Phase Error Research Articles

Monolithic back-end-of-line integration of phase change materials into foundry-manufactured silicon photonics

Monolithic integration of novel materials without modifying the existing photonic component library is crucial to advancing heterogeneous silicon photonic integrated circuits. Here we show the introduction of a silicon nitride etch stop layer at select areas, coupled with low-loss oxide trench, enabling incorporation of functional materials without compromising foundry-verified device reliability. As an illustration, two distinct chalcogenide phase change materials (PCMs) with remarkable nonvolatile modulation capabilities, namely Sb2Se3 and Ge2Sb2Se4Te1, were monolithic back-end-of-line integrated, offering compact phase and intensity tuning units with zero-static power consumption. By employing these building blocks, the phase error of a push-pull Mach–Zehnder interferometer optical switch could be reduced with a 48% peak power consumption reduction. Mirco-ring filters with >5-bit wavelength selective intensity modulation and waveguide-based >7-bit intensity-modulation broadband attenuators could also be achieved. This foundry-compatible platform could open up the possibility of integrating other excellent optoelectronic materials into future silicon photonic process design kits.

Analysis and Simulation of Current Balancer Circuit for Phase-Gain Correction of Unbalanced Differential Signals

The phase and gain imbalance of a balun output can be adjusted by a differential current balancer (DCB) circuit. The performance of DCB circuit, for correcting the phase (gain) imbalance, is analyzed for a wide range of input signal level, and the accuracy is verified with circuit simulation. To illustrate the phase-error/gain-error (PE/GE) correction, a 30–40[Formula: see text]GHz DCB circuit is designed and simulated in a 180-nm CMOS process. The DCB is examined for input PE, [Formula: see text], of [Formula: see text] and input GE, GA, of [Formula: see text][Formula: see text]dB. Analysis and simulation illustrate an output phase error [Formula: see text] of [Formula: see text] and output gain error [Formula: see text] of [Formula: see text][Formula: see text]dB, over frequency range of 20–50[Formula: see text]GHz. The results of DCB circuit for PE (GE) compensation are compared to that of phase-correction technique (PCT) circuit, illustrating the superior phase (gain) imbalance correction of the DCB circuit with lower NF and DC power consumption.

Design and Implementation of C-Band Large-Power Planar Butler Matrix in SRS.

In satellite remote sensing (SRS), there is a demand for large-power microwave components. A Butler matrix is essential to a transmitting antenna array in SRS. This article illustrates the electrical and mechanical design, simulation, and test results of a large-power planar beamforming network for SRS at C-band. It is a 4 × 4 Butler matrix based on square coaxial lines. Short-ended stubs are used in the Butler matrix to broaden its bandwidth by 10%, support inner conductors, and enhance heat transfer in vacuum environments. The simulation results are consistent with the measured results. The reflection coefficient is less than -18 dB, and the isolation is more than 23 dB from 3.8 GHz to 4.2 GHz. The insertion losses are less than 0.6 dB, and the phase errors are better than ±6°. The measured peak microwave power of the proposed Butler matrix is 9 kW. Its size is 440 × 400 × 40 mm3. The proposed Butler matrix beamforming network can be applied to SRS systems.

Spectrally-tuned compact finite-difference schemes with domain decomposition and applications to numerical relativity

Compact finite-difference (FD) schemes specify derivative approximations implicitly, thus to achieve parallelism with domain-decomposition suitable partitioning of linear systems is required. Consistent order of accuracy, dispersion, and dissipation is crucial to maintain in wave propagation problems such that deformation of the associated spectra of the discretized problems is not too severe. In this work we consider numerically tuning spectral error, at fixed formal order of accuracy to automatically devise new compact FD schemes. Grid convergence tests indicate error reduction of at least an order of magnitude over standard FD. A proposed hybrid matching-communication strategy maintains the aforementioned properties under domain-decomposition. Under evolution of linear wave-propagation problems utilizing exponential integration or explicit Runge-Kutta methods improvement is found to remain robust. A first demonstration that compact FD methods may be applied to the Z4c formulation of numerical relativity is provided where we couple our header-only, templated C++ implementation to the highly performant GR-Athena++ code. Evolving Z4c on test-bed problems shows at least an order in magnitude reduction in phase error compared to FD for propagated metric components. Stable binary-black-hole evolution utilizing compact FD together with improved convergence is also demonstrated.

