Fourier Phase Research Articles

An Adaptive Tracking Algorithm for Convection in Simulated and Remote Sensing Data

AbstractA robust and computationally efficient object tracking algorithm is developed by incorporating various tracking techniques. Physical properties of the objects, such as brightness temperature or reflectivity, are not considered. Therefore, the algorithm is adaptable for tracking convection-like features in simulated data and remotely sensed two-dimensional images. In this algorithm, a first guess of the motion, estimated using the Fourier phase shift, is used to predict the candidates for matching. A disparity score is computed for each target–candidate pair. The disparity also incorporates overlapping criteria in the case of large objects. Then the Hungarian method is applied to identify the best pairs by minimizing the global disparity. The high-disparity pairs are unmatched, and their target and candidate are declared expired and newly initiated objects, respectively. They are tested for merger and split on the basis of their size and overlap with the other objects. The sensitivity of track duration is shown for different disparity and size thresholds. The paper highlights the algorithm’s ability to study convective life cycles using radar and simulated data over Darwin, Australia. The algorithm skillfully tracks individual convective cells (a few pixels in size) and large convective systems. The duration of tracks and cell size are found to be lognormally distributed over Darwin. The evolution of size and precipitation types of isolated convective cells is presented in the Lagrangian perspective. This algorithm is part of a vision for a modular platform [viz., TINT is not TITAN (TINT) and Tracking and Object-Based Analysis of Clouds (tobac)] that will evolve into a sustainable choice to analyze atmospheric features.

Characterization of Electrical–Thermal–Mechanical Deformation of Bonding Wires Under Silicone Gel Using LF-OCT

Bonding wires are one of the most failure-prone components of power electronics’ modules, and silicone gel is usually employed to encase bonding wires. To study the deformation of silicone gel-encased bonding wires, in this article, we report the use of line-field optical coherence tomography (LF-OCT) technique to precisely measure the electrical–thermal–mechanical (ETM) deformation of bonding wires. An LF-OCT system was developed to capture the whole cross-sectional image (B-scan) of the bonding wire sample in a single-shot fashion due to its advantageous parallel detection scheme. This, together with the Fourier phase self-referencing technique, allows the deformation of the bonding wires to be quantitatively measured down to the range of 0.1 nm. The maximum sampling rate (framerate) of the deformation measurement achieved was 400 Hz when setting camera imaging size to 1920 × 200 pixels, providing a temporal resolution of 2.5 ms for monitoring the ETM deformation dynamics of the bonding wire. We found that the ETM deformation of the gel-encased bonding wire was about three times smaller than that of the bare bonding wire. These results represent the first experimental demonstration that the LF-OCT could be a useful analytical tool for studying the time-dependent ETM deformation of bonding wires encased by silicone gel.

Research on dynamic characteristics of gear system considering the influence of temperature on material performance

Under high-speed and heavy-load conditions, the influence of temperature on the gear system is extremely important. Basically, the current work on the effect of temperature mostly considers the flash temperature or the overall temperature field to cause expansion at the meshing point and then affects nonlinear factors such as time-varying meshing stiffness, which lead to the deterioration of the dynamic transmission. This work considers the effect of temperature on the material’s elastic modulus and Poisson’s ratio and relates the temperature to the time-varying meshing stiffness. The effects of temperature on the elastic modulus and Poisson’s ratio are expressed as functions and brought into the improved energy method stiffness calculation formula. Then, the dynamic characteristics of the gear system are analyzed. With the bifurcation diagram, phase, Poincaré, and fast Fourier transform plots of the gear system, the influence of temperature on the nonlinear dynamics of the gear system is discussed. The numerical analysis results show that as the temperature increases, the dynamic response of the system in the middle-speed region gradually changes from periodic motion to chaos.

Complexity-guided Fourier phase retrieval from noisy data

Reconstruction of a stable and good quality solution from noisy single-shot Fourier intensity data is a challenging problem for phase retrieval algorithms. We examine behavior of the solution provided by the hybrid input-output (HIO) algorithm for noisy data, from the perspective of the complexity guidance methodology that was introduced by us in an earlier paper [J. Opt. Soc. Am. A36, 202 (2019)JOAOD60740-323210.1364/JOSAA.36.000202]. We find that for noisy data, the complexity of the solution outside the support keeps increasing as the HIO iterations progress. Based on this observation, a strategy for controlling the solution complexity within and outside the support during the HIO iterations is proposed and tested. In particular, we actively track and control the growth of complexity of the solution outside the support region with iterations. This in turn provides us with guidance regarding the level to which the complexity of the solution within the support region needs to be adjusted, such that the total solution complexity is equal to that estimated from raw Fourier intensity data. In our studies, Poisson noise with mean photon counts per pixel in the Fourier intensity data ranges over four orders of magnitude. We observe that the performance of the proposed strategy is noise robust in the sense that with increasing noise, the quality of the phase solution degrades gradually. For higher noise levels, the solution loses textural details while retaining the main object features. Our numerical experiments show that the proposed strategy can uniformly handle pure phase objects, mixed amplitude-phase objects, and the case of dc blocked Fourier intensity data. The results may find a number of applications where single-shot Fourier phase retrieval is critical to the success of corresponding applications.

