Temporal Phase Unwrapping Method Research Articles

Dual frequency composite pattern temporal phase unwrapping for 3D surface measurement

Phase shifting profilometry (PSP) is widely used in three-dimensional (3D) optical metrology applications such as mechanical engineering, industrial monitoring, computer vision, and biomedicine because of its high measurement accuracy. In PSP, multi-frequency temporal phase unwrapping (TPU) plays a dominant role due to its high-accuracy measurement of surfaces with discontinuities and isolated objects. However, it requires a large number of fringe patterns. To reduce the number of required patterns, a new dual-frequency composite-pattern TPU method is developed, which needs only three patterns. The new method combines two fringe patterns of different frequencies into three composite fringe patterns, reconstructs rough 3D points by demodulating the low-frequency fringe pattern using geometric constraints, and reprojects it to obtain a rough low-frequency absolute phase, which is then refined to correct edge errors. Finally, the high-frequency wrapped phase is unwrapped under the guidance of the refined low-frequency phase, thereby the accurate 3D points are reconstructed based on stereo-vision technology. Experimental results demonstrated that the proposed method can achieve 3D surface measurement with only three images, which greatly improves the measurement efficiency. The proposed method has great application potential for the rapid 3D measurement of discontinuous surfaces and isolated objects.

Complementary phase interleaving-based fringe order recognition for temporal phase unwrapping

This paper introduces a complementary phase interleaving-based fringe order recognition method, designed to rectify phase errors encountered in temporal phase unwrapping. Addressing challenges arising from noise interference or misalignment between fringe order and the wrapped phase, this method employs an innovative integration of a smooth-wrapped phase and the interleaved complementary phases with precise π phase shifts. Furthermore, it maximizes measurement accuracy and prevents filtering-induced degradation by back-calculating the fringe order of noise-disturbed phases from the smooth-continuous phase. Its remarkable adaptability across various temporal phase unwrapping methods, without necessitating additional structural patterns, underscores its versatility in addressing a broad spectrum of phase error suppression challenges. Experimental validation substantiates the accuracy and adaptability of this method, demonstrating its efficacy in handling diverse types of phase errors within TPU methods. This advancement stands as a pivotal solution for achieving precise and comprehensive phase error suppression, particularly for multiple isolated objects.

Improved two-frequency temporal phase unwrapping method in fringe projection profilometry

Improved two-frequency temporal phase unwrapping method in fringe projection profilometry

Weakly supervised phase unwrapping for single-camera fringe projection profilometry

Phase unwrapping is essential in fringe projection profilometry (FPP). FPP's primary focus is to simultaneously realize high-speed, high-precision three-dimensional (3D) reconstruction. The dual-frequency hierarchical temporal phase unwrapping method (DF-TPU) technique is one prominent technique for accomplishing this goal. However, phase errors are inevitable and typically limit the DF-TPU approach's maximal period number, reducing reconstruction accuracy. The fully supervised approaches based on deep learning can unwrap dual-frequency phase maps of single-camera FPP systems but require accurate labels of high-frequency absolute phase. This study proposes a novel deep learning phase unwrapping scheme suited to single-camera FPP setups. Without the need for accurate labels corresponding to the high-frequency phase maps, supervisory signals are extracted from the high-frequency phase map, the one-period phase map, and the geometry constraint to guide the training of the phase unwrapping network. This training is a weakly supervised learning, which makes the time-consuming and expertise-demanding precise labeling unnecessary. Data collected in multiple real-world circumstances, such as motion blur, isolated objects, non-uniform reflectivity, and phase discontinuities, are used to validate the effectiveness of this weakly supervised method. Experimental results demonstrate that the proposed method outperforms the fully supervised and conventional DF-TPU methods in terms of depth accuracy and measurement efficiency in terms of fringe pattern number.