Low complexity on-board vector calibration network for optimal microwave wireless power transmission and enhanced RF-to-DC conversion efficiency

A low complexity on-board vector calibration network for optimal microwave wireless power transmission (MWPT) efficiency is proposed in this work. The proposed technique is based on sequentially tracking the minimum power level of two antenna elements in an array for both phase and amplitude error discrimination. Unlike conventional vector calibration networks based on a down-conversion topology, the proposed architecture can perform vector calibration by only monitoring the magnitude of each antenna element. Thus, high system efficiency can be achieved by reducing hardware costs and eliminating any unnecessary power consumption by extra active devices. Further, phase and amplitude imbalances between antenna elements in an array can be accurately captured with higher precision compared to the conventional rotating-element electric-field vector (REV) method. The proposed technique achieved higher resolutions for both amplitude and phase error detection than REV, which suffers from low resolution near the maximum or minimum field crests. To verify the MWPT efficiency improvement based on the proposed calibration network, a 1 × 4 phased array MWPT system was fabricated and tested at 5.8 GHz with a reference rectenna. With the calibrated power transmission, the total RF-DC conversion efficiencies at ± 45° beamforming angles were improved by up to a maximum of 138.79%.

Control of the Optical Wavefront in Phase and Amplitude by a Single LC-SLM in a Stellar Coronagraph Aiming for Direct Exoplanet Imaging

This article presents a novel approach to actively compensate wavefront errors in both phase and amplitude using a Liquid Crystal Spatial Light Modulator (LC-SLM) for direct exoplanet imaging. This method involves controlling the wavefront to address challenges posed by stellar coronagraphy. Experimental results demonstrate successful wavefront error compensation in both phase and amplitude components. This technique shows promise for direct exoplanet imaging and may be applied onboard orbital telescopes in the future.

The optimal algorithm for eliminating nonlinear error in phase measurement profilometry based on global statistical phase feature function

In a digital fringe projection structured light system, the nonlinear phase error is generated by the gamma effect of both the projector, camera, and other electronic devices. One of the existing nonlinear correction methods is active correction by projecting ideal fringes as far as possible, and the other is passive compensation after capturing aberrant fringes. The former has higher accuracy but needs to capture a large number of fringe patterns, while the latter does not need many fringe patterns, but is not only greatly affected by random noise and out-of-focus effects, but also has poor accuracy. In this paper, an optimal algorithm for eliminating nonlinear error based on global statistical phase feature function (GSPF) is proposed. The phase distribution can be estimated from the difference between the global cumulative distribution function (CDF) and the normalized (CDF). For an ideal fringe pattern without nonlinear error and a fringe pattern with nonlinear error, the region wrapped by the x-axis normalized CDF is much smaller than the region wrapped by the x-axis global CDF, and the larger the nonlinear error is, the larger the difference between the two is. Therefore, the GSPF can be used for nonlinear error correction. Then the optimal nonlinear error correction is performed based on the minimum difference between the compensated phase entropy and the ideal phase entropy. The method does not require too many steps of phase-shifting, and only three fringe patterns are needed to realize accurate and robust correction. Experimental results show that the method is fast, highly accurate and robust. Using this technique, high accuracy measurements can be achieved with the traditional three-step phase-shifting algorithm.

Phase Error Reduction for a Structured-Light 3D System Based on a Texture-Modulated Reprojection Method.

Fringe projection profilometry (FPP), with benefits such as high precision and a large depth of field, is a popular 3D optical measurement method widely used in precision reconstruction scenarios. However, the pixel brightness at reflective edges does not satisfy the conditions of the ideal pixel-wise phase-shifting model due to the influence of scene texture and system defocus, resulting in severe phase errors. To address this problem, we theoretically analyze the non-pixel-wise phase propagation model for texture edges and propose a reprojection strategy based on scene texture modulation. The strategy first obtains the reprojection weight mask by projecting typical FPP patterns and calculating the scene texture reflection ratio, then reprojects stripe patterns modulated by the weight mask to eliminate texture edge effects, and finally fuses coarse and refined phase maps to generate an accurate phase map. We validated the proposed method on various texture scenes, including a smooth plane, depth surface, and curved surface. Experimental results show that the root mean square error (RMSE) of the phase at the texture edge decreased by 53.32%, proving the effectiveness of the reprojection strategy in eliminating depth errors at texture edges.

