Piston Error Automatic Correction for Segmented Mirrors via Deep Reinforcement Learning.

The segmented mirror co-phase error identification technique based on supervised learning methods has the advantages of simple application conditions, no dependence on custom sensors, a fast calculation speed, and low computing power requirements compared with other methods. However, it is often difficult to obtain a high accuracy in practical application situations with this method because of the difference between the training model and the actual model. The reinforcement learning algorithm does not need to model the real system when operating the system. However, it still retains the advantages of supervised learning. Thus, in this paper, we placed a mask on the pupil plane of the segmented telescope optical system. Moreover, based on the wide spectrum, point spread function, and modulation transfer function of the optical system and deep reinforcement learning-without modeling the optical system-a large-range and high-precision piston error automatic co-phase method with multiple-submirror parallelization was proposed. Finally, we carried out relevant simulation experiments, and the results indicate that the method is effective.

An In-Run Automatic Demodulation Phase Error Compensation Method for MEMS Gyroscope in Full Temperature Range.

The demodulation phase error will cause the quadrature error to be coupled to the rate output, resulting in performance deterioration of the MEMS gyroscope. To solve this problem, an in-run automatic demodulation phase error compensation method is proposed in this paper. This method applies square wave angular rate input to the gyroscope and automatically identifies the value of the demodulation phase error through the designed automatic identification algorithm. To realize in-run automatic compensation, the demodulation phase error corresponding to the temperature point is measured every 10 °C in the full-temperature environment (-40~60 °C). The relationship between temperature and demodulation phase error is fitted by a third-order polynomial. The temperature is obtained by the temperature sensor and encapsulated in the ceramic packages of the MEMS gyroscope, and the in-run automatic compensation is realized based on the fitting curve. The temperature hysteresis effect on the zero-rate output (ZRO) of the gyroscope is eliminated after compensation. The bias instability (BI) of the three gyroscopes at room temperature (25 °C) is reduced by four to eight times to 0.1°/h, while that at full-temperature environment (-40~60 °C) is reduced by three to four times to 0.1°/h after in-run compensation.

Error Awareness in the Volcano Plots of Oxygen Electroreduction to Hydrogen Peroxide.

Electrocatalysis holds the key to the decentralized production of hydrogen peroxide via the two-electron oxygen reduction reaction (ORR, O2g+2H++e-→H2O2aq). However, cost-effective, active, and selective catalysts are still sought after. While density functional theory (DFT) has already led to the discovery of various enhanced catalysts, it has a severe yet often unnoticed drawback: the ill description of O2 and H2O2. Here, we analyze the impact of the errors in those two species on the most widespread activity plots in the literature, namely free-energy diagrams and Sabatier-type volcano plots. Uncorrected or partially corrected gas-phase energies lead to appreciably different activity plots that may provide inaccurate predictions. Indeed, we show for a variety of electrocatalysts that only when the errors in O2 and H2O2 are corrected can DFT mimic the experiments. In sum, this work provides concrete guidelines to avoid a common pitfall of computational models for electrocatalytic hydrogen peroxide production.

Range-Dependent Channel Calibration for High-Resolution Wide-Swath Synthetic Aperture Radar Imagery.

High-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) imaging with azimuth multi-channel always suffers from channel phase and amplitude errors. Compared with spatial-invariant error, the range-dependent channel phase error is intractable due to its spatial dependency characteristic. This paper proposes a novel parameterized channel equalization approach to reconstruct the unambiguous SAR imagery. First, a linear model is established for the range-dependent channel phase error, and the sharpness of the reconstructed Doppler spectrum is used to measure the unambiguity quality. Furthermore, the intrinsic relationship between the channel phase errors and the sharpness is revealed, which allows us to estimate the optimal parameters by maximizing the sharpness of the reconstructed Doppler spectrum. Finally, the results from real-measured data show that the suggested method performs exceptionally for ambiguity suppression in HRWS SAR imaging.

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.

Large Range of a High-Precision, Independent, Sub-Mirror Three-Dimensional Co-Phase Error Sensing and Correction Method via a Mask and Population Algorithm.

