Search

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.

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.

Estimating unknown absolute phase from a wrapped observation is a challenging and ill-posed problem that possibly leads to misinterpretation of interferometric SAR (InSAR) deformation results. In this study, we introduce a quality index to cluster post-phase unwrapping multi-master InSAR timeseries outputs based on the estimated phase residuals and redundancy of network of interferograms. The index is supposed to indicate the reliability of a timeseries, including the identification of persistent scatterers (PSs) possibly affected by phase unwrapping jumps. The algorithm was tested on two Sentinel-1 interferometric datasets with 622,991 and 95,398 PSs, generated from the PSI processing chain PSIG of the geomatics division of CTTC. Promising result have been achieved-especially in identifying erroneous PSs with phase unwrapping jumps. Along with existing temporal phase consistency checking algorithms, the approach could provide rich information toward a better interpretation of the deformation timeseries results. This work has been funded by AGAUR, Generalitat de Catalunya, in the framework of Resolution EMC/ 2459/2019, FI-2020.

Radar interferograms provide a map of the phase difference between the reference and repeat acquisitions modulo ${2\pi }$ . Under ideal conditions, the phase can be unwrapped to provide an absolute phase connection across the map, although there is always an unknown integer phase ambiguity (i.e., ${N2\pi }$ ) for the entire map. Here, we demonstrate a practical time series method to solve for these integer ambiguities in order to recover the absolute phase change between the first and last SAR images. An important first step is to correct the phase of each SAR image for the well-known solid earth tide, which typically produces a line of sight offset ±150 mm, as well as, trends along and across each image of ~20 mm. This tide correction significantly reduces the noise in the InSAR time series, especially at the L-band. These tidally corrected interferograms are then unwrapped and used to solve for a set of integer ambiguities that achieves phase closure when summing around loops in the stack. There is an infinite number of ambiguity combinations that achieve loop closure; thus, regularization is required. In contrast to previous studies that use a least-squares approach to find the ambiguities, we adopt an ${L}_{1}$ -norm approach to find the minimum number of ambiguity corrections needed to achieve loop closure. We note that the split-spectrum ionospheric correction can introduce ${N\pi }$ ambiguities and suggest two approaches for correcting both ${N2\pi }$ and ${N\pi }$ ambiguities.

Two-dimensional phase unwrapping is a critical processing procedure of synthetic aperture radar interferometry. This operation becomes even more difficult in the presence of noise. Both local and global unwrapping algorithms are used in obtaining the absolute phase from the wrapped ones. However, there are still gaps in the use of these methods. Local methods still let noise propagate. While the global methods are unable to properly formulate the objective function. The aim of this article is to present a new algorithm for interferometric phase unwrapping. An alternative method to consider both local and global constraints of the interferogram is proposed. Local constraints are modeled by a novel quality measure. A weight is then assigned to each pixel of the interferogram based on two criteria-the phase jump ratio and the phase gradient. While the global constraints are modeled by a cost function that calculates the sum of the pixels weights in the interferogram. This cost function is minimized by a genetic algorithm. Validation tests with real and simulated interferograms showed that the proposed algorithm outperforms standard algorithms of phase unwrapping such as branch cuts, minimum cost flow networks, or minimum Lp-norm algorithm.

Accurate interpretation of interferometric image requires an extremely challenging task based on actual phase reconstruction for incomplete noise observation. In spite of the establishment of comprehensive solutions, until now, a guaranteed means of solution method is yet to exist. The initially observed interferometric image is formed by 2π-periodic phase image that wrapped within (-π, π]. Such inverse problem is further corrupted by noise distortion and leads to the degradation of interferometric image. In order to overcome this, an effective algorithm that enables noise suppression and absolute phase reconstruction of interferometric phase image is proposed. The proposed method incorporates an improved order statistical filter that is able to adjust or vary on its filtering rate by adapting to phase noise level of relevant interferometric image. Performance of proposed method is evaluated and compared with other existing phase estimation algorithms. The comparison is based on a series of computer simulated and real interferometric data images. The experiment results illustrate the effectiveness and competency of the proposed method.

