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Multitemporal synthetic aperture radar interferometry (MT-InSAR), capable of detecting both surface deformation and elevation with high precision, is used for many applications in earth observation. Conventional synthetic aperture radar (SAR) missions with a single beam only detect deformation along the line of sight (LOS) and relative elevation due to the undetermined model of phase wrapping. In a multisatellite SAR mission, measurements from different SAR geometry improve the sensitivity of the detectable deformation, especially to the deformation along the north-south (N-S) direction. However, it is difficult to combine the measurements from varying viewing angles since the absolute phase cannot be reconstructed without a ground control point. In this article, a tri-beam SAR system is introduced to detect 3-D deformation and derive multiview 3-D surface model from a single spaceborne platform. The accuracy of the 3-D deformation from the tri-beam SAR is exploited with varying squint and incident angles to obtain the optimal parameters of the three beams. Then a multidimensional coherent scattering model is used to simulate the multitemporal SAR data with different viewing angles. Regarding the tri-beam SAR, potential applications in earth observation including 3-D deformation monitoring, geodetic stereo SAR, and multiview 3-D forest reconstruction are investigated subsequently. The results of this study indicate that the tri-beam SAR is able to measure 3-D deformation and reconstruct 3-D surface model without ground control point.

The recent, sharp increase in the availability of interferometric data captured by different synthetic aperture radar (SAR) interferometry (InSAR) sensors poses a new scientific question that whether there is a processing framework that can combine these observations to obtain a more credible InSAR product (i.e., digital elevation model (DEM) and surface deformation estimation). In this article, we extend our previous two-stage programming-based multibaseline processing framework for combining the interferograms generated from disparate InSAR systems with different system parameters to enhance the InSAR performance at the signal processing stage. The proposed multisystem interferometric data fusion framework, abbreviated as TSDFF, includes three processing steps: multisystem interferogram registration, multisystem phase unwrapping, and absolute phase fusing. The advantage of TSDFF is that it can allow the data sets from different InSAR sensors to help each other to get rid of the limitation of the Itoh condition so that the application scope of each InSAR sensor will be effectively enlarged (e.g., measuring violent surface change or mountainous DEM). In addition, to quantitatively analyze the measurement bias robustness bound of TSDFF, the TSDFF-Fusion theorem is proposed, which offers significant application guidance for TSDFF at different noise levels. The real and simulated experimental results reveal the effectiveness of TSDFF for fusing the data sets from disparate InSAR systems.

Phase retrieval is to calculate the phase from the direct information of the intensity of focus and defocus. Classical methods include the phase retrieval algorithm based on the transport of intensity equation (TIE) and iteration. The phase retrieval algorithm based on TIE can directly obtain the absolute phase without reference beam and phase unwrapping but is sensitive to noise. On the other hand, the intensity difference method needs to be used to approximate the intensity differential when solving the algorithm. Therefore, the defocus distance between intensity images has great influence on the accuracy of retrieval results. The phase retrieval algorithm based on TIE will be limited if it is extended to the phase retrieval of large objects. In order to widen its application range, an adaptive phase retrieval algorithm based on convolutional neural network under all defocus distances is proposed. The new algorithm consists of two important components: phase retrieval algorithm module and convolutional neural network optimization module. Firstly, the preliminary retrieval results are obtained by the phase retrieval algorithm module at different defocus distances, and then the accuracy of the results is further improved by the convolutional neural network module. The experimental results illustrate that the proposed algorithm is not only suitable for different defocus distances but also has good accuracy and stability.

Accurate and stable time and frequency transfer (TFT) is typically required in distributed sensing. While this has historically been a limiting factor in the design of netted radars, the rise of modern TFT techniques has paved the way to nanosecond level time accuracy, absolute phase synchronization, and sub-Hertz frequency accuracy. In particular, netted systems composed of mobile nodes have benefited immensely from TFT based on global navigation satellite systems (GNSS). However, GNSS systems are liable to denial of service interruption. This article demonstrates the use of a fiber-optic White Rabbit (WR) network in an operational multistatic radar—NeXtRAD, and directly compares the results to one-way multichannel GPS disciplined oscillators acting under common-view TFT.