Temporal phase-unwrapping in fringe projection profilometry: Increasing the accuracy with equidistant long time-steps sampling

Temporal phase-unwrapping methods for fringe projection profilometry, mainly represented by the multi-frequency and multi-wavelength classes, are fundamental to recovering the 3D information from the continuous phase, also allowing measure discontinuities and isolated objects. In this paper, it is proposed a temporal phase unwrapping method for fringe projection profilometry. This method is specially designed to unwrap temporal phase sequences with equidistant long-time steps. As will be shown, this kind of temporal sampling allows increasing the accuracy of measurements. Simulated and real experimental results realized on a flat plate demonstrate the superiority of this proposal compared with leading already reported methods. Also, some experiments with complex objects are presented to demonstrate its applicability.

Temporal phase unwrapping based on unequal phase-shifting code.

In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the 2π ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from N-step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the 2π discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed.

Phase extraction accuracy comparison based on multi-frequency phase-shifting method in fringe projection profilometry

For fringe projection profilometry (FPP), phase extraction accuracy determines three-dimensional (3D) measurement precision. The combination of phase-shifting (PS) and multi-frequency temporal phase unwrapping (MTPU) can reconstruct discontinuous or isolated surfaces with high accuracy and robustness. However, due to the introduction of inevitable random noise, the phase extraction is biased. To this end, this paper firstly compares the wrapped phase errors based on various PS methods in detail. Then, the phase errors and unwrapping reliability based on various dual-frequency temporal phase unwrapping methods are compared. Finally, the effects of three-frequency temporal phase unwrapping and reasonable selection of fringe frequency on phase extraction accuracy are further discussed. The accuracy of the wrapped and unwrapped phase extraction and the phase unwrapping reliability are compared experimentally. This paper can provide a reference for algorithm selection in 3D measurement applications.

Novel absolute phase measurement method with few-patterns

The temporal phase unwrapping method can obtain the absolute phase of an object with large discontinuities and isolated objects in phase measuring profilometry. But it needs many frames fringe patterns, which may consume a significant amount of time in 3D surface measurement. In the light of this problem, we proposed a novel absolute phase measurement method with few-patterns. The proposed method combines an object reflectivity correction and a half-period gray-coded phase unwrapping algorithm. One group of precoded three-step phase-shifting fringe patterns are used to calculate the wrapped phase, divide the whole measurement region into many sub-regions, correct the surface reflectivity of the tested object. A frame of half-period gray-coded pattern and the index number of the sub-region are used to determine the fringe order. The proposed method can obtain a large number of codewords for fringe order without decreasing the intensity level for each stair. To verify the effectiveness of the proposed method, we measured two isolated masks and compared the result with Chen's method [1]. The result shows that the accuracy of our method is similar to Chen's method, but our method has two images less than Chen's method, which improves the measurement speed. Then we measured two complex isolated sculptures. The result shows that our method is also effective for complex surfaces.

Two-frequency phase-shifting method vs. Gray-coded-based method in dynamic fringe projection profilometry: A comparative review

Two-frequency phase-shifting phase unwrapping and Gray-coded-based phase unwrapping are two typical temporal phase unwrapping methods to recover discontinuous or spatially isolated surfaces in fringe projection profilometry (FPP). But in dynamic measurement, environmental noise, required number of patterns and inter-frame motion affect the performance of these two methods on measuring anti-noise ability, efficiency and robustness in varying degrees. So, it is a challenge to quantitatively compare these methods’ abilities and determine the optimum one with appropriate system parameters and under a certain condition. In this paper, a detailed comparative study is conducted for the two-frequency phase-shifting method including hierarchical, number-theoretical and heterodyne approaches and the Gray-coded-based method including traditional Gray code approach, complementary Gray code approach and Gray code approach with tripartite phase unwrapping (Tri-PU). First, the principles of six approaches are reviewed; then, their anti-noise ability was quantitatively compared based on the proposed noise model; next, theoretical comparison of measuring efficiency, comparative review of improved methods and recommendation on usage are given to boost their efficiency; finally, motion-induced error model in phase unwrapping was presented to determine the appropriate system parameters in dynamic measurement. Theoretical analysis, numerical simulation and experimental results are consistent and demonstrate that (i) Gray-coded-based method has better anti-noise ability than two-frequency phase-shifting method; (ii) two-frequency phase-shifting method is more efficient than traditional Gray-coded-based method when the number of encoding fringe periods exceeds 8; (iii) hierarchical approach and Gray-coded approach with Tri-PU have best performance to resist motion-induced error in their respective types of methods. Comparative results can give a helpful guidance to choose the “best” approach in different application scenes and quantitatively determine the projected fringe periods and imaging or projecting speed in dynamic measurement for FPP.

