Low-frequency Errors Research Articles

Research on case rotating modulation for nuclear-spin comagnetometer in space-stable INS

To restrain the effect of the bias error of nuclear-spin comagnetometer in space-stable Inertial Navigation System (INS) for long-endurance independent navigation, the case rotating modulation for comagnetometer was researched. The structure of comagnetometer case rotating in space-stable INS was presented and the modulation equation is derived. By comparing the modulation results of three types of rotating schemes, the four-positing rotating scheme was considered optimal. Modulation result showed that comagnetometer constant bias and partial magnetic-field related errors can be averaged out, low-frequency random errors in one rotating modulation period can be averaged out as constant errors; high-frequency random errors are affected by rotating modulation. Semi-physical simulation test results show that the accuracy of the K-Rb-21Ne comagnetometer data is effectively improved by case rotating modulation with the bias mean value decreasing from the magnitude of 0.01°/h to 10−4°/h and the bias stability improving from the magnitude of 0.01°/h to 0.001°/h.

Fast shading correction for cone-beam CT via partitioned tissue classification

The quantitative use of cone beam computed tomography (CBCT) in radiation therapy is limited by severe shading artifacts, even with system embedded correction. We recently proposed effective shading correction methods, using planning CT (pCT) as prior information to estimate low-frequency errors in either the projection domain or image domain. In this work, we further improve the clinical practicality of our previous methods by removing the requirement of prior pCT images.Clinical CBCT images are typically composed of a limited number of tissues. By utilizing the low frequency characteristic of shading distribution, we first generate a ‘shading-free’ template image by enforcing uniformity on CBCT voxels of the same tissue type via a technique named partitioned tissue classification. Only a small subset of voxels in the template image are used in the correction process to generate sparse samples of shading artifacts. Local filtration, a Fourier transform based algorithm, is employed to efficiently process the sparse errors to compute a full-field distribution of shading artifacts for CBCT correction. We evaluate the method’s performance using an anthropomorphic pelvis phantom and 6 pelvis patients.The proposed method improves the image quality of CBCT for both phantom and patients to a level matching that of pCT. On the pelvis phantom, the signal non-uniformity (SNU) is reduced from 12.11% to 3.11% and 8.40% to 2.21% on fat and muscle, respectively. The maximum CT number error is reduced from 70 to 10 HU and 73 to 11 HU on fat and muscle, respectively. On patients, the average SNU is reduced from 9.22% to 1.06% and 11.41% to 1.67% on fat and muscle, respectively. The maximum CT number error is reduced from 95 to 9 HU and 88 to 8 HU on fat and muscle, respectively. The typical processing time for one CBCT dataset is about 45 s on a standard PC.

Improving Precision Force Control With Low-Frequency Error Amplification Feedback: Behavioral and Neurophysiological Mechanisms.

Although error amplification (EA) feedback has been shown to improve performance on visuomotor tasks, the challenge of EA is that it concurrently magnifies task-irrelevant information that may impair visuomotor control. The purpose of this study was to improve the force control in a static task by preclusion of high-oscillatory components in EA feedback that cannot be timely used for error correction by the visuomotor system. Along with motor unit behaviors and corticomuscular coherence, force fluctuations (Fc) were modeled with non-linear SDA to contrast the reliance of the feedback process and underlying neurophysiological mechanisms by using real feedback, EA, and low-frequency error amplification (LF-EA). During the static force task in the experiment, the EA feedback virtually potentiated the size of visual error, whereas the LF-EA did not channel high-frequency errors above 0.8 Hz into the amplification process. The results showed that task accuracy was greater with the LF-EA than with the real and EA feedback modes, and that LF-EA led to smaller and more complex Fc. LF-EA generally led to smaller SDA variables of Fc (critical time points, critical point of Fc, the short-term effective diffusion coefficient, and short-term exponent scaling) than did real feedback and EA. The use of LF-EA feedback increased the irregularity of the ISIs of MUs but decreased the RMS of the mean discharge rate, estimated with pooled MU spike trains. Beta-range EEG–EMG coherence spectra (13–35 Hz) in the LF-EA condition were the greatest among the three feedback conditions. In summary, amplification of low-frequency errors improves force control by shifting the relative significances of the feedforward and feedback processes. The functional benefit arises from the increase in the common descending drive to promote a stable state of MU discharges.