Model-Driven Deep Neural Network for Enhanced AoA Estimation Using 5G gNB

High-accuracy positioning has become a fundamental enabler for intelligent connected devices. Nevertheless, the present wireless networks still rely on model-driven approaches to achieve positioning functionality, which are susceptible to performance degradation in practical scenarios, primarily due to hardware impairments. Integrating artificial intelligence into the positioning framework presents a promising solution to revolutionize the accuracy and robustness of location-based services. In this study, we address this challenge by reformulating the problem of angle-of-arrival (AoA) estimation into image reconstruction of spatial spectrum. To this end, we design a model-driven deep neural network (MoD-DNN), which can automatically calibrate the angular-dependent phase error. The proposed MoD-DNN approach employs an iterative optimization scheme between a convolutional neural network and a sparse conjugate gradient algorithm. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed method in enhancing spectrum calibration and AoA estimation.

Robustness of different modifications of Grover’s algorithm based on generalized Householder reflections with different phases

In this work we study five Grover’s algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various characteristics of the dependence between the probability to find solution and the phase errors. The first of them is the robustness of the probability to errors in the phase. The second one is how quickly the probability falls beyond the stability interval. And finally, the average success rate of the algorithm when the parameters are in the range of the highly robust interval. Two of the modifications require usage of the same Grover operator each iteration and in the other three it differs. Those semi-empirical methods give us the tool to make prediction of the quantum algorithm modifications’ overall behavior and compare them for even larger register size.

Research on Non-Invasive Voltage Measurement Method Based on Impedance Adaptation

Transformer-based contact voltage measurement requires electrically charged installation during use. Moreover, there are problems with large sizes and restricted installation locations. The current non-contact voltage measurement technology is based on the principle of capacitive coupling in measurement. The capacitance between the probe and the wire is affected by the diameter of the wire and the insulation material. This results in an unstable sensor gain relationship, which leads to low measurement accuracy. This paper proposes a non-contact multi-wire adaptive voltage measurement method, and self-calibration of the sensor gain is achieved through practical measurements. First, the basic principle of capacitively coupled voltage measurement is introduced, from which the existing problems are condensed. An impedance-based adaptive method is proposed, based on which a new sensor probe is developed. The accuracy test reveals that the maximum relative error of voltage amplitude is 0.89 percent, the relative error of phase is 0.38%, and the relative phase error is within 1 degree for a specified voltage range (100 V-300V). The scenario adaptability test shows that the maximum relative error is 1.7% when performing tests on different types of lines. This sensor has the advantages of compactness, convenience, low cost, and high practicality.

Research on the phase error of a Sagnac interferometer induced by modulation of a multifunctional integrated optical modulator.

High-precision IFOG requires an optical sensitivity of up to 10-8 rads-1 for interferometers; noise and error are two of the main reasons limiting its accuracy improvement. Any potential source of the signal error is worth being studied. This article introduces work on the modulation signal error caused by the mechanical vibration energy loss of MIOC crystals. This article theoretically derives and simulates the frequency spectrum of an energy loss from the perspective of electromechanical coupling and verifies it through experiments. This article also verifies the influence of MIOC mechanical loss on the output of a Sagnac interferometer through experiments. This study is an indispensable part of the bottleneck for improving the accuracy of ultrahigh-precision closed-loop IFOG and has potential engineering application value.

Simulation-based benchmarking of ancient haplotype inference for detecting population structure

Paleogenomic data has informed us about the movements, growth, and relationships of ancient populations. It has also given us context for medically relevant adaptations that appear in present-day humans due to introgression from other hominids, and it continues to help us characterize the evolutionary history of humans. However, ancient DNA (aDNA) presents several practical challenges as various factors such as deamination, high fragmentation, environmental contamination of aDNA, and low amounts of recoverable endogenous DNA, make aDNA recovery and analysis more difficult than modern DNA. Most studies with aDNA leverage only SNP data, and only a few studies have made inferences on human demographic history based on haplotype data, possibly because haplotype estimation (or phasing) has not yet been systematically evaluated in the context of aDNA. Here, we evaluate how the unique challenges of aDNA can impact phasing and imputation quality, we also present an aDNA simulation pipeline that integrates multiple existing tools, allowing users to specify features of simulated aDNA and the evolutionary history of the simulated populations. We measured phasing error as a function of aDNA quality and demographic history, and found that low phasing error is achievable even for very ancient individuals (∼ 400 generations in the past) as long as contamination and average coverage are adequate. Our results show that population splits or bottleneck events occurring between the reference and phased populations affect phasing quality, with bottlenecks resultingin the highest average error rates. Finally, we found that using estimated haplotypes, even if not completely accurate, is superior to using the simulated genotype data when reconstructing changes in population structure after population splits between present-day and ancient populations. We also find that the imputation of ancient data before phasing can lead to better phasing quality, even in cases where the reference individuals used for imputation are not representative of the ancient individuals.