In many engineering applications the phase angle of a signal is a key parameter. Especially when measuring small angles, the measurement accuracy is of a vital importance. Often, the absolute phase error of a digitizer, which is defined as the phase displacement between the digitized output and the input analog waveform and which represent a systematic measurement error, is neglected. Therefore, in this paper a new measurement technique for the evaluation of this absolute phase error is discussed, along with a deep theoretical analysis on the uncertainty sources and how to handle them. The measurement technique is validated through a high accuracy experimental setup. Experimental tests demonstrate that even high accuracy digitizers can show non-linear behavior in the absolute phase errors., The work reported here has received support from the EMPIR programme co-financed by the Participating States and from the European Union's

Although the traditional phase-coding method for absolute phase retrieval possesses strong robustness, the method leads to unwrapping artifacts as a mass of codewords required. To solve this problem, a novel improved method is proposed in this paper. The incorrect points in the recovered phase via the traditional method are located using a computational framework, and the path-following algorithm is adopted as an aid to correct the unwrapping artifacts. The effectiveness of the proposed method is experimentally verified by an established measurement system. The reconstructed geometry of standard sphere has sufficient accuracy and the absolute phase retrieval of a complex star object has high quality.

Fast 3D optical sensing of complex shapes remains challenging. While in the passive techniques, there is the correspondence problem, in the active techniques based on fringe projection, there is the challenge of phase recovery and disambiguation. We propose a stereo system that combines active and passive approaches in a complete 3D measurement system. A modified version of the Fourier transform profilometry technique is combined with the beating technique for absolute phase estimation. Stereo correspondence is performed using the obtained phase images. The results demonstrate that one or two frames are enough to estimate the 3D shape of complex objects, and therefore, the proposed approach can be applied for fast shape characterization.

This paper presents a simplified method for realizing absolute phase and ac resistance for current shunts using only impedance ratio measurements. The method is based on three geometrically identical current shunts with different resistances, but with the same inductance, capacitance, and ac–dc resistance change. We demonstrate how the inductance, capacitance, and ac resistance can be calculated from the complex impedance ratio measurements, therefore realizing absolute current shunt impedance. The method gives competitive uncertainties of around $200~ \mu \Omega / \Omega $ for amplitude and $400~ \mu $ rad for phase at 1 MHz in the 1- $\Omega $ range.

The accurate three-dimensional shape measurement of a complex surface is significantly important in industrial testing. However, three-dimensional profilometry by conventional sinusoidal fringe projection using a phase-shifting algorithm performs suboptimally because of the nonlinear intensity response of projectors. To overcome this problem, the present paper proposes using a combined optimizing sinusoidal pulse width modulation (SPWM) technique and stair phase-coding approach to obtain the unwrapped phase. Properly optimizing SPWM with a small degree of a defocusing projector to generate sinusoidal fringe patterns can overcome the undesired harmonics and nonlinear gamma effect. Two groups of four-step phase-shifting fringe patterns are used. One group of the stripes contains four sinusoidal patterns generated by the SPWM technique, which is used to determine the wrapped phase. The other group of stripes contains four sinusoidal patterns with the codeword embedded into the stair phase, whose stair changes are perfectly aligned with the 2 π discontinuities of the sinusoidal fringe phase, which is used to determine the fringe order for the phase unwrapping. Moreover, for the defocusing projection, because the frequency of the phase-coding fringe increases, the fringe order decision becomes less reliable. Thus, a self-correction phase unwrapping method is applied for phase retrieval. Experiments were conducted to verify the performance of the proposed method.

Wrapped phase extraction is an essential process for the retrieval of absolute phase and even the computation of object height information in fringe projection profilometry. Over the past few decades, tremendous efforts have been devoted to developing various techniques for computing wrapped phase. By comparison, four-step phase-shifting techniques play an important vehicle for obtaining the wrapped phase of 3D objects. At present, a variety of four-step phase-shifting algorithms show the comprehensive mathematical deduction and their theories are very clear. Analysis from the perspective of theoretical integrity, however, the phase-shifting techniques lack the exploration of arbitrary phase shift. In view of this, inspired by the prosthaphaeresis in trigonometric, we present a novel four-step phase-shifting algorithm. The proposed method includes 16 kinds of four-step phase-shifting fringe combination and corresponding calculation formula of wrapped phase, which are deduced with two frames fringe images of sines and two ones of cosines. Furthermore, simulations and experiments have been carried out to reveal the influence law of variable phase shift on the performance of these approaches.

