Phase Difference Distribution Research Articles

A new Method for Processing Time Averaged Vibration Patterns: Linear Regression

AbstractSpeckle‐based interferometry systems are useful tools for measuring vibration patterns at harmonically vibrating objects. The standard method for processing the speckle patterns acquired is to eliminate additive background noise and speckle phase, yielding Bessel‐type fringe patterns whose values are proportional to the absolute value of the Bessel function. Fringes are covered by multiplicative speckle intensity noise on the Bessel‐modulated vibration amplitude. Sine–cosine filtering is not an option because the Bessel‐type fringe pattern is not a phase pattern, and thus, sine–cosine filtering would only degrade the results. Improvements can be reached by involving additional measurements acquired in the stationary state. An alternative method for processing vibration patterns using linear regression is proposed, yielding patterns where the vibration amplitude is an argument of a true Bessel function, not its absolute value. As a result, spatial frequencies of the vibration fringe pattern are only half of those obtained with standard methods, and results can be filtered and normalised conveniently. While other contributions to improve the results rely on determining indexed skeletons for high Bessel fringe densities, the proposed method aims at a very limited number of low‐order fringes, allowing demodulation of the Bessel fringe pattern based on the actual Bessel values in the pattern. The method provides an effective alternative for spatial filtering. Phase differences between the stationary and vibrating states have an adverse effect on the results. Two methods, capable of handling phase jumps of 2π in the phase difference distribution, are presented to correct this.

Coherence and phase structure of compressional ULF waves at low‐Earth orbit observed by the Swarm satellites

AbstractIn this paper we present results of a study of Pc3 compressional waves observed at low‐Earth orbit (LEO) by the Swarm satellites. The particular emphasis has been to investigate the distribution of wave coherence and phase difference as functions of magnetic latitude and local time. This is the first time that a study of this nature has been carried out using magnetic field data from multiple LEO satellites. We have also for the first time shown how our analysis technique can be used to discriminate between static spatial and simultaneous temporal wave structures observed in the ionosphere. We believe that our study provides the first observational evidence to support the prediction by the inductive thin ionosphere model that incident Alfvén mode waves are partially converted into compressional mode waves by the ionosphere.

Determination of the wave structure of closed flows with nonuniform rotation of the boundaries by the method of an instantaneous phase difference

Unsteady axially symmetric flows of a viscous incompressible liquid in a spherical layer, which are formed by modulation of the rotation rate of one of the spherical boundaries, are considered. The wave structures of such flows are investigated by the method based on determination of the instantaneous difference in phases between the sphere velocity and the azimuthal velocity at each flow point. The steady-state character of the distribution of the instantaneous phase difference in the meridional plane of flows is established. The possibility of applying the method at very low vibrational amplitudes is shown.

Precipitation-snowmelt timing and snowmelt augmentation of large peak flow events, western Cascades, Oregon

This study tested multiple hydrologic mechanisms to explain snowpack dynamics in extreme rain-on-snow floods, which occur widely in the temperate and polar regions. We examined 26, 10 day large storm events over the period 1992–2012 in the H.J. Andrews Experimental Forest in western Oregon, using statistical analyses (regression, ANOVA, and wavelet coherence) of hourly snowmelt lysimeter, air and dewpoint temperature, wind speed, precipitation, and discharge data. All events involved snowpack outflow, but only seven events had continuous net snowpack outflow, including three of the five top-ranked peak discharge events. Peak discharge was not related to precipitation rate, but it was related to the 10 day sum of precipitation and net snowpack outflow, indicating an increased flood response to continuously melting snowpacks. The two largest peak discharge events in the study had significant wavelet coherence at multiple time scales over several days; a distribution of phase differences between precipitation and net snowpack outflow at the 12–32 h time scale with a sharp peak at π/2 radians; and strongly correlated snowpack outflow among lysimeters representing 42% of basin area. The recipe for an extreme rain-on-snow event includes persistent, slow melt within the snowpack, which appears to produce a near-saturated zone within the snowpack throughout the landscape, such that the snowpack may transmit pressure waves of precipitation directly to streams, and this process is synchronized across the landscape. Further work is needed to understand the internal dynamics of a melting snowpack throughout a snow-covered landscape and its contribution to extreme rain-on-snow floods.

Detection of Nonverbal Synchronization through Phase Difference in Human Communication.