Design of two-wheel self-balancing vehicle based on visual identification

Poor user experience is caused by the current unstable operation of the two-wheel self-balancing vehicle control system, the high failure rate, and the poor accuracy and sensitivity of the control system (prone to deviation). Therefore, the work studied the two-wheel self-balancing vehicle system with the visual recognition of vehicle attitude. Kalman filtering and PID control algorithm were adopted to reduce the high frequency interference of the accelerometer and the low frequency error of the gyroscope, improve the response speed and control precision of motor to error, and ensure vertical control. The road images were acquired by a charge-coupled device vision sensor with the edge information extracted by the Laplacian operator, which ensures autonomous navigation control of a balance car. Based on the calculation of the distance between road axis and the existence detection of forward obstacles, the early warning mechanism was established through the calculation of the group agent to improve the safety performance of a balance vehicle. Experiments showed the improved control system has good stability, fast walking speed, strong anti-interference, and high security.

Howland Current Source Applied to Magnetic Field Generation in a Tri-Axial Helmholtz Coil

This work describes the design and testing of a power Voltage-Controlled Current Source (VCCS) based on the Howland Current Source (HCS) topology. This source is part of a system that contains a three-axial Helmholtz coil and is used to generate a controlled magnetic field environment for aerospace applications. Initially, the paper presents the HCS theory and practical limitations on the premise that the system must be built using low-cost off-the-shelf components. The paper also carefully address on how to design and plan the VCCS matching physical and electrical parameters/limitations of a specific Helmholtz coil. All project details as well as the built VCCS electronics and its results are shown. These include linearity and a first order calibration test, stability and low-frequency error measurement, step response and a frequency limitation analysis. The built source is capable of sourcing up to ±1.5 A at ±25 V, maintaining its linearity and achieving an error smaller than 0.5% with a first order calibration. The final HCS prototype together with the Helmholtz coil allows an excellent capability regarding magnetic field generation for both open and closed-loop applications.

Vision-based systems for structural deformation measurement: case studies

Vision-based systems offer a promising way to measure displacement and are receiving increased attention in civil structural monitoring. However, the working performance of vision-based systems, especially their measurement accuracy and robustness to different field conditions, is not fully understood. This study reports three cases studies of vision-based monitoring tests including one in a laboratory, one on a short-span bridge and one on a long-span bridge. The tracking accuracy is quantified in laboratory conditions in the range from 0·02 to 0·20 pixel, depending on the target patterns as well as the tracking method selected. The measurement performance under several field challenges is investigated, including long-range measurement (e.g. camera-to-target distance of 710 m), low-contrast target patterns, changes of target patterns and changes in lighting conditions. Three representative tracking methods for the video processing, namely, correlation-based template matching, Lucas–Kanade optical flow estimation and scale-invariant feature transform were used for the analysis, indicating their advantages and shortcomings for field measurement. One of the main observations in field application is that changes in lighting conditions might cause some low-frequency measurement errors that could be misunderstood without prior knowledge regarding structural loading conditions.

Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

We propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Various numerical experiments are used to demonstrate the robustness of the proposed solver.

Optimal illumination pattern for transport-of-intensity quantitative phase microscopy.

The transport-of-intensity equation (TIE) is a well-established non-interferometric phase retrieval approach, which enables quantitative phase imaging (QPI) of transparent sample simply by measuring the intensities at multiple axially displaced planes. Nevertheless, it still suffers from two fundamentally limitations. First, it is quite susceptible to low-frequency errors (such as "cloudy" artifacts), which results from the poor contrast of the phase transfer function (PTF) near the zero frequency. Second, the reconstructed phase tends to blur under spatially low-coherent illumination, especially when the defocus distance is beyond the near Fresnel region. Recent studies have shown that the shape of the illumination aperture has a significant impact on the resolution and phase reconstruction quality, and by simply replacing the conventional circular illumination aperture with an annular one, these two limitations can be addressed, or at least significantly alleviated. However, the annular aperture was previously empirically designed based on intuitive criteria related to the shape of PTF, which does not guarantee optimality. In this work, we optimize the illumination pattern to maximize TIE's performance based on a combined quantitative criterion for evaluating the "goodness" of an aperture. In order to make the size of the solution search space tractable, we restrict our attention to binary-coded axis-symmetric illumination patterns only, which are easier to implement and can generate isotropic TIE PTFs. We test the obtained optimal illumination by imaging both a phase resolution target and HeLa cells based on a small-pitch LED array, suggesting superior performance over other suboptimal patterns in terms of both signal-to-noise ratio (SNR) and spatial resolution.