In order to obtain a higher quantity absolute phase, a novel phase unwrapping model by combination of dual-frequency heterodyne and segmented quantifization phase coding method is proposed in this research. This model also provides a generalized phase order error correction method for eliminate phase order jump errors. Only ten fringe patterns are used for the projection in this study. The workflow of the devised model starts with acquisition of the low frequency wrapped phase by using the classic double-frequency heterodyne method, and then it moves to obtain the fringe order of low frequency wrapped phase based on the projected segmented quantifization phase coding patterns. In this step, two-dimensional scanning lookup method is used to eliminate the noise points caused by the rounding operation. Then, new fringe order can be obtained by combination of the obtained fringe order of low frequency wrapped phase and the new projected binary fringe pattern with complementarity, and this new fringe order combined with the previous fringe order can be used to unwrap the heterodyne phase. Finally, the wrapped phase of the dual-frequency is unwrapped through unwrapped heterodyne phase and the highest frequency phase. This study applies metal workpiece measurements as case studies to test the validity of the proposed model. The experimental results show that the error effects of fringe order can be eliminated, and the high frequency fringes retain more information on the measure workpiece surfaces.

Phase encoding and phase-shift profilometry are two commonly used 3D measurement techniques. However, the acquired phases in the techniques are subject to jump errors due to phase ambiguity and phase errors caused by multiple heterodyne. The phase-shifting profilometry also makes the selection of fringe period difficult. To overcome this problem and achieve high-precision measurement, a phase unwrapping method that combines dual-frequency heterodyne with double complementary phase encoding is proposed. First, two wrapped phases are obtained by two groups of sinusoidal fringes; the heterodyne phase is obtained after heterodyne processing, and the high-frequency phase is expanded by heterodyne phase. Second, the fringe levels are obtained using the complementary phase encoding fringes that are shifted by half an order, and then the absolute phase is obtained by selecting different phase coding levels according to different regions for the first phase unwrapping; Finally, the phase noise is removed by exploiting the difference between the phase slopes of adjacent pixels. Experimental results show that a system with the proposed method achieves an RMS error of 0.015 mm. In addition, the period of dual-frequency heterodyne synthesis does not need to cover the whole field of view, which breaks the limitation of frequency selection of the traditional dual-frequency heterodyne method and triple frequency heterodyne method, enabling high-precision measurement with higher frequency fringes. This method overcomes the limitations of the phase principal value error when using higher frequency fringes for high-precision measurement, improves the measurement effect of reflective objects, and effectively avoids the error caused by phase jump.

Phase unwrapping is a key step of interferometric synthetic aperture radar (InSAR), which transforms wrapped phase into the absolute phase. The accurate phase unwrapping requires high signal-to-noise ratio (SNR) value. Thus phase filtering is necessary to filter out the noise. This paper proposes an improved U-Net neural network for phase filtering. The images of noisy and noiseless interferometric phase are fed into the network for training. With the trained neural network, the noisy input interferometric phase can be directly smoothed to obtain high SNR phase image. Experiments show that the network can filter out phase noise effectively in the phase contiguous region, meanwhile it keeps the structure information of phase ambiguous edge region.

In this paper the effectiveness of a CNN based interferometric phase unwrapping algorithm combined with phase noise filtering is analysed. In particular, the considered processing chain relies on a pre-processing step with the nonlocal filter InSAR-BM3D followed by a deep CNN solution for restoring the absolute phase. The analyses is conducted on simulated data with different coherence values and aims at comparing the performance of the unwrapping with and without the pre-processing step. This paper is the first step towards a unique deep learning solution for jointly unwrapping and restoring the absolute phase.