The emergence of segmented mirrors is expected to solve the design, processing, manufacturing, testing, and launching of space telescopes of large apertures. However, with the increase in the number of sub-mirrors, the sensing and correction of co-phase errors in segmented mirrors will be very difficult. In this paper, an independent three-dimensional method for sub-mirror co-phase error sensing and correction method is proposed. The method is based on a wide spectral modulation transfer function (MTF), mask, population optimization algorithm, and online model-free correction. In this method, the sensing and correction process of each sub-mirror co-phase error is independent of each other, so the increase in the number of sub-mirrors will not increase the difficulty of the method. This method can sense and correct the co-phase errors of three dimensions of the sub-mirror, including piston, tip, and tilt, even without modeling the optical system, and has a wide detection range and high precision. And the efficiency is high because the sub-mirrors can be corrected simultaneously in parallel. Simulation results show that the proposed method can effectively sense and correct the co-phase errors of the sub-mirrors in the range [-50λ, 50λ] in three dimensions with high precision. The average RMSE value in 100 experiments of the true co-phase error values and the experimental co-phase error values of one of the six sub-mirrors is 2.358 × 10-7λ.

Interactive Errors Analysis and Scale Factor Nonlinearity Reduction Methods for Lissajous Frequency Modulated MEMS Gyroscope.

Although the Lissajous frequency modulated (LFM) mode can improve the long-term and temperature stability of the scale factor (SF) for mode mismatch MEMS gyroscopes, its SF nonlinearity poses a significant limitation for full-scale accuracy maintenance. This paper examines the interaction effects among stiffness coupling, system phase delay, readout demodulation phase shift, and velocity amplitude mismatch within the control process. Based on the completion of frequency difference control and demodulation phase matching, we clarify that the remaining stiffness coupling and residual system phase error are the primary factors influencing SF nonlinearity. Furthermore, SF nonlinearity is reduced through error compensation. On one hand, this paper suppresses stiffness coupling through the observation of the instantaneous frequency difference and the application of the quadrature voltage. On the other hand, system phase error is compensated by observing the amplitude control force and tuning the reference in the Phase-Locked Loops (PLLs). Subsequent simulations of these methods demonstrated a remarkable 97% reduction in SF nonlinearity within the measurement range of ±500°/s. In addition, an observed rule dictates that maintaining a sufficiently large frequency split effectively constrains the SF nonlinearity.

The Design, Fabrication, and Evaluation of a Phase-Resolved Partial Discharge Sensor Embedded in a MV-Class Bushing.

This paper proposes a novel phase-resolved partial discharge (PRPD) sensor embedded in a MV-class bushing for high-accuracy insulation analysis. The design, fabrication, and evaluation of a PRPD sensor embedded in a MV-class bushing aimed to achieve the detection of partial discharge (PD) pulses that are phase-synchronized with the applied primary HV signal. A prototype PRPD sensor was composed of a flexible printed circuit board (PCB) with dual-sensing electrodes, utilizing a capacitive voltage divider (CVD) for voltage measurement, the D-dot principle for PD detection, and a signal transducer with passive elements. A PD simulator was prepared to emulate typical PD defects, i.e., a metal protrusion. The voltage measurement precision of the prototype PRPD sensor was satisfied with the accuracy class of 0.2 specified in IEC 61869-11, as the maximum corrected voltage error ratios and corrected phase errors in 80%, 100%, and 120% of the rated voltage (13.2 kilovolts (kV)) were less than 0.2% and 10 min, respectively. In addition, the prototype PRPD sensor had good linearity and high sensitivity for PD detection compared with a conventional electrical detection method. According to performance evaluation tests, the prototype PRPD sensor embedded in the MV-class bushing can measure PRPD patterns phase-synchronized with the primary voltage without any additional synchronization equipment or system. Therefore, the prototype PRPD sensor holds potential as a substitute for conventional commercial PD sensors. Consequently, this advancement could lead to the enhancement of power system monitoring and maintenance, contributing to the digitalization and minimization of power apparatus.

At-wavelength characterization of X-ray wavefronts in Bragg diffraction from crystals.

The advent of next-generation synchrotron radiation sources and X-ray free-electron lasers calls for high-quality Bragg-diffraction crystal optics to preserve the X-ray beam coherence and wavefront. This requirement brings new challenges in characterizing crystals in Bragg diffraction in terms of Bragg-plane height errors and wavefront phase distortions. Here, a quantitative methodology to characterize crystal optics using a state-of-the-art at-wavelength wavefront sensing technique and statistical analysis is proposed. The method was tested at the 1-BM-B optics testing beamline at the Advanced Photon Source for measuring silicon and diamond crystals in a self-referencing single-crystal mode and an absolute double-crystal mode. The phase error sensitivity of the technique is demonstrated to be at the λ/100 level required by most applications, such as the characterization of diamond crystals for cavity-based X-ray free-electron lasers.