Instant 3D photography

We present an algorithm for constructing 3D panoramas from a sequence of aligned color-and-depth image pairs. Such sequences can be conveniently captured using dual lens cell phone cameras that reconstruct depth maps from synchronized stereo image capture. Due to the small baseline and resulting triangulation error the depth maps are considerably degraded and contain low-frequency error, which prevents alignment using simple global transformations. We propose a novel optimization that jointly estimates the camera poses as well as spatially-varying adjustment maps that are applied to deform the depth maps and bring them into good alignment. When fusing the aligned images into a seamless mosaic we utilize a carefully designed data term and the high quality of our depth alignment to achieve two orders of magnitude speedup w.r.t. previous solutions that rely on discrete optimization by removing the need for label smoothness optimization. Our algorithm processes about one input image per second, resulting in an end-to-end runtime of about one minute for mid-sized panoramas. The final 3D panoramas are highly detailed and can be viewed with binocular and head motion parallax in VR.

Investigation on the influence of aerostatic pressure upon surface generation in flycutting

Single-point diamond flycutting is an important technology for cutting flat KH2PO4 (potassium dihydrogen phosphate) crystals of large size. However, there always exist some undesirable waviness errors on the machined surface, which can directly reduce the optical performance of the potassium dihydrogen phosphate crystals. This article presents a kind of low-frequency waviness errors with wavelength about 26 mm along the feeding direction in single-point diamond flycutting, which has not been described yet. In order to find the main source of the mentioned waviness errors, the relationship between the displacement of the cutting tool and the aerostatic pressure was quantitatively studied for the first time. And then, surface simulation considering the aerostatic pressure fluctuations was carried out based on the relationship. Besides, a novel method that can achieve online submicron feeding along axial direction in single-point diamond flycutting without complex structure was proposed considering the spindle motion errors, the spindle dynamic characteristics and the aerostatic pressure. The experimental results validate that the mentioned waviness errors are mainly generated by the bolt stretched phenomenon and deformation of the big disk flycutting head due to the aerostatic pressure fluctuations. And the proposed method can achieve a cutting depth of about 120 nm when the aerostatic pressure increases from 0.52 to 0.56 MPa, which can reduce the cutting force and is beneficial for the performance of single-point diamond flycutting.

Reprojection Alignment for Trajectory Perturbation Estimation in Microtomography

For standard laboratory microtomography systems, acquired radiographs do not always adhere to the strict geometrical assumptions of the reconstruction algorithm. The consequence of this geometrical inconsistency is that the reconstructed tomogram contains motion artifacts, e.g., blurring, streaking, double-edges. To achieve a motion-artifact-free tomographic reconstruction, one must estimate, and subsequently correct for, the per-radiograph experimental geometry parameters. In this paper, we examine the use of re-projection alignment (RA) to estimate per-radiograph geometry. Our simulations evaluate how the convergence properties of RA vary with: motion-type (smooth versus random), trajectory (helical versus discrete-sampling ‘space-filling’ trajectories) and tomogram resolution. The idealized simulations demonstrate for the space-filling trajectory that RA convergence rate and accuracy is invariant with regard to the motion-type and that the per-projection motions can be estimated to less than 0.25 pixel mean absolute error by performing a single quarter-resolution RA iteration followed by a single half-resolution RA iteration. The direct impact is that, for the space-filling trajectory, one can incorporate RA in an iterative multi-grid reconstruction scheme with only a single RA iteration per multi-grid resolution step. We also find that for either trajectory, slowly varying vertical errors cannot be reliably estimated by employing the RA method alone; such errors are indistinguishable from a trajectory of different pitch. This has minimal effect in practice because RA can be combined with reference frame correction which is effective for correcting low-frequency errors.