Actively Driven Fluctuations in a Fibrin Network

Understanding force propagation through the fibrous extracellular matrix can elucidate how cells interact mechanically with their surrounding tissue. Presumably, due to elastic nonlinearities of the constituent filaments and their random connection topology, force propagation in fiber networks is quite complex, and the basic problem of force propagation in structurally heterogeneous networks remains unsolved. We report on a new technique to detect displacements through such networks in response to a localized force, using a fibrin hydrogel as an example. By studying the displacements of fibers surrounding a two-micron bead that is driven sinusoidally by optical tweezers, we develop maps of displacements in the network. Fiber movement is measured by fluorescence intensity fluctuations recorded by a laser scanning confocal microscope. We find that the Fourier magnitude of these intensity fluctuations at the drive frequency identifies fibers that are mechanically coupled to the driven bead. By examining the phase relation between the drive and the displacements, we show that the fiber displacements are, indeed, due to elastic couplings within the network. Both the Fourier magnitude and phase depend on the direction of the drive force, such that displacements typically propagate farther, but not exclusively, along the drive direction. This technique may be used to characterize the local mechanical response in 3-D tissue cultures, and to address fundamental questions about force propagation within fiber networks.

Optical fiber interferometer for temperature-independent refractive index measuring over a broad range

The present work relates to manufacturing of a simple interferometric optical fiber refractometer that features broad refractive index measuring range without ambiguity. The device consists of a cylindrical polymer cavity whose shape and dimensions are easily controllable. This in turn allows to control the performance of the refractometer. The signal processing is simple; it consists of calculating the amplitude and phase of the fast Fourier transform of the normalized interference spectra. In this manner, the refractive index value of the sample is obtained independently of the temperature. The refractometer can be used to measure the refractive index of liquids or viscous samples and can operate in a broad wavelength range. As an application, we demonstrate the measuring of the refractive index of gels at different temperatures from which the thermo-optic coefficient can be calculated.

Maximum entropy models from phase harmonic covariances

The covariance of a stationary process X is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. They are defined as the covariance of Hˆ(LX), where L is a complex linear operator and Hˆ is a non-linear phase harmonic operator which multiplies the phase of each complex coefficient by integers. The operator Hˆ can also be calculated from rectifiers, which relates Hˆ(LX) to neural network coefficients. If L is a Fourier transform then the covariance is a sparse matrix whose non-zero off-diagonal coefficients capture dependencies between frequencies. These coefficients have similarities with high order moments, but smaller statistical variabilities because Hˆ is Lipschitz. If L is a complex wavelet transform then off-diagonal coefficients reveal dependencies across scales, which specify the geometry of local coherent structures. We introduce maximum entropy models conditioned by these wavelet phase harmonic covariances. The precision of these models is numerically evaluated to synthesize images of turbulent flows and other stationary processes.

Fearful face scrambles increase early visual sensory processing in the absence of face information

Emotional facial expressions elicit distinct increased early electrophysiological responses. Many studies report even emotional modulations of very early sensory processing at about 80 and 100ms after stimulus presentation, indexed by the P1. These early effects are often interpreted to index differential responses to biologically relevant expressions. Since specific spatial frequencies differ between fearful and neutral expressions, it has recently been suggested that these early modulations are substantially driven by such low-level visual differences. However, it remains unclear whether similar P1 effects are also observed in experiments in which no recognizable face information is presented at all. This study investigated this question and explored also whether any effects depend on colour information and attentional conditions. Participants (N=20) performed a continuous perceptual task of low or high difficultly and were presented with task-irrelevant black/white and colour images of fearful and neutral faces, rendered unrecognizable by doing Fourier phase transformation. ERP findings revealed increased P1 amplitudes for fearful scrambles regardless of experimental conditions. Taken together, our findings show early emotional effects in the absence of any facial expression. Specific low-level frequency information seems to increase P1 amplitudes which thus might have implications for the interpretation of very early sensory emotional expression effects.

Innovative Seismic Simulation Methodology Using Fourier Phase Matrix

In dynamic analysis for seismic design, frequency domain methodology has been utilized for input ground motion generation since the 1960s. An innovative scheme is proposed in the article for seismic simulation based on the matrix of Fourier phase spectra. Compared to the conventional methodology, the proposed scheme enables stability of the simulation results for each trail with different random phase spectra. In the certain scheme, manual modification and screening for random results are avoided and computational efficiency is improved. The scheme is evaluated with a representative response spectrum for seismic design of the nuclear equipment. The simulation result shows that the stability for each trial of simulation is maintained by the modified methodology and the computational efficiency is improved considerably. It is approved that the scheme manages to generate design ground motions reliably and efficiently.