Evaluation of the Relative Phase Comparison Method at Its Limits Used for Absolute Phase Determination of an AC Cage Current Shunt Group.

AC current shunts are used for precise current measurements. The application of AC current shunts requires that their amplitude phase characteristics are known. A group of three geometrically identical current shunts and a reference shunt are observed in this paper. The phase characteristics of the reference shunt have been previously obtained. A relative phase comparison has been made between the three geometrically identical shunts, and phase displacement values for each have been obtained. After this, the results are verified with the reference shunt. The relative method is most suitable for shunts, where their respective RC and L/R values are small (compared with 1/ω) and of the same order. The ratios of the nominal resistance values of the shunts used in this paper are at the limit of the given statement. The conclusion is that the method applied at the mentioned limits, in terms of the metrology-grade phase angle determination of current shunts, is not to be considered reliable at frequencies higher than 1 kHz.

Near-Field Beamforming Algorithms for UAVs.

This study presents three distributed beamforming algorithms to address the challenges of positioning and signal phase errors in unmanned aerial vehicle (UAV) arrays that hinder effective beamforming. Firstly, the array's received signal phase error model was analyzed under near-field conditions. In the absence of navigation data, a beamforming algorithm based on the Extended Kalman Filter (EKF) was proposed. In cases where navigation data were available, Taylor expansion was utilized to simplify the model, the non-Gaussian noise of the compensated received signal phase was approximated to Gaussian noise, and the noise covariance matrix in the Kalman Filter (KF) was estimated. Then, a beamforming algorithm based on KF was developed. To further estimate the Gaussian noise distribution of the received signal phase, the noise covariance matrix was iteratively estimated using unscented transformation (UT), and here, a beamforming algorithm based on the Unscented Kalman Filter (UKF) was proposed. The proposed algorithms were validated through simulations, illustrating their ability to suppress the malign effects of errors on near-field UAV array beamforming. This study provides a reference for the implementation of UAV array beamforming under varying conditions.

Saturation-Induced Phase Error Compensation Method Using Complementary Phase.

Intensity saturation can induce phase error and, thus, measurement error in fringe projection profilometry. To reduce saturation-induced phase errors, a compensation method is developed. The mathematical model of saturation-induced phase errors is analyzed for N-step phase-shifting profilometry, and the phase error is approximately N-folder of the frequency of the projected fringe. Additional N-step phase-shifting fringe patterns with initial phase-shift π/N are projected for generating a complementary phase map. The final phase map is obtained by averaging the original phase map extracted from the original fringe patterns and the complementary phase map, and then the phase error can be canceled out. Both simulations and experiments demonstrated that the proposed method can substantially reduce the saturation-induced phase error and realize accurate measurements for a highly dynamic range of scenarios.

3D diffusion MRI with twin navigator-based GRASE and comparison with 2D EPI for tractography in the human brain.

PURPOSE: 3D pulse sequences enable high-resolution acquisition with a high SNR and ideal slice profiles, which, however, is particularly difficult for diffusion MRI (dMRI) due to the additional phase errors from diffusion encoding. METHODS: We proposed a twin navigator-based 3D diffusion-weighted gradient spin-echo (GRASE) sequence to correct the phase errors between shots and between odd and even spin echoes for human whole-brain acquisition. We then compared the SNR of 3D GRASE and 2D simultaneous multi-slice EPI within the same acquisition time. We further tested the performance of 2D versus 3D acquisition at equivalent SNR on fiber tracking and microstructural mapping, using the diffusion tensor and high-order fiber orientation density-based metrics. RESULTS: The proposed twin navigator approach removed multi-shot phase errors to some extent in the whole brain dMRI, and the 2D navigator performed better than the 1D navigator. Comparisons of SNR between the 2D simultaneous multi-slice EPI and 3D GRASE sequences demonstrated that the SNR of the GRASE sequence was 1.4-1.5-fold higher than the EPI sequence at an equivalent scan time. More importantly, we found a significantly higher fiber cross-section in the cerebrospinal tract, as well as richer subcortical fibers (U-fibers) using the 3D GRASE sequence compared to 2D EPI. CONCLUSION: The twin navigator-based 3D diffusion-weighted-GRASE sequence minimized the multishot phase error and effectively improved the SNR for whole-brain dMRI acquisition. We found differences in fiber tracking and microstructural mapping between 2D and 3D acquisitions, possibly due to the different slice profiles.