An improved temporal phase unwrapping based on super-grayscale multi-frequency grating projection

Multi-frequency temporal phase unwrapping (TPU) is an essential algorithm in phase-shifting profilometry, especially when measuring surface discontinuities and isolated objects. The unit-frequency phase with primary contour information guides the high-frequency wrapped phase with measured objects' detail information unwrapping. Ordinary, the projected digital grating is of 256-grayscale at most for the 256-grayscale standard of the projector. The digital error will inevitably be introduced into the projection grating, leading to the phase error in each wrapped phase calculation. Using unit-frequency phase with error will directly affect the low-frequency and high-frequency wrapped phases unwrapping, thus limiting the phase unwrapping accuracy to some extent. In this work, by skillfully using the time-division multiplexing characteristic of projector and the integral characteristic of CCD camera, a high accuracy temporal phase unwrapping method based on super-grayscale multi-frequency grating projection is proposed. The expected super-grayscale rather than traditional 256-grayscale multi-frequency gratings are purposefully designed to reduce the digital error initially. The captured realistic super-grayscale patterns can calculate the high-resolution phase information, so that the reliable unit-frequency phase can guide the low-frequency and high-frequency fringe order calculation more precisely, and improve the measurement accuracy initially. The experimental results verify the validity and practicability of the proposed method.

A general phase ambiguity suppression algorithm combining geometric constraints and temporal phase unwrapping

In fringe projection profilometry, various sophisticated temporal phase unwrapping (TPU) methods are conceived to recover a continuous absolute phase map. However, phase ambiguity is a thorny problem that affects measurement accuracy, which is deeply troubled by researchers. Dealing with the challenge, a universal algorithm (G-TPU) uniting geometric constraints phase unwrapping (GCPU) and TPU is proposed to comb out the phase ambiguity. Firstly, The invalid phase map or continuous relative phase map is unwrapped by GCPU with the minimum artifact. Then the unwrapped phas map is divided into several object regions, and the effective phase range (EPR) and invalid phase range (IPR) of each object region are determined by the proposed edge determination and image filling algorithm. Finally, through the statistical analysis of the decoded codewords, the relative orders are added to each EPR and IPR, and the absolute phase map is obtained. The proposed method inherits the complementary advantages of absolute position determination and strong robustness in TPU and GCPU respectively. Since GCPU does not need additional fringe patterns, it can be perfectly integrated into all TPU methods. The experimental results demonstrate the success of the proposed method combining GCPU and TPU.

An Optimizing Diffusion Kernel-Based Binary Encoding Strategy With Genetic Algorithm for Fringe Projection Profilometry

The binary encoding fringe projection profilometry has the potential of achieving high-speed 3-D measurement. Error diffusion is one of the most widely investigated binary encoding techniques. However, the existing error diffusion usually utilizes the same diffusion kernel to encode sinusoidal (S) fringe patterns without considering the fringe pitch-widths, leading to inevitable measurement error due to the demodulated phase error. In this article, a fringe binary encoding strategy based on genetic algorithm is proposed to reduce the phase error recovered by the temporal phase unwrapping (TPU) method. We design an optimization equation that combines phase error and intensity error to calculate the encoding error, which ensures that the optimized diffusion kernel is robust to defocusing changes. Both simulation and experiments have proved the effectiveness and accurateness of the proposed method. Comparative experiments indicate that the extracted phase error is greatly reduced for two types of extensively adopted TPU methods at different defocusing levels. Especially for multi wavelength method, the phase error can be reduced by up to 68%.