Amplitude and phase sorting of orbital angular momentum states at low light levels

We present a method of photon orbital angular momentum selection at very low light levels using spatial interference between a strong local oscillator field and a weak beam. By using Fourier phase recovery techniques familiar in classical interferometry, we can experimentally obtain a quantum-limited Q distribution with a standard deviation consistent with the quantum noise floor. Further, by projecting the complex Fourier peak on a Laguerre–Gauss basis, we can distinguish states of different orbital angular momentum with high fidelity for small numbers of counts per acquisition frame. The noise equivalent photoelectron count for this measurement is 10 − 5 counts per pixel per frame.

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

Comparing the dual phase lag, Cattaneo-Vernotte and Fourier heat conduction models using modal analysis

This paper deals with phase lag (or time-lagged) heat conduction models: the Cattaneo-Vernotte (or thermal wave) model and the dual phase lag model. The main aim is to show that modal analysis of these second order partial differential equations provides a valid and effective approach for analysing and comparing the models. It is known that reliable values for the phase lags of the heat flux and the temperature gradient are not readily available. The modal solutions are used to determine a range of realistic values for these lag times. Furthermore, it is shown that using partial sums of the series solutions for calculating approximate solutions is an efficient procedure. These approximate solutions converge in terms of a so-called energy norm which is stronger than the maximum norm. A model problem where a single heat pulse is applied to a specimen, is used for comparing these models with the Fourier (or parabolic) heat conduction model.

Tensor-Free Proximal Methods for Lifted Bilinear/Quadratic Inverse Problems with Applications to Phase Retrieval

We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved numerically by singular value thresholding methods. However, a direct realization of these algorithms for, e.g., image recovery problems is often impracticable, since computations have to be performed on the tensor-product space, whose dimension is usually tremendous. To overcome this limitation, we derive tensor-free versions of common singular value thresholding methods by exploiting low-rank representations and incorporating an augmented Lanczos process. Using a novel reweighting technique, we further improve the convergence behavior and rank evolution of the iterative algorithms. Applying the method to the two-dimensional masked Fourier phase retrieval problem, we obtain an efficient recovery method. Moreover, the tensor-free algorithms are flexible enough to incorporate a priori smoothness constraints that greatly improve the recovery results.

Dynamics of a nonlinear energy harvester with subharmonic responses

A frequency transmission band of the nonlinear energy harvester shall be studied numerically. For the analysis, the nonlinear piezoelectric energy harvesting system based on a cantilever elastic beam has been applied to harvest the kinetic energy of the moving frame. We used a double-well potential induced by permanent magnets for a ferromagnetic beam resonator. A piezoelectric patch attached along the beam was used as a transducer of the mechanical into electrical energy. It occurred that the system could work in a wide interval of frequency beyond the linear resonance. Besides the response with a period of excitation, solutions with dominating sub-harmonics of the harmonic inertial force excitation have been found. Particular solutions were illustrated, classified, and discussed using phase portraits and Fourier spectra of the output signals.

Position Sensorless Control of Switched Reluctance Motor under Magnetic Field Saturation

When the switched reluctance motor is running, as the motor phase current increases, the magnetic circuit of the motor will gradually saturate, which affects the estimation of the special position of the motor rotor. Aiming at the above problems, this paper proposes a positionless control method for switched reluctance motors under the condition of magnetic field saturation. Firstly, the Fourier phase inductance function of switched reluctance motor is established, and then the component of Fourier phase inductance function affected by magnetic field saturation is eliminated mathematically. Research the method of estimating the position and angle of the rotor based on the inductance positioning point. This paper takes a 12\8 motor as an example to verify the effectiveness of the method by simulation.

Single-Phase Fault Line Selection in Distribution Network Based on Signal Injection Method

The distribution network with small current grounding mode can ensure high power supply reliability, but it is difficult to locate single-phase grounding fault line. Most of the faults in distribution network are single-phase to ground fault. It is important to locate the fault line timely and accurately for the normal operation of the power grid. In this article, a fault line selection method based on signal injection is proposed. The dynamic selection of parameters and injection frequency in real-time monitoring distribution network by injection method is analyzed. The accuracy of signal frequency domain conversion is improved by using all phase Fourier transform. Taking the active power consumption of injected signal after fault as the criterion, the accuracy of line selection is improved. Through theoretical analysis and simulation, as well as experiments in a 600V distribution system, the fault line can be accurately selected.