Development of an Optoelectronic Integrated Sensor for a MEMS Mirror-Based Active Structured Light System.

Micro-electro-mechanical system (MEMS) scanning micromirrors are playing an increasingly important role in active structured light systems. However, the initial phase error of the structured light generated by a scanning micromirror seriously affects the accuracy of the corresponding system. This paper reports an optoelectronic integrated sensor with high irradiance responsivity and high linearity that can be used to correct the phase error of the micromirror. The optoelectronic integrated sensor consists of a large-area photodetector (PD) and a receiving circuit, including a post amplifier, an operational amplifier, a bandgap reference, and a reference current circuit. The optoelectronic sensor chip is fabricated in a 180 nm CMOS process. Experimental results show that with a 5 V power supply, the optoelectronic sensor has an irradiance responsivity of 100 mV/(µW/cm2) and a -3 dB bandwidth of 2 kHz. The minimal detectable light power is about 19.4 nW, which satisfies the requirements of many active structured light systems. Through testing, the application of the chip effectively reduces the phase error of the micromirror to 2.5%.

A New Gain-Phase Error Pre-Calibration Method for Uniform Linear Arrays.

In this paper, we consider the gain-phase error calibration problem for uniform linear arrays (ULAs). Based on the adaptive antenna nulling technique, a new gain-phase error pre-calibration method is proposed, requiring only one calibration source with known direction of arrival (DOA). In the proposed method, a ULA with M array elements is divided into M-1 sub-arrays, and the gain-phase error of each sub-array can be uniquely extracted one by one. Furthermore, in order to obtain the accurate gain-phase error in each sub-array, we formulate an errors-in-variables (EIV) model and present a weighted total least-squares (WTLS) algorithm by exploiting the structure of the received data on sub-arrays. In addition, the solution to the proposed WTLS algorithm is exactly analyzed in the statistical sense, and the spatial location of the calibration source is also discussed. Simulation results demonstrate the efficiency and feasibility of our proposed method in both large-scale and small-scale ULAs and the superiority to some state-of-the-art gain-phase error calibration approaches.

A 10-20 GHz 6-Bit High-Accuracy Digital Step Attenuator with Low Insertion Loss in 0.15 µm GaAs p-HEMT Technology.

In a beamforming circuit for a modern broadband phased-array system, high accuracy and compactness have received sufficient attention as they are directly related to side lobe level and fabrication cost, respectively. In order to meet the low phase error required, this paper proposed an ultra-broadband 6-bit digital step switched-type attenuator (STA) with capacitive/inductive compensation networks. Compared to the conventional methods, the proposed technique employs an improved simplified T-structure with capacitive compensation networks, which simultaneously achieves low insertion loss and high-accuracy amplitude/phase control. In addition, on-chip level shifting circuit is integrated to avoid complex control schemes. The strategy of prioritizing return loss is adopted to alleviate the performance degradation caused by impedance mismatch after cascade. As a proof-of-principle demonstration, a wideband 6-bit STA with core area of only 0.5 mm × 1.8 mm was designed via 0.15-micrometer GaAs pHEMT technology. It exhibits ultra-broadband operation with a 31.5 dB amplitude tuning range and a 0.5 dB tuning step. The insertion loss of the reference state is 4-5.3 dB. The return loss is better than 15 dB for all the 64 states. The RMS amplitude and phase errors are less than 0.2 dB and 2° over the 10 to 20 GHz.

Comprehensive Design Method of a High-Frequency-Response Fast Tool Servo System Based on a Full-Frequency Error Control Algorithm.