Nonverbal communication is an important factor in human communication, and body movement synchronization in particular is an important part of nonverbal communication. Some researchers have analyzed body movement synchronization by focusing on changes in the amplitude of body movements. However, the definition of “body movement synchronization” is still unclear. From a theoretical viewpoint, phase difference is the most important factor in synchronization analysis. Therefore, there is a need to measure the synchronization of body movements using phase difference. The purpose of this study was to provide a quantitative definition of the phase difference distribution for detecting body movement synchronization in human communication. The phase difference distribution was characterized using four statistical measurements: density, mean phase difference, standard deviation (SD) and kurtosis. To confirm the effectiveness of our definition, we applied it to human communication in which the roles of speaker and listener were defined. Specifically, we examined the difference in the phase difference distribution between two different communication situations: face-to-face communication with visual interaction and remote communication with unidirectional visual perception. Participant pairs performed a task supposing lecture in the face-to-face communication condition and in the remote communication condition via television. Throughout the lecture task, we extracted a set of phase differences from the time-series data of the acceleration norm of head nodding motions between two participants. Statistical analyses of the phase difference distribution revealed the characteristics of head nodding synchronization. Although the mean phase differences in synchronized head nods did not differ significantly between the conditions, there were significant differences in the densities, the SDs and the kurtoses of the phase difference distributions of synchronized head nods. These results show the difference in nonverbal synchronization between different communication types. Our study indicates that the phase difference distribution is useful in detecting nonverbal synchronization in various human communication situations.

Phase shifting interferometry from two normalized interferograms with random tilt phase-shift.

We propose a novel phase shifting interferometry from two normalized interferograms with random tilt phase-shift. The determination of tilt phase-shift is performed by extracting the tilted phase-shift plane from the phase difference of two normalized interferograms, and with the calculated tilt phase-shift value the phase distribution can be retrieved from the two normalized frames. By analyzing the distribution of phase difference and utilizing special points fitting method, the tilted phase-shift plane is extracted in three different cases, which relate to different magnitudes of tilts. Proposed method has been applied to simulations and experiments successfully and the satisfactory results manifest that proposed method is of high accuracy and high speed compared with the three step iterative method. Additionally, both open and closed fringe can be analyzed with proposed method. What's more, it cannot only eliminate the small tilt-shift error caused by slight vibration in phase-shifting interferometry, but also detect the large tilt phase-shift in phase-tilting interferometry. Thus, it will relaxes the requirements on the accuracy of phase shifter, and the costly phase shifter may even be useless by applying proposed method in high amplitude vibrated circumstance to achieve high-precision analysis.

Simulation and experimental study of phase characteristics in high-gain relativistic klystron amplifier

In order to realize the combination of the coherent high power microwave, an S-band high gain relativistic klystron amplifier with high phase stability is presented and studied theoretically and experimentally. The phase characteristics of the output microwave are explored in particle-in-cell code and experiment. The experimental results accord well with the simulation results, which indicates that the parasitic oscillation excited by retrograde electrons is the main cause of phase variation in the development of high-gain relativistic klystron with high phase stability. When the input RF power is 10 kW, a microwave pulse with about ± 10° in relative phase difference fluctuation between output and input is obtained in experiment. And the corresponding locking duration is about 90 ns. Accordingly, the expectation of power combination efficiency of 10 high-gain relativistic klystron amplifiers can be achieved to be 99% with continuous uniform distribution of random relative phase difference.

Fatigue Strength Analysis of Compressor Impeller under Non-typical Aerodynamic Load

The frequency characteristics of aerodynamic load and the resonance of compressor impeller are studied for the fatigue failure of compressor impeller.The frequency,amplitude and phase of aerodynamic load are obtained from the unsteady computational fluid dynamics(CFD) results of compressor impeller using fast Fourier transform(FFT).The aerodynamic excitation phase between adjacent blades is analyzed in detail.For typical load with cyclic symmetric distribution of phase difference between adjacent blades,the interference diagram is used to determine the resonance modal.For non-typical load with non-cyclic symmetric distribution of phase difference,the resonance modal is determined by the result of dynamic stress in all nodal diameters under aerodynamic excitation frequency.Fatigue analysis is performed based on the static stress and resonance dynamic stress of impeller,which shows that the predicted fatigue position matches with the actual crack position.The zero nodal diameter resonance excited by non-typical fluid load with non-cyclic symmetric distribution of phase difference is proved to be the main cause of impeller fatigue failure.