Partial null astigmatism-compensated interferometry for a concave freeform Zernike mirror

Partial null interferometry without using any null optics is proposed to measure a concave freeform Zernike mirror. Oblique incidence on the freeform mirror is used to compensate for astigmatism as the main component in its figure, and to constrain the divergence of the test beam as well. The phase demodulated from the partial nulled interferograms is divided into low-frequency phase and high-frequency phase by Zernike polynomial fitting. The low-frequency surface figure error of the freeform mirror represented by the coefficients of Zernike polynomials is reconstructed from the low-frequency phase, applying the reverse optimization reconstruction technology in the accurate model of the interferometric system. The high-frequency surface figure error of the freeform mirror is retrieved from the high-frequency phase adopting back propagating technology, according to the updated model in which the low-frequency surface figure error has been superimposed on the sag of the freeform mirror. Simulations verified that this method is capable of testing a wide variety of astigmatism-dominated freeform mirrors due to the high dynamic range. The experimental result using our proposed method for a concave freeform Zernike mirror is consistent with the null test result employing the computer-generated hologram.

Theoretical compensation of static deformations of freeform multimirror substrates.

Varying temperatures influence the figure errors of freeform metal mirrors by thermal expansion. Furthermore, different materials lead to thermo-elastic bending effects. The paper presents a derivation of a compensation approach for general static loads. Utilizing perturbation theory, this approach works for shape compensation of substrates that operate in various temperature environments. Verification is made using a finite element analysis, which is further used to produce manufacturable CAD models. The remaining low spatial frequency errors are deterministically correctable using diamond turning or polishing techniques.

Study on Surface Morphology of Vibration Assisted Cutting

Vibration assisted cutting is widely regarded as an effective technique due to the characteristics of friction reversal and intermittent cutting. However, there are few studies on surface morphology of vibration assisted cutting machining. The high frequency error (surface roughness) and low frequency error (surface error) of the surface topography are obtained by the decomposition and reconstruction of the wavelet packet in this paper for the in-depth investigating of the surface morphology. The influence of vibration assisted cutting parameters on surface topography are revealed by calculating the surface evaluation parameters such as surface roughness, PV value and root mean square error. In this paper, two-dimensional wavelet packet analysis is conducted on the surface morphology of vibration assisted cutting. Finally, the influence of surface roughness and shape error on vibration assisted cutting are obtained. Through the analysis, it can be found that, along with the increase of the minor axis of vibration assisted cutting parameters, the surface roughness, PV value and root mean square deviation become larger during the processing.

A Time-Frequency PID Controller Design for Improved Anti-Interference Performance of a Solenoid Valve Applicable to Hydraulic Cylinder Actuation

PID control is widely used in electro-hydraulic systems. However, enhancing PID control performance in response to system nonlinearity, fluctuations of external load, and noise inevitably renders the chattering of the system that are also telltale indications of poor efficiency and dynamic instability. On the other hand, tuning down PID parameters would alleviate chatter at the expenses of reduced performance and inefficient use of resources. To address the particular issue, a novel controller concept termed as the time-frequency PID (TFPID) is developed. Firstly, a nonlinear electro-hydraulic dynamic model to be controlled is built for numerical and physical studies. Next, the working principle of the TFPID control is elaborated where the discrete wavelet transform is employed to decompose the error signal into high frequency error and low frequency error. Two unique PID controllers incorporating proportion, differential, and integral control are designed to mitigate the two error signals. The TFPID controller and system model are developed in MATLAB/Simulink to optimize the parameters and a hardware-in-the-loop test bench is employed to establish the performance of the system subject to interferences. Physical test results show that TFPID performs significantly better in anti-interference, stability, and dynamic response.

Preasymptotic convergence of randomized Kaczmarz method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the initial error is smooth (e.g. sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.

Bulk-Density Representations of Branched Planar Ice Crystals: Errors in the Polarimetric Radar Variables

AbstractRecent interest in interpreting polarimetric radar observations of ice and evaluating microphysical model output with these observations has highlighted the importance of accurately computing the scattering of microwave radiation by branched planar ice crystals. These particles are often represented as spheroids with uniform bulk density, reduced from that of solid ice to account for the complex, nonuniform structure of natural branched crystals. In this study, the potential errors that arise from this assumption are examined by comparing scattering calculations of branched planar crystals with those of homogeneous, reduced-density plate crystals and spheroids with the same mass, aspect ratio, and maximum dimension. The results show that this assumption leads to significant errors in backscatter cross sections at horizontal and vertical polarization, specific differential phase (KDP), and differential reflectivity (ZDR), with the largest ZDR errors for ice crystals with the most extreme aspect ratios (<0.01) and effective densities < 250 kg m−3. For example, the maximum errors in X-band ZDR are 4.5 dB for 5.6-mm branched planar crystals. However, substantial errors are present at all weather radar frequencies, with resonance scattering effects at Ka and W band amplifying the low-frequency errors. The implications of these results on the interpretation of polarimetric radar observations and forward modeling of the polarimetric radar variables from microphysical model output are discussed.