Performance analysis of IRS-aided MISO system under spatial correlation and interference

In this paper, we investigate the performance of an intelligent reflecting surface (IRS) aided multiple-input single-output (MISO) wireless system in the absence of direct link. We focus on the practical scenario where the N reflecting elements of the IRS have a spatial correlation between them, and both the destination and IRS are subject to interferences. Moreover, the IRS design with discrete phase shifting is considered. In order to quantify the impact of spatial correlation, phase error and interference on the system performance, we provide closed-form and asymptotic expressions for the system outage probability. Additionally, approximations for the average channel capacity are also derived. To gain further insight, the achievable diversity gain of both partial and full correlation cases is quantified. The analytical and simulation results reveal that spatial correlation has a dominant effect and reduces the system diversity order, but it is beneficial to the average channel capacity. Phase error results in performance degradation. Interference degrades the system performance only by reducing the coding gain. Compared to the direct path, interference from the reflected path plays a major role in reducing the system performance.

Simulation-based benchmarking of ancient haplotype inference for detecting population structure

Paleogenomic data has informed us about the movements, growth, and relationships of ancient populations. It has also given us context for medically relevant adaptations that appear in present-day humans due to introgression from other hominids, and it continues to help us characterize the evolutionary history of humans. However, ancient DNA (aDNA) presents several practical challenges as various factors such as deamination, high fragmentation, environmental contamination of aDNA, and low amounts of recoverable endogenous DNA, make aDNA recovery and analysis more difficult than modern DNA. Most studies with aDNA leverage only SNP data, and only a few studies have made inferences on human demographic history based on haplotype data, possibly because haplotype estimation (or phasing) has not yet been systematically evaluated in the context of aDNA. Here, we evaluate how the unique challenges of aDNA can impact phasing and imputation quality, we also present an aDNA simulation pipeline that integrates multiple existing tools, allowing users to specify features of simulated aDNA and the evolutionary history of the simulated populations. We measured phasing error as a function of aDNA quality and demographic history, and found that low phasing error is achievable even for very ancient individuals (∼ 400 generations in the past) as long as contamination and average coverage are adequate. Our results show that population splits or bottleneck events occurring between the reference and phased populations affect phasing quality, with bottlenecks resulting in the highest average error rates. Finally, we found that using estimated haplotypes, even if not completely accurate, is superior to using the simulated genotype data when reconstructing changes in population structure after population splits between present-day and ancient populations. We also find that the imputation of ancient data before phasing can lead to better phasing quality, even in cases where the reference individuals used for imputation are not representative of the ancient individuals.

Technical advances in motion-robust MR thermometry.

Proton resonance frequency shift (PRFS) MR thermometry is the most common method used in clinical thermal treatments because of its fast acquisition and high sensitivity to temperature. However, motion is the biggest obstacle in PRFS MR thermometry for monitoring thermal treatment in moving organs. This challenge arises because of the introduction of phase errors into the PRFS calculation through multiple methods, such as image misregistration, susceptibility changes in the magnetic field, and intraframe motion during MRI acquisition. Various approaches for motion correction have been developed for real-time, motion-robust, and volumetric MR thermometry. However, current technologies have inherent trade-offs among volume coverage, processing time, and temperature accuracy. These tradeoffs should be considered and chosen according to the thermal treatment application. In hyperthermia treatment, precise temperature measurements are of increased importance rather than the requirement for exceedingly high temporal resolution. In contrast, ablation procedures require robust temporal resolution to accurately capture a rapid temperature rise. This paper presents a comprehensive review of current cutting-edge MRI techniques for motion-robust MR thermometry, and recommends which techniques are better suited for each thermal treatment. We expect that this study will help discern the selection of motion-robust MR thermometry strategies and inspire the development of motion-robust volumetric MR thermometry for practical use in clinics.