Reproducibility of Functional Connectivity and Graph Measures Based on the Phase Lag Index (PLI) and Weighted Phase Lag Index (wPLI) Derived from High Resolution EEG

Functional connectivity (FC) and graph measures provide powerful means to analyze complex networks. The current study determines the inter-subject-variability using the coefficient of variation (CoV) and long-term test-retest-reliability (TRT) using the intra-class correlation coefficient (ICC) in 44 healthy subjects with 35 having a follow-up at years 1 and 2. FC was estimated from 256-channel-EEG by the phase-lag-index (PLI) and weighted PLI (wPLI) during an eyes-closed resting state condition. PLI quantifies the asymmetry of the distribution of instantaneous phase differences of two time-series and signifies, whether a consistent non-zero phase lag exists. WPLI extends the PLI by additionally accounting for the magnitude of the phase difference. Signal-space global and regional PLI/wPLI and weighted first-order graph measures, i.e. normalized clustering coefficient (gamma), normalized average path length (lambda), and the small-world-index (SWI) were calculated for theta-, alpha1-, alpha2- and beta-frequency bands. Inter-subject variability of global PLI was low to moderate over frequency bands (0.12<CoV<0.28), higher for wPLI (0.25<CoV<0.55) and very low for gamma, lambda and SWI (CoV<0.048). TRT was good to excellent for global PLI/wPLI (0.68<ICC<0.80), regional PLI/wPLI (0.58<ICC<0.77), and fair to good for graph measures (0.32<ICC<0.73) except wPLI-based lambda in alpha1 (ICC = 0.12). Inter-electrode distance correlated very weakly with inter-electrode PLI (−0.06<rho<0) and weakly with inter-electrode wPLI (−0.22<rho<−0.18). Global PLI/wPLI and topographic connectivity patterns differed between frequency bands, and all individual networks showed a small-world-configuration. PLI/wPLI based network characterization derived from high-resolution EEG has apparently good reliability, which is one important requirement for longitudinal studies exploring the effects of chronic brain diseases over several years.

Performance analysis of 3-D shape measurement algorithm with a short baseline projector-camera system.

A number of works for 3-D shape measurement based on structured light have been well-studied in the last decades. A common way to model the system is to use the binocular stereovision-like model. In this model, the projector is treated as a camera, thus making a projector-camera-based system unified with a well-established traditional binocular stereovision system. After calibrating the projector and camera, a 3-D shape information is obtained by conventional triangulation. However, in such a stereovision-like system, the short baseline problem exists and limits the measurement accuracy. Hence, in this work, we present a new projecting-imaging model based on fringe projection profilometry (FPP). In this model, we first derive a rigorous mathematical relationship that exists between the height of an object’s surface, the phase difference distribution map, and the parameters of the setup. Based on this model, we then study the problem of how the uncertainty of relevant parameters, particularly the baseline’s length, affects the 3-D shape measurement accuracy using our proposed model. We provide an extensive uncertainty analysis on the proposed model through partial derivative analysis, relative error analysis, and sensitivity analysis. Moreover, the Monte Carlo simulation experiment is also conducted which shows that the measurement performance of the projector-camera system has a short baseline.

Generalized Polarimetric Model-Based Decompositions Using Incoherent Scattering Models

The model-based scattering decomposition pioneered by Freeman and Durden has stimulated research in characterizing polarimetric synthetic aperture radar (PolSAR) scattering phenomenon and its applications. The Freeman and Durden decomposition as originally developed is based on three scattering models for volume, surface, and double bounce. It is known that the decomposition often produces negative scattering powers for a large number of pixels. This implies that the scattering models are inconsistent with the data. In this paper, we investigate the model deficiency problem and propose several algorithms to mitigate it. To achieve this, we developed an incoherent scattering model based on the polarization orientation angle distribution of phase differences. Two approaches are taken to reduce the number of negative power pixels: 1) adopt a volume scattering model by including variable shape factor while keeping the original surface and double bounce models unchanged, and 2) incorporate the incoherent surface or double bounce model while keeping the original volume model. In addition, the combination of 1) and 2) is explored, and the effect of polarization orientation compensation on these algorithms is investigated. The effectiveness of these approaches is compared using L-band AIRSAR and E-SAR PolSAR data. It will be shown that model efficiency is improved with occurrence of negative power reduced to an insignificant level.