An SC Interface With Programmable-Gain Embedded $\Delta \Sigma $ ADC for Monolithic Three-Axis 3-D Stacked Capacitive MEMS Accelerometer

This paper presents a switched capacitor interface circuit for a monolithic three-axis capacitive micro-electro-mechanical system (MEMS) accelerometer. The MEMS sensor and the interface circuit of our system-in-package-type MEMS accelerometer are 3-D stacked to optimize integration density with a small package footprint. The proposed fully integrated interface circuit includes a capacitance-to-voltage converter followed by a $\Delta \Sigma $ analog-to-digital converter (ADC). To optimize system power and area, the programmable-gain functionality is embedded to the second-order $\Delta \Sigma $ ADC without any stability degradation. The offset and 1/ $f$ noise of the fully differential interface circuit are mitigated by a correlated double sampling technique. The rest of the low-frequency error from system mismatch is also suppressed by calibration using fine metal-oxide–semiconductor capacitor array. The measurement results of our MEMS accelerometer show a 13.7-b maximum effective resolution with the 197- $\mu \text{g}$ / $\surd $ Hz noise floor in a conversion time of 1 ms with a maximum nonlinearity of 1.09%. Implemented in a standard 0.18- $\mu \text{m}$ CMOS technology, the fabricated chip consumes only 247- $\mu \text{A}$ current from a 3.3-V supply, and 37- $\mu \text{A}$ current from a 1.8-V supply.

Beam drift error and control technology for scanning beam interference lithography.

To improve the quality of grating masks made by scanning beam interference lithography, this article established a mathematical model of step-scanning exposure and analyzed the effects of the beam drift error on the interference image. Beam angle drift can be decomposed into the drift error δx in the exposure plane (XOZ plane) and the drift error δy perpendicular to the plane. Analysis shows that the δx has a major impact on the interference fringes during exposure, which may affect the precision of phase lock. δy leads to the appearance of deflected interference strips and affects the exposure dose. When a low-frequency drift error appears in the light path, the exposure contrast on the photoresist will decrease with the exposure process, which makes the fabrication of large-size diffraction gratings difficult. Furthermore, taking advantage of the characteristics of a scanning beam interference lithography system, an exposed beam stable system was designed that can effectively suppress the low-frequency drift of the beam. The total beam angle control accuracy is better than the 2.7μrad, and position control accuracy is better than 3.9μm (both for 1σ), which achieves the expected goal of the design.

Multiple-model adaptive estimator for spacecraft attitude sensor calibration

PurposeThis paper aims to present a multiple-model adaptive estimator (MMAE) to calibrate the star sensor low frequency error (LFE). The star sensor LFE, which is caused primarily by the periodic thermal distortion, has a great impact on spacecraft attitude determination accuracy.Design/methodology/approachThe unfavorable effect of the LFE can be partly eliminated by using the calibration algorithm based on the augmented Kalman filter (AKF). However, the AKF may be worse than the traditional Kalman filter (KF) in the absence of the LFE. To cope with this problem, the MMAE is applied first time for combining the AKF and the KF in the spacecraft attitude determination system, such that satisfactory performance can be achieved in different operating scenarios.FindingsThe convergence of the presented MMAE is demonstrated through a formal derivation. A novel method is proposed to tune the MMAE design parameter, such that the convergence rate of the estimator is increased. It is shown via numerical studies that the presented algorithm outperforms the AKF and the KF.Practical implicationsThe calibration algorithm is applicable for spacecraft attitude determination.Originality/valueAn effective star sensor LFE calibration algorithm based on the MMAE is developed. In addition, a novel method is proposed to increase convergence rate of the estimator.