Distribution of a high-stability clock signal is an important topic for many applications. Recently, optical frequency comb transfer through outdoor atmosphere has become a valuable tool for the clock distribution due to its versatility. To extend the benefits of comb-based open-air clock distribution, one-way radiofrequency (RF) transfer with a single optical frequency comb is an attractive approach due to its simplicity and broad application span. Here, we transfer an L-band RF signal across 820-m-scale outdoor beam path with a single optical frequency comb. We measured the absolute phase noise of the transferred RF signal, and analyzed it with Kolmogorov’s f −8/3 power law and Taylor’s hypothesis of frozen turbulence. We also show that the residual-phase noise of the transferred RF signal can be suppressed to the femtosecond regime by a delay-locked loop. Our results may benefit remote ranging at km-range, inter-building clock distribution, and optical communication through aerial drones.

To overcome the invalid phase and phase jump phenomenon generated during the phase unwrapping, a phase error correction method based on the Gaussian filtering algorithm and intensity variance is proposed in this paper. First, a threshold of fringe intensity variance is set to identify and clear the phase in the invalid region. Then, the Gaussian filtering algorithm is employed to correct the phase order at the fringe junction, and then the absolute phase is corrected. Finally, the phase correction experiments of different geometric objects are carried out to verify the feasibility and accuracy of the proposed method. The method proposed in this paper can be extended to the correction of absolute phase error obtained by any coding method.

The phase-coding method for absolute phase measurement possesses a strong robustness because its codewords are encoded into phase domain rather than intensity. However, a misalignment problem arise...

This article establishes sufficient conditions for the uniqueness of AC power flow solutions via the monotonic relationship between real power flow and the phase angle difference. More specifically, we prove that the $P-\Theta$ power flow problem has at most one solution for any acyclic or GSP graph. In addition, for arbitrary cyclic power networks, we show that multiple distinct solutions cannot exist under the assumption that angle differences across the lines are bounded by some limit related to the maximal girth of the network. In these cases, a vector of voltage phase angles can be uniquely determined (up to an absolute phase shift) given a vector of real power injections within the realizable range. The implication of this result for the classical power flow analysis is that under the conditions specified above, the problem has a unique physically realizable solution if the phasor voltage magnitudes are fixed. We also introduce a series–parallel operator and show that this operator obtains a reduced and easier-to-analyze model for the power system without changing the uniqueness of power flow solutions.

Codewords used to determine fringe orders are significant for absolute phase retrieval based on the phase-coding method. However, because of inevitable interference from image blurring, image noise, and system nonlinearity, it is challenging to significantly increase the number of codewords for high-accuracy phase retrieval. To address this challenge, this article proposes a joint coding strategy to perform the coding of high-density stripes. More specifically, codewords are simultaneously embedded into the phase domain and the intensity domain of composite fringe patterns, which greatly extends the encoding range of valid codewords. Moreover, to improve the anti-interference capability of the proposed coding strategy, a regional correction technique (RCT) is presented to remove jump phase errors induced by the inevitable interference. The results of experiments indicate that the proposed method is effective and accurate for both complex objects and a standard sphere.

Phase unwrapping (PU) has always been a critical and challenging step in interferometric synthetic aperture radar (InSAR) data processing. Inspired by existing research, i.e., the PGNet, we propose a novel quality-guided 2-D InSAR PU method via deep learning, and regard PU as a two-stage process. In the first stage, the ambiguity gradient is estimated using the proposed global attention U-Net (GAUNet) architecture, which combines the classic U-Net structure and global attention mechanism. Then, in the second stage, the classical PU framework (e.g., the L1- or L2-norm) is applied as a post-processing operation to retrieve the absolute phase. Since class imbalance is a key factor affecting the estimation of ambiguity gradient, different strategies based on four commonly used quality maps are adopted to deal with the problem. The quality map is not only input as additional information for the guidance of the training process, but also participates in the construction of loss function. As a result, GAUNet can pay more attention to the nonzero ambiguity gradients. By using the number of residues as the evaluation metric, we can choose the optimum strategy for the restoration of the absolute phase. In addition to the simulated interferograms, the proposed method is tested both on a real topographic interferogram exhibiting rugged topography and phase aliasing and a differential interferogram measuring the deformation from MW 6.9 Hawaii earthquake, all yield state-of-art performance when comparing with the widely used traditional 2-D PU methods.