Coherent combination of mutual injection phase-locked fiber lasers with a corner cube reflector

We present a new method of the mutual injection phase-locked coherent combination of fiber lasers based on corner cube reflector (CCR). The theoretic calculation of phase difference and far-field intensity distribution of coherent beams obtained by the CCR has been carried out on this work. The relation between the far-field optical intensity distribution and the CCR rotation angles is analyzed in the case of mutual injection. The coherent combination experiments of mutual injection phase-locked with two and four fiber lasers are performed. The experimental results reveal that the far-field intensity distribution in the two free running fiber lasers is good agreement with the theoretical calculation. In the two internal mutual injection structures, the coherent combination output power goes up as high as 54W, and power combined efficiency of more than 90% and fringe contrast about 90% are obtained. The far-field intensity distribution is the same as the typical coherent combination pattern of two-dimensional fiber laser arrays, the experimental results also show that the coherent combination output with more laser beams and higher power with a good beam quality could be realized by the current scheme.

Two-dimensional magnetic field dependence of zero and finite voltage steps in current–voltage characteristics of rectangular shape niobium tunnel junctions

► Josephson current I c through Nb superconducting junction was measured. ► I c dependence on H x , H y magnetic fields was product of Fraunhofer pattern. ► Numerical simulation of I c −( H x , H y ) matched the measured result. ► Modulation period inversely proportional to the vertical edge length of junction. ► Resonant current steps studied by superconducting planar circuit model. Modulation characteristics of Josephson current through rectangular shape niobium/aluminum-oxide/niobium superconducting junctions have been studied by two-dimensional (2-D) scanning of the external magnetic field. In order to obtain the magnetic field dependence automatically, two pairs of Helmholtz coils are driven by two current sources with GPIB (General Purpose Interface Bus) system. The 2-D magnetic field dependences of the Josephson current and the resonant current steps of the current–voltage characteristics of the Nb/Al-oxide/Nb tunnel junction have been measured. The I c −( H x − H y ) characteristics are the product of two Fraunhofer diffraction patterns in H x and H y directions parallel to each junction edge, and are also numerically calculated by assuming that distribution of phase difference γ and the junction current density I 0 inside the rectangular shape junction area have been modulated in perpendicular direction to the external magnetic field. This modulation period is inversely proportional to the junction length perpendicular to the external magnetic field. The resonant current steps are also considered using superconducting planar circuit model. The distributions of the magnetic flux, the electrode current and the junction current have been studied.

基于窗口傅里叶变换剪切干涉法波前检测

A wavefront reconstruction technique which obtains wavefront from a radial shearing interferometer with high precision based on two-dimensional windowed Fourier transform (WFT) is presented. First, the radial shearing fringe is processed by WFT, and by inverse WFT after setting threshold and frequency range of integration. Then wavefront phase difference distribution is obtained by the treatment of removal-carrier frequency and phase unwrapping. Finally, the actual wavefront can be reconstructed from phase difference by wavefront iterative algorithm. The simulations show that the maximum phase reconstruction error is 0.82%, RMS is 0.020 9 rad. Also corresponding experiments are conducted for comparison. In addition, window function selection, window size and threshold setting are briefly discussed. Compared with the traditional Fourier transform method (FFT), shearing interferometer wavefront measurement based on windowed Fourier transform has higher precision and stability, which provides a new processing method for wavefront measurement.

On the Co-Polarized Phase Difference of Rough Layered Surfaces: Formulae Derived From the Small Perturbation Method

We determine the statistical distribution of the co-polarized phase difference of fields scattered from a stack of two two-dimensional rough interfaces in the incidence plane. The electromagnetic fields are represented by Rayleigh expansions and a perturbation method is used to solve the boundary value problem and to determine the first-order scattering amplitudes. For slightly rough interfaces with infinite length and Gaussian height distributions, we show that the probability density function is only a function of two parameters. For a sand layer on a granite surface in backscattering configurations, we study the influence of the incidence angle, the layer thickness, the cross-spectral density and the wave frequency upon both parameters of the probability law.

Investigation of refractive index profile and mode field distribution of optical fibers using digital holographic phase shifting interferometric method

In this paper a digital holographic phase shifting interferometric method is used to characterize the graded index (GR-IN) optical fibers. Off-axis digital holographic Mach–Zehnder like arrangement in aid of phase shifting tool is applied. Numerical reconstruction of phase shifted holograms is applied to calculate the optical phase difference distribution in the image plane, and then the optical phase differences across GR-IN fibers are extracted considering image enhancement and noise reduction steps. Also, a simple algorithm is presented to modify the position of the extracted optical phase differences across the fibers to be perpendicular to x-axis, so that it becomes easy to calculate the mean optical phase differences along the fiber. The mean optical phase differences in combination with multilayer model are applied to calculate the refractive index profiles across GR-IN optical fibers. An analytical model is presented to predict the mode distribution associated with the effective indices and the propagation coefficient of the parabolic refractive index profile GR-IN fiber.