A deep learning-based method is proposed to recover the absolute phase value from a single fringe pattern. We propose a deep neural network architecture that includes two subnetworks used for wrapping phase calculation and phase unwrapping, respectively. The training set is generated with the absolute phase obtained by the combination of phase shifting and gray coding. In addition, a reference plane is adopted to provide periodic range information for phase unwrapping. Then according to the output of the well-trained network, a high-quality absolute phase is obtained through only a single fringe pattern of the measured object. Experiments on the test set verify that high accuracy for complex texture objects is acquired using the proposed method, which indicates its potential in high-speed measurement.

This paper describes the initial stage of implementing an absolute phase measurement system for the current “cage” type shunts built at Inmetro. The phase characterization of the shunts includes phase difference measurements that allow the realization of the absolute phase using three geometrically equal shunts calibrated in DC resistance. The measurement results of three shunts are presented and analyzed in comparison with the values obtained through the lumped equivalent circuit model. The results demonstrate the high capacity of the method of determining the absolute phase of shunts that have small phase shift errors. This method allowed, for the first time, the absolute phase measurement of impedances (shunts) below 10 ohms at Inmetro. The lowest measurement error was 0.4 microradians with an expanded uncertainty of 1.4 microradians for the 10 A shunt at 54 Hz.

Fiber-optic time and frequency synchronization technology demonstrates ultra-high synchronization performance and has been gradually applied in various fields. Based on frequency synchronization, this study addressed the problems of period ambiguity and initial phase uncertainty of the phase signal to realize the coherent transmission of the phase. An absolute phase marking technology was developed based on high-speed digital logic with zero-crossing detection and an optimized control strategy. It can realize picosecond-level absolute phase marking and provide a picosecond-level ultra-low peak-to-peak jitter pulse marking signal to eliminate phase period ambiguity and determine initial phase and transmission delay. Thus, by combining the high-precision phase measurement capability of the synchronized frequency signal and long-distance ambiguity elimination capability of the pulse-per-second signal, a high-precision remote coherent phase transmission over an optical fiber is realized. After frequency synchronization, the peak-to-peak jitter between the local and remote phase-marking signals can be only 3.3 ps within 10,000 s measurement time. The uncertainty of the coherent phase transmission is 2.577 ps. This technology can significantly improve the phase coherence of fiber-optic time and frequency transmission and provide a new approach to achieve peak-to-peak picosecond-level reference phase marking and high-precision fiber-optic remote coherent phase transmission. This demonstrates broad application prospects in coherence fields such as radar networking.

As a fundamental step in fringe projection profilometry, absolute phase unwrapping via single-frequency fringe patterns is still a challenging ill-posed problem, which attracts lots of interest in the research area. To solve the problem above, additional constraints were constructed, such as spatial smoothness constraint (SSC) in spatial phase unwrapping algorithm and viewpoint consistency constraint (VCC) in multi-view systems (e.g., stereo and light-field cameras). However, there still exists phase ambiguity in the unwrapping result based on SSC. Moreover, VCC-based methods rely on additional cameras or light-field cameras, which makes the system complicated and expensive. In this paper, we propose to construct a novel constraint directly from photometric information in captured image intensity, which has never been fully exploited in phase unwrapping. The proposed constraint, named photometric constraint (PC), provides a prospective constraint for absolute phase unwrapping from single-frequency fringe patterns without any additional cameras. Extensive experiments have been conducted for the validation of the proposed method, which achieved comparable performance with the state-of-the-art method, given a traditional camera-projector setup and single high-frequency fringe patterns.