The traditional 3d reconstruction method of stereo vision is based on image feature point extraction, but it is very inconvenient to extract feature points in more complex cases, and the reconstructed 3D information is not comprehensive. In this paper, a 3d reconstruction method based on three-frequency heterodyne four-step phase shift method is proposed. System parameters is obtained by binocular calibration algorithm first, and then using digital grating projector to the object under test of three groups of different frequency phase shift fringe and collecting images, using the four step phase-shift and three phase frequency heterodyne method to get the main value and get the absolute phase of continuous distribution, combining with the polar correction and phase matching reconstruction of 3 d point cloud data of the object to be tested, finally complete 3 d measurement in 3 d software. The experimental results show that the system can realize 3d dimension measurement of heterogeneous castings with high detection efficiency.

Temporal phase unwrapping is among the most robust and efficient phase unwrapping methods in fringe projection profilometry. They can recover the fringe orders even in the presence of surface discontinuities. However, fringe order errors may occur due to phase noise and poor measurement conditions. Such errors often exhibit an impulsive nature and introduce errors to the absolute phase map. Most existing fringe order error correction methods detect and correct the errors in a pixel-by-pixel manner, which may under-utilize the correlation of the fringe orders on different pixels. In this paper, we propose a new method to cope with the fringe order errors associated with temporal phase unwrapping. By exploiting the low-rankness of the fringe order map and sparse nature of the impulsive fringe order errors, we develop a robust principal component analysis (RPCA)-based approach to remove the impulsive fringe order errors. Experiments demonstrate that the proposed method is valid in eliminating the fringe order errors.

The direct measurement of distance-dependent information between wireless units represents a challenge for wireless locating systems, because it requires the exact time synchronization of separate wireless units. To avoid these synchronization efforts, many wireless locating systems only evaluate phase difference of arrival (PDOA) measurements. While simple PDOA localization techniques rely on multiangulation, advanced PDOA concepts like the holographic extended Kalman filter (HEKF) directly evaluate the measured phases without non-linear preprocessing. However, these differential phase measurement approaches are less sensitive than systems that can measure absolute phase variations, which allow the tracking of much smaller position changes than the signal’s carrier wavelength. This paper proposes to extend the HEKF by the evaluation of absolute phases in an incoherent measurement setup, which consists of a continuous wave (CW) beacon and several receivers. The developed quasi-coherent holographic extended Kalman filter (QCHEKF) uses the overdetermined PDOA measurements to estimate the phase–frequency relation between each beacon–receiver pair. Then, the established phase–frequency relations allow the evaluation of absolute phase measurements and, thus, the accurate localization and tracking of a simple, unsynchronized, narrowband CW beacon, even under severe multipath conditions. This novel concept is experimentally validated via 3D localization results in a challenging indoor scenario using a 24 GHz CW measurement setup. Here, the QCHEKF improves the achieved localization accuracy in comparison to the HEKF by 35 % from 0.78 cm to 0.51 cm, while the maximum deviation from the trajectory reduces by 68 % from 5 cm to 1.6 cm. Furthermore, the QCHEKF enables the exact tracking of fast changes in direction, which is usually a significant challenge for standard wireless target tracking systems.

This article provides a detailed presentation of the dual-aperture synthetic aperture radar (SAR) data processing scheme for the retrieval of ocean surface radial velocities.This scheme includes processing of raw SAR data, coregistration of along-track interferometric samples, magnitude and absolute phase calibration, and coherent averaging (multilooking). Several approaches for the absolute phase calibration are provided and compared. Some of the attempted approaches can potentially be used over open ocean (i.e., in scenes that do not contain any land). Main goal of attempting different approaches for the absolute phase calibration was to determine their relative performance, and determine the potential feasibility of some approaches over open ocean. The data processing scheme is applied to a RADARSAT-2 dual-channel MODEX-1 acquisition over a section of the Florida Current. For the dataset used in this study, different absolute phase calibration methods yielded similar radial velocity estimates, with relative mean and RMS differences within approximately 0.1 m/s. Estimates from SAR ATI were also compared to estimates from NASA’s OSCAR dataset. Comparison of visually identified currents showed close spatial overlap between estimates from the two sources. The RMS difference was found to be approximately 0.30 m/s. This difference can be attributed to the physical and temporal differences between the estimates.