Data-driven modeling of phase interactions between spontaneous MEG oscillations.

Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required. Based on the assumption that the recorded rhythms can be described as weakly coupled oscillators, we propose a method for characterizing their phase-interaction dynamics. We propose to model ongoing magnetoencephalographic (MEG) oscillations as weakly coupled oscillators. Based on this model, the phase interactions between simultaneously recorded signals are characterized by estimating the modulation in instantaneous frequency as a function of their phase difference. Furthermore, we mathematically derive the effect of volume conduction on the model and show how indices for strength and direction of coupling can be derived. The methodology is tested using simulations and is applied to ongoing occipital-frontal MEG oscillations of healthy subjects in the alpha and beta bands during rest. The simulations show that the model is robust against the presence of noise, short observation times, and model violations. The application to MEG data shows that the model can reconstruct the observed occipital-frontal phase difference distributions. Furthermore, it suggests that phase locking in the alpha and beta band is established by qualitatively different mechanisms. When the recorded rhythms are assumed to be weakly coupled oscillators, a dynamical model for the phase interactions can be fitted to data. The model is able to reconstruct the observed phase difference distribution, and hence, provides a dynamical explanation for observed phase locking.

Analysis of Topographic Change at Mount Sakurajima, South Kyushu, Japan, using JERS-1 SAR Interferometry

Mount Sakurajima, situated in the southern Kyusyu district of southwest Japan, is known as one of the most active volcanoes in Japan. It has erupted intermittently, ejecting large volumes of volcanic materials including lava, scoria, and ash. We have adopted a SAR interferometry method using JERS-1 images to monitor volcanic activity and estimate accompanying topographic changes in order to mitigate hazard from the inevitable eruptions and debris flows. A map expressing the phase-difference distribution for pairs of images recorded on two acquisition dates is produced for this purpose. This map, obtained by subtracting orbital and topographic fringes from the initial interferogram, is capable of quantifying vertical displacements at each point on the SAR image. Considering the acquisition-date intervals for the images used, three phase-difference maps are generated for the period from January 1996 to March 1997. These show that relatively large displacements occurring along the valleys on the northern slopes of the volcano are common to the three pairs. Because the volcanic activity was low during the period, the displacements may be caused chiefly by the erosion of the surface materials. Differential SAR interferometry is thus thought to be capable of estimating temporal fluctuations of topography during arbitrary periods, detecting regions that are readily aggraded or eroded, and helping to determine the position and dimensions of debris barriers.

Efficiency optimization and symmetry-breaking in a model of ciliary locomotion

A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for such ciliary locomotion where the dynamics of the individual cilia are replaced by that of a continuous overlaying surface allowed to deform tangentially to itself. Employing a variational approach, we determine numerically the time-periodic deformation of such surface which leads to low-Reynolds locomotion with minimum rate of energy dissipation (maximum efficiency). Employing both Lagrangian and Eulerian points of views, we show that in the optimal swimming stroke, individual cilia display weak asymmetric beating, but that a significant symmetry-breaking occurs at the organism level, with the whole surface deforming in a wavelike fashion reminiscent of metachronal waves of biological cilia. This wave motion is analyzed using a formal modal decomposition, is found to occur in the same direction as the swimming direction, and is interpreted as due to a spatial distribution of phase differences in the kinematics of individual cilia. Using additional constrained optimizations, as well as a constructed analytical ansatz, we derive a complete optimization diagram where all swimming efficiencies, swimming speeds, and amplitudes of surface deformation can be reached, with the mathematically optimal swimmer, of efficiency one-half, being a singular limit. Biologically, our work suggests therefore that metachronal waves may allow cilia to propel cells forward while reducing the energy dissipated in the surrounding fluid.

Quadrature phase-shifting interferometer with a polarization imaging camera

We present a new high-speed phase distribution measurement, in which a polarization imaging camera is applied to a quadrature phase-shifting interferometer. The polarization imaging camera composed of a polarizer-mask on a detector array can provide simultaneously two phase-shifted data in quadrature. Two sets of two phase-shifted data in quadrature are obtained before and after a change of the interferometer such as object displacement or environmental disturbances. Phase sum and difference distributions of the interferograms between two states with arbitrary phase-shift in the interferometer are calculated with the two sets of two phase-shifted data in quadrature. This phase calculation method in the pixel displaced phase-shift method has such advantage that phase-shifted data required for the calculation of phase distributions can be obtained by only two pixels in the polarizer-mask detector array, which means no reduction of the image resolution in the other direction. The principle of this technique and experimental results are presented.