The phase-to-height imaging model, as a three-dimensional (3D) measurement technology, has been commonly applied in fringe projection to assist surface profile measurement, where the efficient and accurate calculation of phase plays a critical role in precise imaging. To deal with multiple extra coded patterns and 2π jump error caused to the existing absolute phase demodulation methods, a novel method of phase demodulation is proposed based on dual variable-frequency (VF) coded patterns. In this paper, the frequency of coded fringe is defined as the number of coded fringes within a single sinusoidal fringe period. First, the effective wrapped phase (EWP) as calculated using the four-step phase shifting method was split into the wrapped phase region with complete period and the wrapped phase region without complete period. Second, the fringe orders in wrapped phase region with complete period were decoded according to the frequency of the VF coded fringes and the continuous characteristic of the fringe order. Notably, the sampling frequency of fast Fourier transform (FFT) was determined by the length of the decoding interval and can be adjusted automatically with the variation in height of the object. Third, the fringe orders in wrapped phase region without complete period were decoded depending on the consistency of fringe orders in the connected region of wrapped phase. Last, phase demodulation was performed. The experimental results were obtained to confirm the effectiveness of the proposed method in the phase demodulation of both discontinuous objects and highly abrupt objects.

Absolute phase unwrapping in the phase-shifting profilometry (PSP) is significant for dynamic 3-D measurements over a large depth range. Among traditional phase unwrapping methods, spatial phase unwrapping can only retrieve a relative phase map, and temporal phase unwrapping requires auxiliary projection sequences. We propose a shading-based absolute phase unwrapping (SAPU) framework for in situ 3-D measurements without additional projection patterns. First, the wrapped phase map is calculated from three captured images. Then, the continuous relative phase map is obtained using the phase histogram check (PHC), from which the absolute phase map candidates are derived with different fringe orders. Finally, the correct absolute phase map candidate can be determined without additional patterns or spatial references by applying the shading matching check (SMC). The experimental results demonstrate the validity of the proposed method.

Far-field infrared (IR) spectroscopy techniques, such as ellipsometry and FTIR, can yield extremely accurate measurements of the optical constants (n,k) which characterize the electronic and lattice-structural degrees of freedom in novel materials and devices. However, large systematic uncertainty has plagued extensions of these techniques to small length scales. A low uncertainty embodiment would enable high quality studies of, for example, the newest correlated condensed matter systems - where typically only a small sample is available early on. Here we present mature far-field IR microscope. Most notably, an asymmetric interferometer is used to directly measure the infrared reflectance amplitude and absolute phase shift. The complex optical constants can then be extracted without the large uncertainty that arises with an amplitude measurement alone.

In this work, the novel enhancement to multichannel scatterometry data collection, Spectral Interferometry, is introduced and discussed. The Spectral Interferometry technology adds unique spectroscopic data by providing absolute phase information. This enhances metrology performance by improving sensitivity to weak target parameters and reducing parameter correlations. Spectral Interferometry enhanced OCD capabilities were demonstrated for one of the most critical and challenging applications of gate-all-around nanosheet device manufacturing: lateral etching of SiGe nanosheet layers to form inner spacer indentations. The inner spacer protects the channel from the source/drain regions during channel release and defines the gate length of the device. Additionally, a methodology is presented, which enables reliable and reproducible manufacturing of reference samples with engineered sheet-specific indent variations at nominal etch processing. Such samples are ideal candidates for evaluating metrology solutions with minimal destructive reference metrology costs. Two strategies, single parameter and sheet-specific indent monitoring are discussed, and it was found that the addition of spectroscopic information acquired by Spectral Interferometry improved both optical metrology solutions. In addition to improving the match to references for single parameter indent monitoring, excellent sheet-specific indent results can be delivered