Signal-to-noise ratio enhancement of temporal phase unwrapping using video grating projection

Temporal phase unwrapping (TPU) has important application in fringe projection phase-shifting profilometry to measure multi-isolate objects and discontinuities surfaces. Due to the gray-scale standard of the digital projector, the gray-scale of the deformed pattern is of 256 at most. Suppose the frequency of the high-frequency patterns is enlarged for improving accuracy. In that case, it may lead to the vulnerability of intensity noise, particularly in terms of unit-frequency and low-frequency patterns. To some extent, it may challenge the reliable measurement range of the TPU method. To this end, the signal-to-noise ratio (SNR) enhancement of temporal phase unwrapping (SETPU) using video grating projection is proposed. By projecting the specially designed video grating onto the measured object instead of the traditional static grating, adequately controlling the exposure time and the gain of camera allows for the broader gray-scale patterns to be captured. The further analysis shows that the intensity modulation with the SETPU method is more than 3.7 times that with the traditional TPU method, and the SNR with the SETPU method is stronger than that with the traditional TPU method due to the broader gray-scale range so as to efficiently broaden the reliable measurement range of TPU method. The experimental results verify the validity and practicability of the proposed method.

A comparative study on temporal phase unwrapping methods in high-speed fringe projection profilometry

Phase unwrapping, either spatial or temporal, plays an important role in fringe projection profilometry (FPP) to recover a continuous phase map. Compared with the spatial phase unwrapping (SPU), the temporal phase unwrapping (TPU), including multi/two-frequency, phase coding, and gray code methods, is more widely used due to its ability to measure discontinuous objects. However, multiple patterns are required in TPU, which limits the measurement speed and the application of dynamic object measurement. To overcome this problem, different techniques, such as binary defocusing projection, two-plus-one phase-shifting algorithm, geometry/continuity constrained phase unwrapping, and ternary/quaternary gray code phase unwrapping have been proposed and actively studied recently, which either enhance the projection speed or reduce the number of projected patterns. However, there are very few studies on how these techniques affect the accuracy of TPU and which TPU method is most accurate under the scenario of high-speed measurement. This paper compares the accuracy of the two-frequency (TF), phase coding (PC), and gray code (GC) methods with different situations, including the traditional 8-bit focused FPP (aFPP), the high-speed binary defocused FPP (bFPP), and the geometry/continuity constrained binary defocused FPP (cFPP). We classify the phase unwrapping errors caused by system noises into uniformly and non-uniformly distributed errors, and analyze their distributions and rates in different TPU methods and different FPP systems. By comparative simulations and experiments, we find that, for low-frequency phase unwrapping, all the three TPU methods have a good result, while for high-frequency phase unwrapping which is desired in high-quality measurement, GC in aFPP and TF in cFPP provide higher accuracy. Thus, for measurement where accuracy is more concerned than the speed GC in aFPP is preferred, for dynamic measurement where extreme high speed is required, TF in cFPP is suggested.

High-accuracy 3D surface measurement using hybrid multi-frequency composite-pattern temporal phase unwrapping.

Multi-frequency temporal phase unwrapping (TPU) has been extensively used in phase-shifting profilometry (PSP) for the high-accuracy measurement of objects with surface discontinuities and isolated objects. However, a large number of fringe patterns are commonly required. To reduce the number of required patterns, a new hybrid multi-frequency composite-pattern TPU method was developed using fewer patterns than conventional TPU. The new method combines a unit-frequency ramp pattern with three low-frequency phase-shifted fringe patterns to form three composite patterns. These composite patterns are used together with three high-frequency phase-shifted fringe patterns to generate a high-accuracy phase map. The optimal high frequency to achieve high measurement accuracy and reliable phase unwrapping is determined by analyzing the effect of temporal intensity noise on phase error. Experimental results demonstrated that new grayscale hybrid and color hybrid multi-frequency composite-pattern TPU methods can achieve a high-accuracy measurement using only six and three images, respectively.

Unwrapped phase correction for robust 3D scanning.