Phase unwrapping is a fundamental task in phase-based profilometry. Existing spatial and temporal approaches are facing challenges such as error propagation and low efficiency. In this study, the authors propose a learning-based method that uses a support vector machine (SVM) to perform phase unwrapping, where the problem is solved as a classification task. To be specific, seven elements, extracted from the captured patterns and the wrapped phase, form the input feature vector and the fringe order is the output class. Besides, a radial basis function kernel SVM is adopted as the model. The proposed method is conducted independently for every pixel, and does not suffer from error propagation in the spatial unwrapping. Moreover, it needs fewer patterns than temporal unwrapping since only one phase map is required. Simulation and experimental results demonstrate that the proposed scheme produces precise depth maps, which are comparable with the complex quality-guided methods but at a much faster speed.

Two-dimensional phase unwrapping (2-D PU) is one of the key processes in reconstructing the topography or displacement of the Earth surface from its interferometric synthetic aperture radar (InSAR) data. Estimating the absolute phase gradient information is an unavoidable step utilized by almost all the 2-D PU methods. Traditionally, the gradient estimation step relies on the phase continuity assumption, which requests that the observed area has spatial continuity. However, the abrupt topographic changes and system noise usually results in the failure of the phase continuity assumption in reality. Under this condition, it is difficult for the traditional 2-D PU to provide the correct absolute phase over the area with abrupt interferometric fringe change or with strong system noise. To solve the issue, we propose a novel deep convolutional neural network (DCNN), abbreviated as PGNet, to estimate the phase gradient information instead of the phase continuity assumption in this article. The major advantage of PGNet lies in its deep architecture to learn the characteristics of phase gradients from enormous training images with different noise levels and topographic features. Subsequently, the $L^{1}$ -norm objective function is used to minimize the difference between unwrapped phase gradients and the gradients estimated by PGNet for obtaining the final PU result. Taking the phase gradient pattern of the TerraSAR-X-TanDEM-X interferogram as the learning object, experimental results demonstrate the absolute phase gradient estimated by PGNet is more credible than that from the phase continuity assumption such that the corresponding PU result outperforms those obtained by the traditional 2-D PU methods.

In the ultra-precision manufacturing of large optics, industrial robots have the potential to become an intelligent and economical choice of surface polishing. However, the transport of the workpieces between the polishing platform and the measurement instrument seriously limits the manufacturing efficiency. Therefore, an in-situ measurement system based on the monoscopic deflectometry is developed to determine the form quality of the optical lenses during rough polishing. Stray light reflected from the lower surface of transparent lenses may degrade the measuring quality, thus an effective absolute phase retrieval algorithm is developed to decouple the superposed fringes associated with the upper and lower surfaces. Then, the form of the upper surface under polishing can be reconstructed to guide the subsequent polishing. Experimental results demonstrate that the accuracy of the method is comparable to that of the coordinate measuring machine, consequently the manufacturing efficiency and reliability of large optical workpieces can be greatly improved.

This article presents a beamforming Doherty power amplifier (B-DPA) for the 28-GHz fifth-generation (5G) new-radio band. The proposed B-DPA is based on a new combiner topology that allows the current profile in the auxiliary branch of the DPA to be relaxed while simultaneously canceling the amplitude-to-phase (AM-PM) distortion exhibited in the active devices. This approach enables efficiency and linearity enhancements. In addition, the DPA is augmented with high-accuracy digitally assisted vector multipliers at its input stage to provide the required relative and absolute phase adjustments for proper Doherty operation and the overall phase shift required for beamforming. A proof-of-concept prototype was implemented in the 45-nm silicon on insulator (SOI)-CMOS technology. Measurement results reveal that the proposed B-DPA demonstrated good Doherty operation with drain efficiencies of 18%–20% and 33%–35% at 6-dB back-off and saturation power (Psat, 18 dBm) levels, respectively, between 28 and 30 GHz. In particular, excellent AM-PM characteristics were noted with a peak value of only 1.5° up to Psat, which remained below 2.5° as the B-DPA was swept with a 0° to 360° phase shift. Finally, modulated-signal tests revealed error vector magnitudes of 3.1% and 0.9% for 4-MHz $\times100$ -MHz orthogonal frequency division multiplexing (OFDM) signals before and after applying digital predistortion, respectively.