Phase-sensitive, angle-resolved light-scattering microscopy of single cells.

We report what is to our knowledge the first use of Fourier phase microscopy (FPM) to estimate diameters of individual single-micrometer beads and to classify cells based upon changes in scatterer size distribution. FPM, a quantitative phase imaging (QPI) method, combines the planar illumination typically used in off-axis QPI (ideal for Mie theory analysis) with the common-path geometry typically used in on-axis QPI (ideal for optimizing angular scattering range). Low-spatial-frequency imaging artifacts inherent to FPM have negligible impact upon these angular-domain applications. The system is simple to align and stable, and requires no external reference beam. Angular scattering patterns obtained from single 1 µm polystyrene beads in glycerol (Δn=0.11) display unprecedented fidelity to Mie theory, produce diameter estimates consistent with the manufacturer's specifications, and offer precision on the scale of tens of nanometers. Measurements of macrophages at different stages of antibody-dependent cellular phagocytosis demonstrate the ability to detect changes in a cell's scattering caused by the presence of phagocytosed material within.

Line Scanning Thermography Reconstruction Algorithm for Defects Inspection With Novel Velocity Estimation and Image Registration

Line scanning thermography (LST) is a fast non-destructive inspection (NDI) method for large-scale components. However, the current reconstruction algorithms for LST require the match between the frame rate and the scanning velocity. Moreover, these algorithms bring in spatial distortions. This paper proposes a non-orthogonal reconstructed space for LST. In such a space, the excitation motion in the line scanning process is described as a function of time delay, the moving velocity is estimated by the derived position map, and the reconstruction is achieved by image registration. The LST data are registered spatially by allowing the temporal misalignment among the pixels within the same reconstructed frame. The effectiveness of the proposed reconstruction algorithm is validated by both numerical simulations and experiments. The reconstruction results of experimental data indicate that the velocity is finely estimated so that the temporal alignment error is controlled within one pixel. Besides, no spatial distortions occur no matter how the frame rate and scanning velocity change. Furthermore, the Fourier phase image of the reconstructed LST reaches the diameter-to-depth ratio of 1.25 when inspecting a planar specimen with flat-bottom holes.

The Evaluation and Research of step profiler about the measurement uncertainty

The step profiler has the advantages of excellent repeatability and high resolution. However, as a new contact measurement equipment, it has specific measurement errors. This paper proposes a novel method to evaluate a step profiler’s accuracy by measuring the nano grating standard structure. These standard step height and pitch samples are used in the measurement process. The samples’ morphological characteristics were obtained by Fourier transformation, phase modulation, and phase splicing of the sampled data. The experimental results show that the step profiler’s vertical and horizontal relative measurement uncertainty is 4.0% and 1.2%.

Long-term follow-up of cardiac resynchronization therapy patients with non-ischemic dilated cardiomyopathy assessed by radionuclide angiography

Abstract Background While the beneficial effects of cardiac resynchronization therapy (CRT) have been widely investigated soon after CRT implantation, relatively few data are available on long-term clinical outcomes of CRT recipients. Aim To investigate long-term outcomes of CRT patients with non-ischemic dilated cardiomyopathy stratified as responders and non-responders according to radionuclide angiography. Methods Consecutive heart failure patients with non-ischemic dilated cardiomyopathy undergoing CRT implantation at our University Hospital between 2007 and 2013 were enrolled. All patients were assessed with equilibrium Tc99 radionuclide angiography at baseline and after 3 months of CRT. Left ventricular (LV) ejection fraction was computed on the basis of relative end-diastolic and end-systolic counts, and intraventricular dyssynchrony was derived by Fourier phase analysis. Response to CRT was defined by an absolute increase in LV ejection fraction (LVEF) ≥5% at 3-month follow-up. Clinical outcome was assessed after 10 years through hospital records review. Results Forty-seven patients (83% men, 63±11 years) were included in the study. At 3 months, 25 (53%) patients were identified as CRT responders according to LVEF increase (from 26±8 to 38±12%, p<0.001). In these patients, LV dyssynchrony decreased from 59±30° to 29±18° (p<0.001). Twenty-two (47%) patients were defined as non-responders. No significant changes in LVEF and LV dyssynchrony (50±30° vs. 38±19°, p=0.07) were observed in non-responders. At long-term follow-up (11±2 years), all-cause and cardiac mortality rates were 24% and 12% in responders vs. 32% and 27% in non-responders, respectively (p=ns). Heart transplantation was performed in 3 patients. One (4%) patient among CRT responders compared with 6 (27%) patients among non-responders died of worsening heart failure (p=0.03). Conclusions Although late overall mortality of non-ischemic CRT recipients was not significantly different between mid-term responders and non-responders, CRT responders were at lower risk of worsening heart failure death. Funding Acknowledgement Type of funding source: None