A temporal phase unwrapping method is proposed to generate an unwrapped phase map for a robust three-dimensional (3D) scan. The proposed algorithm seeks to improve the accuracy of the 3D data points obtained through the phase unwrapping process. By applying the k-nearest-neighbor search method, the error bound of the wrapped phase is controlled with improved flexibility. To achieve the desired scanning quality, a series of fringe patterns is generated with multiple phases at three different frequencies. For this method, the pattern is shifted by utilizing a six-step temporal phase unwrapping process. In this unwrapping process, the error bound is controlled by employing the k-nearest-neighbor search method and spatial comparison method to obtain an accurate fringe order. Through our correction method, the wrapped phases can be unwrapped more accurately and thus enhance the robustness of the scanning system compared to previous phase unwrapping methods.

Reconstruction of isolated moving objects with high 3D frame rate based on phase shifting profilometry

Recently, moving object reconstruction based on PSP has been attracted intensive research. The errors caused by the inner movement of PSP have been addressed successfully. However, when the object with discontinuities or isolated surface is measured and the temporal phase unwrapping method is applied, additional fringe patterns are required to unwrap the phase map. The object movement between the PSP fringe patterns and additional fringe patterns will cause unwrapping errors. This paper proposes a new method to reconstruct the moving object with discontinuous or isolated surface. The object movement is tracked and the influence on the phase map caused by the movement is analyzed. Then, the phase variation caused by the movement is obtained. The phase map of the object before movement is obtained by compensating the phase map of the object after movement based on the phase variations. Finally, the object is reconstructed by dual-frequency phase unwrapping method. A new projection strategy increasing the efficiency of the 3D frame rate is also presented in this paper. The 3D frame rate achieves half of the camera capture speed. The proposed method has high potential to be applied in industrial applications for real-time measurement of moving objects. Experiments are presented to verify the effectiveness.

An arc-clustering-based phase ambiguity estimation method for persistent scatterer interferometry

ABSTRACTThe reliability of persistent scatterer interferometry (PSI) is directly related to the accurate phase unwrapping (PU) of the 3-D (2-D space and time) sparse data stack. Phase ambiguities estimated using temporal phase unwrapping (TPU) are crucially exploited in most 3-D PU algorithms. However, most TPU methods are not noise-robust owing to the independent processing of each arc in the persistent scatterer network. To solve this problem, the cluster-analysis-based PU method for digital elevation model (DEM) construction is adapted to the phase ambiguity estimation problem for PSI in this letter. First, for each arc, the interior relation among phase ambiguities in multiple interferograms is derived to be linear and can be represented by an intercept vector. Subsequently, arcs with the same ambiguities are clustered according to their intercept vectors because arcs with identical phase ambiguities are verified to have the same intercept vectors. Moreover, a more reliable intercept vector can be calculated for each arc cluster by combining the intercept vectors within the cluster. Finally, more precise phase differences are estimated for each cluster using the corresponding intercept vector so that all the arcs are better unwrapped. Both the simulated and real experiments indicate the effectiveness and superiority of the proposed algorithm.

Background and amplitude encoded fringe patterns for 3D surface-shape measurement

This paper presents a new fringe projection method for surface-shape measurement that uses background and amplitude encoded high-frequency fringe patterns. The background and amplitude, combined as a codeword, identify the wrapped phase fringe order to partially unwrap the phase to a low frequency. The low-frequency wrapped phase map is then directly used to reconstruct the surface based on geometry constraints without requiring additional images as in other temporal phase-unwrapping methods. Measurements performed on a double-hemisphere, mask, and manikin head, using projected fringe patterns with 48 periods, demonstrated the ability of the method to perform 3D shape measurement with only four projected patterns and captured images, using a single camera and projector.

Temporal phase unwrapping for fringe projection profilometry aided by recursion of Chebyshev polynomials

This paper presents a temporal phase-unwrapping method for fringe projection profilometry. With it, a sequence of phase-shifting fringe patterns is projected onto the measured object for getting the wrapped phase map and achieving a high measurement resolution, and an additional sequence corresponding to Chebyshev polynomials is used for determining their fringe orders. For effectuating this method, we deduce an algorithm by use of the recursive property of Chebyshev polynomials. This algorithm, combined with a correction operation in the least-squares sense, allows us to accurately estimate the fringe orders in the presence of noise. Experimental results demonstrate the proposed method to be effective in restoring the absolute phase maps of fringe patterns.