Fringe projection profilometry (FPP) is a popular three-dimensional (3D) shape measurement technique and has been widely used in industry. However, measuring surface with high reflectivity is still challenging because image saturation leads to absolute phase errors and reconstruction errors. In this paper, a novel adaptive fringe projection method is proposed. First, a projection intensity model is built. Adjusting the exposure time only once can easily calculate the low projection intensity. Then, using fringe patterns with low intensity we can get the coordinate mapping relationship. By mapping and filtering the sub-pixel coordinates in the projector image, we can obtain more accurate coordinate correspondence and gray value correspondence of the projector and the camera. Finally, the parameters of the projection intensity model are fitted to calculate the optimal intensity and generate accurate adaptive fringe patterns. The measurement experiments demonstrate that the proposed method is effective in obtaining high-precision and complete 3D profile of surface with high reflectivity.

Phase unwrapping plays a vital role in fringe projection profilometry which is an outstanding three-dimensional (3D) shape measurement method. This paper proposed a novel phase unwrapping algorithm that requires no extra patterns needed in conventional temporal phase unwrapping algorithms. The proposed method unwraps the wrapped phase map of the newest measurement with the help of the unwrapped one from the previous measurement. It applies temporal phase unwrapping algorithm first, and then detects the wrongly unwrapped points caused by the misalignment of phase edges, and finally corrects the phase of these points using spatial phase unwrapping algorithm. The method proposed can largely reduce the number of patterns needed for continuous dynamic measurement. Meanwhile, it can resist larger noise than multifrequency phase unwrapping algorithm because the noise of the reference phase map is not amplified. Besides, it can effectively solve the problem of abnormal phases caused by the misalignment between the phase edges of successive phase maps due to object motion. Moreover, the proposed algorithm is capable of retrieving the absolute phase map of multiple surfaces. The system developed with this algorithm can obtain the 3D shape of the object by just a single shot during the continuous dynamic measurement.

Although various camera calibration methods have been proposed, most of these methods cannot deliver accurate determination of the intrinsic camera parameters, because of the coupling errors existing between intrinsic and extrinsic camera parameters and the use of explicit distortion models. Here, we propose a model-free method for accurate camera calibration, which utilizes phase-shifted fringe patterns shown on a liquid crystal display (LCD) screen for estimating the intrinsic parameters of a camera and correcting lens distortion. Horizontal and vertical fringe patterns are consecutively displayed on the LCD screen, which is placed at two positions parallel to the camera sensor plane. These fringe patterns are captured by the camera from the front viewpoint for calculating the absolute phase maps. Then, the images with lens distortion can be transformed to the distortion-free images using an inverse mapping operation. Subsequently, the principal point coordinates are calculated according to the geometric imaging relationship between the positions of the two LCD screens. Finally, the focal length can be estimated using the similarity of triangles formed by the obtained principal point coordinates and the obtained phase maps at the two positions. Both simulated and real experiments are performed to verify the validity of the proposed method. The results demonstrate that this method not only successfully eliminates coupling errors but also perfectly corrects lens distortion.

In the process of structured light three-dimensional measurement, the absolute phase can be obtained from the wrapped phase and the period value K. The period value K directly determines the quality of the point cloud. This paper proposes a novel structured light fringe encoding and decoding scheme, which can quickly and accurately solve the period value K and the wrapped phase: it only needs to project four fringe patterns to recover the absolute phase. This method calculates the high-frequency wrapped phase based on two sinusoidal fringe patterns, then uses the step fringe pattern and the uniform fringe pattern to calculate the period value K of the wrapped phase, and uses the wrapped phase and the period value K to recover the absolute phase. Experimental tests show that the proposed method is accurate for fast 3D reconstruction.

This paper describes the setup of a traceable calibration system for conventional or non-conventional current sensors even with digital output. The system is lately developed at PTB within the frame of the European project ���FUTUREGRID II���. Details of the system components are presented. The absolute phase errors of the two-channel generator related to the pulse per second time reference of the global positioning system can be configured to almost zero. The accuracies of the reference current transformers are within ��10 ��A/A and ��rad at power frequency. The sampled value receiver box is firstly validated for the sample rate of 4 kHz according to the IEC standard 61869-9 [1]., Cite as Y. Chen, E. Mohns, M. Seckelmann and S. de Rose, "Traceable calibration system for non-conventional current sensors with analogue or digital output," 2021 IEEE 11th International Workshop on Applied Measurements for Power Systems (AMPS), 2021, pp. 1-6, doi: 10.1109/AMPS50177.2021.9586012.