Phase Error Criterion Based Adaptive Algorithm for Frequency Estimation

A simple phase error criterion (PEC-)-based adaptive algorithm for estimating the frequency of a complex sinusoidal signal in additive white Gaussian and impulsive noises is proposed. The proposed technique makes use of the instantaneous phase response of a first-order complex linear predictor (CLP) as a driving function to update the frequency parameter of the CLP. The proposed PEC is attractive due to its simplicity and high impulsive noise robustness. Theoretical analysis for the mean value of the estimated frequency and the steady-state mean square error (MSE) of the frequency estimate are derived in closed forms. Computer simulations are drawn to show the performance of the proposed frequency estimator.

A wideband and low-power mm-wave variable-gain phase shifter based on a source-switching scheme

This article presents a low-power and wideband variable-gain phase shifter (VGPS) designed and simulated in a CMOS 65 nm technology. It introduces a source-switching scheme for designing a variable gain amplifier (SSVGA) characterized by invariant linearity, impedance, and phase characteristics, showcasing improved gain and bandwidth compared to conventional VGAs. The current-reuse and staggered-tuning techniques are used to reduce power consumption and extend the bandwidth, respectively. The proposed VGPS enables gain tuning without the need for an additional gain tuning block, resulting in reduced chip area and sidelobe levels in phased array radar systems. The proposed VGPS, with a 5-bit resolution, achieves a 3-dB bandwidth of 18 GHz (53.5–71.5 GHz) and exhibits RMS gain error range from 0.23 to 0.5 dB and RMS phase error range from 0.54° to 2.65° with phase calibration based on simulation results. It achieves a peak average gain of 1.2 dB at 58.5 GHz while consuming a DC power consumption of only 5 mW with a 1.2 V power supply voltage. Moreover, it demonstrates a wide gain tuning of 20.6 dB, allowing for flexible gain adjustments.

RF direct sampling and processing electronics for SHINE cavity BPM system

Cavity BPMs are crucial for achieving submicron beam alignment in X-ray Free-Electron Lasers (XFEL), particularly in undulator sections. These monitors typically generate RF signals in the S, C, or X band regions. Due to the limitations of analog-to-digital converter's (ADC) bandwidth and sampling rates, and digital signal processing capabilities, heterodyne and homodyne receivers are often employed to down-convert the RF signal to an intermediate frequency (IF) or baseband (Zero IF) respectively before digital sampling. The digitized signal is then processed by Field Programmable Gate Array (FPGA) to get the beam position and phase information. An RF direct-sampling beam signal processor has been developed using ADCs with a bandwidth of 9 GHz and a sampling rate of 2.6 GSPS, and a powerful system-on-chip FPGA. In addition, a prototype RF module without complex down conversion devices has been designed for the SHINE (Shanghai High Repetition Rate XFEL and Extreme Light Facility) cavity BPM. The processor and the RF module make a novel RF direct sampling and processing cavity BPM electronics for SHINE. This is the first attempt to use direct sampling electronics in the C band cavity BPM system. The analog signal processing chain is greatly simplified compared to the down-conversion structure. The performance of this electronics has been analyzed and evaluated in laboratory. The amplitude relative error is 2.0 × 10-4, surpassing the required accuracy of 1 × 10-3 for cavity BPM systems. The phase error is 14 femtoseconds (fs), which also meets the requirements for an RF Beam Arrival Time Monitor (BAM) system. Additionally, the paper introduces the cavity BPM signal processing algorithms and their implementation in FPGA. The processor can deliver pulse-to-pulse beam position measurement above 1 MHz. The RF direct-sampling electronics represents significant advancements in cavity BPM system, large-scale application can be carried out in accelerator facilities like SHINE.

Comparative analysis of circular and linear fringe projection profilometry: from calibration to 3D reconstruction

This study compares the accuracy of circular and linear fringe projection profilometry in the aspects of system calibration and 3D reconstruction. We introduce, what we believe to be, a novel calibration method and 3D reconstruction technique using circular and radial fringe patterns. Our approach is compared with the traditional linear phase-shifting method through several 2 × 2 experimental setups. Results indicate that our 3D reconstruction method surpasses the linear phase-shifting approach in performance, although calibration efficiency does not present a superior performance. Further analysis reveals that sensitivity and estimated phase error contribute to the relative underperformance in calibration. This paper offers insights into the potentials and limitations of circular fringe projection profilometry.