2) it cannot be extended to the four-step phase-shifting algorithm, because inverted fringe patterns are the repetition of regular fringe patterns; (3) for every pixel in the fringe patterns, only three unsaturated intensity values can be chosen for phase demodulation, leaving the other unsaturated ones idle. We propose a method to enhance high dynamic range 3D shape measurement based on a generalized phase-shifting algorithm, which combines the complementary techniques of inverted and regular fringe patterns with a generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely the regular and the inverted fringe patterns, are projected and collected. Then, all unsaturated intensity values at the same camera pixel from two sets of fringe patterns are selected and employed to retrieve the phase using a generalized phase-shifting algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Jiangs method, demonstrating that our method not only expands the scope of Jiangs method, but also improves measurement accuracy.

Precise and fast phase wraps reduction in fringe projection profilometry

Abstract Phase wraps in a 2D wrapped phase map can be completely eliminated or greatly reduced by frequency shifting. But it usually cannot be optimally reduced using conventional fast Fourier transform (FFT) because the spectrum can be shifted only by a integer number in the frequency domain. In order to achieve a significant phase wrap reduction, we propose a fast and precise two-step method for phase wraps reduction in this paper, which is based on the iterative local discrete Fourier transform (DFT). Firstly, initial estimate of the frequency peak is obtained by FFT. Then sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial peak location. Finally, frequency shifting algorithm that operates in the spatial domain is used to eliminate phase wraps. Simulations and experiments are conducted to demonstrate the superb computing efficiency and overall performance of the proposed method.

Enhanced two-frequency phase-shifting method based on generalized phase-shifting algorithm

Abstract In this paper, we develop a novel dual-frequency pattern which not only releases the restriction of conventional two-frequency phase-shifting algorithm that at least six fringe patterns are needed, but reduces the noise impact by decreasing the frequency ratio between the high- and low-components. To decrease the number of necessary patterns to five, a novel composite dual-frequency pattern scheme combining together a high- with a low-frequency pattern is employed. To make the algorithm less sensitivity to noise, the low-frequency component is with more than one period fringes, which is relatively prone to recover the continuous result by simple spatial phase unwrapping approach. Besides, the restriction of special phase shifts between two-frequency components in conventional methods is released by the generalized phase-shifting algorithm. Simulations and experiments are conducted to demonstrate that in addition to maintaining the minimum number of patterns, the proposed method reveals higher accuracy of phase retrieval.

Modified Fourier transform profilometry based on digital time-multiplexing technique

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.

Simple tilt compensation algorithm for off-axis digital holography

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.

Enhanced dual-frequency pattern scheme based on spatial-temporal fringes method

Abstract One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method.

Extended Depth-range Dual-wavelength Interferometry Based on Iterative Two-step Temporal Phase-unwrapping

Abstract For dual-wavelength interferometry (DWI), we propose an extended depth-range phase-shifting interferometry technique of extracting phase distributions from randomly phase-shifted interferograms. First, the generalized phase-shifting algorithm is utilized to retrieve the single-wavelength phase from interferograms with random phase shifts. Then, the phase difference and phase-sum are calculated from the wrapped single-wavelength phases, and iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum. Finally, the height of objects is determined. Simulations and experiments are conducted to demonstrate the excellent precision and overall performance of the proposed method. As the limitation of being exclusively applicable to interferograms with special phase shifts is broken, the proposed method will greatly facilitate the practical application of DWI. Furthermore, because the phase-sum and iterative two-step temporal phase-unwrapping is introduced to extend the depth-range, the sensitivity and precision of the retrieved phase are greatly improved.

Robust wrapping-free phase retrieval method based on weighted least squares method

Abstract Phase unwrapping is one of the most challenging processes in many profilometry techniques. To sidestep the phase unwrapping process, Perciante et al. (2015) proposed a wrapping-free method to retrieve the phase based on the direct integration of the spatial derivatives of the fringe patterns. However, this method is only applicable to objects with phase continuity, so it may fail to handle fringe patterns containing complicated singularities such as noise, shadows, shears and surface discontinuities. In the light of this problems, a robust wrapping-free phase retrieval method is proposed that is based on the combined use of Perciantes method and the weighted least squares method. Two partial derivatives of the desired phase are obtained from the fringe patterns, while the carrier is eliminated using the direct phase difference method. The phase singularities are determined using a derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Perciantes method demonstrating that in addition to maintaining the advantage of sidestepping the phase unwrapping process, the proposed method is available for measuring objects with some types of singularities sources.

A simple spatial domain algorithm to increase the residues of wrapped phase maps

Abstract In phase unwrapping, the locations and densities of the residues are indicative of the severity of the unwrapping problem. Gdeisat et al. proposed an algorithm to increase the number of residues in a wrapped phase map to improve the results of phase unwrapping. The method proposed, though, is extremely time-consuming involving the computation of a Fourier transform along with the selection and shift of its spectral components. Moreover, there is no theoretical analysis on the reasons why the frequency shift should be able to increase the number of residues. In an attempt to address these problems, we propose a simple algorithm to increase the number of residues in a wrapped phase map. The algorithm uses a simple multiply operation in spatial domain to realize the frequency shift exploiting the frequency shift property of Fourier transform. We also discuss the relationship between the number of residues and frequency shift. Experimental results have demonstrated that the proposed method can speed up by more than 50% of the calculation time.

Improved phase-unwrapping method using geometric constraints

Abstract Conventional dual-frequency fringe projection algorithm often suffers from phase unwrapping failure when the frequency ratio between the high frequency and the low one is too large. Zhang et al. proposed an enhanced two-frequency phase-shifting method to use geometric constraints of digital fringe projection (DFP) to reduce the noise impact due to the large frequency ratio. However, this method needs to calibrate the DFP system and calculate the minimum phase map at the nearest position from the camera perspective, these procedures are relatively complex and more time-consuming. In this paper, we proposed an improved method, which eliminates the system calibration and determination in Zhang’s method, meanwhile does not need to use the low-frequency fringe pattern. In the proposed method, we only need a set of high-frequency fringe patterns to measure the object after the high frequency is directly estimated by the experiment. Thus, the proposed method can simplify the procedure and improve the speed. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The results demonstrate that the proposed method can overcome the main disadvantages encountered by Zhang’s method.