With the development of optoelectronic information technology, high-performance optical systems require an increasingly higher surface accuracy of optical mirrors. The fast tool servo (FTS) based on the piezoelectric actuator is widely used in the compensation machining of high-precision optical mirrors. However, with the low natural frequency of mechanical structures, hysteresis of the piezoelectric actuators, and phase delay of the control systems, conventional FTS systems face problems such as a low working frequency and a large tracking error. This study presents a method for the design of a high-performance FTS system. First, a flexure hinge servo turret with a high natural frequency was designed through multi-objective optimization and finite element simulations. Subsequently, a composite control algorithm was proposed, targeting the problems of hysteresis and phase delay. The modified Prandtl-Ishlinskii inverse hysteresis model was used to overcome the hysteresis effect and a zero-phase error tracker was designed to reduce the phase error. The experimental results reveal that the tracking error of the designed FTS system was <10% in the full frequency range (0-1000 Hz).

Phase Error Analysis and Correction for Crossed-Grating Phase-Shifting Profilometry.

Crossed-grating phase-shifting profilometry (CGPSP) has great utility in three-dimensional shape measurement due to its ability to acquire horizontal and vertical phase maps in a single measurement. However, CGPSP is extremely sensitive to the non-linearity effect of a digital fringe projection system, which is not studied in depth yet. In this paper, a mathematical model is established to analyze the phase error caused by the non-linearity effect. Subsequently, two methods used to eliminate the non-linearity error are discussed in detail. To be specific, a double five-step algorithm based on the mathematical model is proposed to passively suppress the second non-linearity. Furthermore, a precoding gamma correction method based on probability distribution function is introduced to actively attenuate the non-linearity of the captured crossed fringe. The comparison results show that the active gamma correction method requires less fringe patterns and can more effectively reduce the non-linearity error compared with the passive method. Finally, employing CGPSP with gamma correction, a faster and reliable inverse pattern projection is realized with less fringe patterns.

Clock signal distribution with second order nodes: Design hints.

Despite being in use since the 1960's, clock distribution networks continue to be important, mainly since the digitalization of numerous electronic tasks, which demands precise time measures for synchronizing internal and external processes in computational and instrumentation applications. Designing clock distribution networks requires determination/estimation of the appropriate topologies and parameters that guarantee the mutual synchronization of the coupled oscillators. This problem has been largely studied in the telecommunications context, with digital hierarchies succeeding at providing precise multiplexing and switching, integrating services, and in the process, giving rise to a new era of communication. From a mathematical viewpoint, this work considers linear coupling factors, with the study of nonlinear effects still open. As the nodes of time distribution networks are phase-locked loops, considering nonlinearities is helpful for the design and operation of such systems. Herein, an overview of possible solutions concerning topologies and parameters is presented, allowing performance hints regarding network architectures and parameters to help designers. The main contribution is to put together and compare each solution while taking nonlinearities into account and to associate the application to be supported with the best clock distribution solution, thus providing simple rules of thumb for system design.

DeepResp: Deep learning solution for respiration-induced B0 fluctuation artifacts in multi-slice GRE.

Respiration-induced B0 fluctuation corrupts MRI images by inducing phase errors in k-space. A few approaches such as navigator have been proposed to correct for the artifacts at the expense of sequence modification. In this study, a new deep learning method, which is referred to as DeepResp, is proposed for reducing the respiration-artifacts in multi-slice gradient echo (GRE) images. DeepResp is designed to extract the respiration-induced phase errors from a complex image using deep neural networks. Then, the network-generated phase errors are applied to the k-space data, creating an artifact-corrected image. For network training, the computer-simulated images were generated using artifact-free images and respiration data. When evaluated, both simulated images and in-vivo images of two different breathing conditions (deep breathing and natural breathing) show improvements (simulation: normalized root-mean-square error (NRMSE) from 7.8 ± 5.2% to 1.3 ± 0.6%; structural similarity (SSIM) from 0.88 ± 0.08 to 0.99 ± 0.01; ghost-to-signal-ratio (GSR) from 7.9 ± 7.2% to 0.6 ± 0.6%; deep breathing: NRMSE from 13.9 ± 4.6% to 5.8 ± 1.4%; SSIM from 0.86 ± 0.03 to 0.95 ± 0.01; GSR 20.2 ± 10.2% to 5.7 ± 2.3%; natural breathing: NRMSE from 5.2 ± 3.3% to 4.0 ± 2.5%; SSIM from 0.94 ± 0.04 to 0.97 ± 0.02; GSR 5.7 ± 5.0% to 2.8 ± 1.1%). Our approach does not require any modification of the sequence or additional hardware, and may therefore find useful applications. Furthermore, the deep neural networks extract respiration-induced phase errors, which is more interpretable and reliable than results of end-to-end trained networks.