GNSS antennas are a key factor in precise GNSS positioning. With the increasing availability of low-cost dual-frequency GNSS receivers also the demands on low-cost GNSS antennas increases. Unfortunately, the electronic center of most GNSS antennas is not located in the mechanical Antenna Reference Point (ARP). As a consequence, Phase Center Corrections (PCC) have to be introduced to correct for frequency-dependent signal delays within the antenna system. The PCCs are typically in the range of several millimeters to centimeters. Thus, uncorrected phase center variations can be a significant error source in precise positioning.For the purpose of antenna calibration, the Institute of Geodesy and Photogrammetry at ETH Zürich acquired a six-axis industrial robot of type KUKA AGILUS KR 6 R900 sixx. In an initial study, the absolute accuracy of the robot has been determined to be better than 1.5 mm (standard deviation). By introducing a set of extended Denavit-Hartenberg parameters, the absolute position accuracy of the robot is further increased to 0.3 mm over the entire workspace and 0.1 mm for a predefined sequence of robot poses, respectively. Therefore, the robot operates well below the phase noise of the GNSS measurements (typically around 1 mm) and is therefore seen as suitable for the calibration of GNSS antennas with sub-millimeter accuracy.Besides the numerous benefits of absolute field calibration with an industrial robot, several challenges remain if it comes to low-cost GNSS antennas. The main challenges are that for each antenna a specific mounting system has to be built and that low-cost antennas are in general less shielded against multipath (compared to geodetic antennas). Besides, only little information exists about the stability of the electronic reference point and how much the electronic properties change when the antenna is mounted on different platforms (cars, drones, cubesats, etc).To address the critical issues in low-cost GNSS antenna calibration and study the impact of the PCCs on the positioning solution, a calibration campaign has been initiated at ETH Zürich in autumn 2020. In this campaign, a set of low-cost multi-GNSS dual-frequency patch and loop antennas - suited for centimeter-positioning - has been calibrated and tested. Therefore, in the vicinity of the GNSS reference station (ETH2) the robot has been installed and a sequence of randomized robot poses has been executed in which the ARP of each antenna was defined as rotation point. The GNSS signals recorded during this sequence were processed together with the robot attitude information using the time-differencing approach defined by D. Willi (2019) using a spherical harmonics parameterization.The PCCs obtained from the calibration campaign were stored in ANTEX files for a subsequent validation. In this presentation, we will highlight the developed calibration procedures for low-cost GNSS antennas, summarize the main results of the calibration and validation campaign, and will give the framework in which a calibration of low-cost GNSS antennas is considered beneficial.Willi D., GNSS receiver synchronization and antenna calibration, PhD Thesis, ETH Zürich, 2019, https://www.research-collection.ethz.ch/handle/20.500.11850/308750

In fringe projection profilometry, the wrapped phase extraction is an essential process for absolute phase unwrapping and even the computation of object height information. Over the past few decades, tremendous efforts have been devoted to developing various techniques for computing wrapped phase. By contrast, the phase-shifting techniques process more advantages including higher accuracy, higher spatial resolution, and lower sensitivity to variations of background intensity and surface reflectivity. At present, a variety of phase-shifting algorithms show the comprehensive mathematical deduction and their theories are very clear. Analysis from the perspective of theoretical integrity, however, the phase-shifting techniques lack the exploration of geometric algebra. For that reason, inspired by the orthogonal resolution and resultant of forces in physics, we present a geometric analysis method. Furthermore, exploiting the proposed method to explore the double three-step algorithm, four-step algorithm and extended averaging technique, we obtain three new discoveries. Simulations and experiments have been carried out to verify the performance of these new discoveries. In addition, these results also reflect the necessity of the geometric analysis method for phase-shifting techniques.

A phase correction method that utilizes fringe color-coding in phase-measuring profilometry is proposed. Original and additional fringes are encoded into the R and B channels, respectively. The R + B channel patterns are projected onto an object, captured using a camera, where the R and B channels are extracted. Then, phase shifts obtained from the R and B channels are utilized for absolute phase calculation and correction. Simulations and experiments demonstrate that this method can correct edge order errors and avoid increasing the fringe number. Experiments performed using the R + G, G + B, and R + B channels demonstrate that R + B exhibits the least color crosstalk.

Phase unwrapping aims to reconstruct the absolute phase from its values mod 2π, which is a key problem in many non-contact optical metrologies and is still a challenging issue in the presence of noise. We present a robust phase unwrapping method with two steps based on local denoising and the accumulation of residual map (ARM). In the first step, based on the local polynomial approximations and intersection of confidence intervals, we adopt a sine–cosine filtering and iteration algorithm to denoise the wrapped phase, which uses the periodicity of the trigonometric function to avoid the influence of phase jumps effectively. In the second step, the denoised wrapped phase is unwrapped by the improved ARMs method, in which we modify the edge regular term to avoid over-fitting and maintain edge information. The algorithm is tested with a set of numerical simulations under various noise levels, and the experimental results confirm its effectiveness and robustness.