Phase Difference Distribution Research Articles

Experimental observation of direct current voltage-induced phase synchronization

The dynamics of two uncoupled distinct Chua circuits driven by a common direct current voltage is explored experimentally. It was found that, with increasing current intensity, the dominant frequencies of these two Chua circuits will first vary at different speeds, approach an identical value for a certain current intensity and then separate. Techniques such as synchronization index and phase difference distribution were employed to analyze the phase coherence between these two Chua circuits.

Simultaneous Measurement of Out-of-Plane and In-Plane Displacements by Phase-Shifting Digital Holographic Interferometry

In this paper, we apply phase-shifting digital holographic interferometry to simultaneous measurement for out-of-plane and in-plane displacements by employing two beam illuminations for an object. Phase-shifted holograms before and after displacements of the object using each of two beams are recorded by a CCD camera, separately. The complex amplitude at each pixel of the CCD plane is analyzed from the holograms taken with phase-shifting. The complex amplitude of he object is reconstructed from the complex amplitude distribution on the CCD plane using the Fresnel diffraction integral. Each directional phase difference distribution is obtained by calculating the phases before and after deformation for each directional beam. The phase distribution for out-of-plane displacements is obtained by calculating the sum of the two phase difference distributions. The phase distribution for in-plane displacements is obtained by calculating the difference of the two phase difference distributions. The phase values provide accurate displacement distribution information. Actually, when the object deforms in both out-of-plane and in-plane directions, it is possible to analyze the displacement distribution in each direction. The theory and an experiment are shown.

Robust speaker's location detection in a vehicle environment using GMM models

Abstract-Human-computer interaction (HCI) using speech communication is becoming increasingly important, especially in driving where safety is the primary concern. Knowing the speaker's location (i.e., speaker localization) not only improves the enhancement results of a corrupted signal, but also provides assistance to speaker identification. Since conventional speech localization algorithms suffer from the uncertainties of environmental complexity and noise, as well as from the microphone mismatch problem, they are frequently not robust in practice. Without a high reliability, the acceptance of speech-based HCI would never be realized. This work presents a novel speaker's location detection method and demonstrates high accuracy within a vehicle cabinet using a single linear microphone array. The proposed approach utilize Gaussian mixture models (GMM) to model the distributions of the phase differences among the microphones caused by the complex characteristic of room acoustic and microphone mismatch. The model can be applied both in near-field and far-field situations in a noisy environment. The individual Gaussian component of a GMM represents some general location-dependent but content and speaker-independent phase difference distributions. Moreover, the scheme performs well not only in nonline-of-sight cases, but also when the speakers are aligned toward the microphone array but at difference distances from it. This strong performance can be achieved by exploiting the fact that the phase difference distributions at different locations are distinguishable in the environment of a car. The experimental results also show that the proposed method outperforms the conventional multiple signal classification method (MUSIC) technique at various SNRs.

Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates

We investigate the relaxation effects on the dynamics of two-component dilute gas Bose-Einstein condensates (BEC) with relatively different two-body interactions and Josephson couplings between the two components. Three types of relaxation effects, i.e., one- and three-body losses and a pure phase relaxation caused by elastic two-body collision between condensed and noncondensed atoms, are examined on the dynamical behavior of a macroscopic superposition, i.e., Schrodinger cat state, of two states with atom-number differences between the two components, which is known to be created by the time evolution in certain parameter regimes. Although three-body losses show a relatively large suppression of the revival behavior of Schrodinger cat state and the Pegg-Barnett phase-difference distribution between the two components for a small-size Schrodinger cat state, one- and three-body loss effects are not shown to directly depend on the size of Schrodinger cat state. In contrast, the pure-phase relaxation effects, causing a reduction of phase-difference distribution and then decaying the Schrodinger cat state, significantly increase with the increase of the size of Schrodinger cat state. These features suggest that a detection of damped collapse-revival behavior is highly possible for medium-size Schrodinger cat states in small-size two-component BECs.

Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals

The quantification of phase synchrony between brain signals is of crucial importance for the study of large-scale interactions in the brain. Current methods are based on the estimation of the stability of the phase difference between pairs of signals over a time window, within successive frequency bands. This paper introduces a new approach to study the dynamics of brain synchronies, Frequency Flows Analysis (FFA). It allows direct tracking and characterization of the nonstationary time-frequency dynamics of phase synchrony among groups of signals. It is based on the use of the one-to-one relationship between frequency locking and phase synchrony, which applies when the concept of phase synchrony is not taken in an extended ‘statistical’ sense of a bias in the distribution of phase differences, but in the sense of a continuous phase difference conservation during a short period of time. In such a case, phase synchrony implies identical instantaneous frequencies among synchronized signals, with possible time varying frequencies of synchronization. In this framework, synchronous groups of signals or neural assemblies can be identified as belonging to common frequency flows, and the problem of studying synchronization becomes the problem of tracking frequency flows. We use the ridges of the analytic wavelet transforms of the signals of interest in order to estimate maps of instantaneous frequencies and reveal sustained periods of common instantaneous frequency among groups of signal. FFA is shown to track complex dynamics of synchrony in coupled oscillator models, reveal the time-frequency and spatial dynamics of synchrony convergence and divergence in epileptic seizures, and in MEG data the large-scale ongoing dynamics of synchrony correlated with conscious perception during binocular rivalry.

Phase distribution and phase correlation of financial time series

The scaling, phase distribution, and phase correlation of financial time series are investigated based on the Dow Jones Industry Average and NASDAQ 10-min intraday data for a period from 1 Aug. 1997 to 31 Dec. 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Lévy's alpha stable distribution condition. An approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation. Analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9/11 attack, and this change persisted in later trading activities.

Phase dynamics in cerebral autoregulation

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index gamma = (sin delta phi)2 + (cos delta phi)2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 +/- 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.

Interferometric 3-D displacement measurement using wavefront analysis

We propose and demonstrate a novel interferometric technique for 3-D displacement measurement. The method is based on the analysis of the phase difference distribution measured when two coherent curved wavefronts originating from different locations interfere. Both the in-plane and out-of-plane displacements are found simultaneously from a single phase difference distribution. We find that our system could measure with an accuracy better than 1.5 μm for in-plane displacements and 36 μm for out-of-plane displacements over 1 mm range. This accuracy was limited by the output lens performance. Theoretical analysis reveals that sub-micron accuracy may be possible with more careful calibration.

Least-squares calibration method for fringe projection profilometry

This paper presents a novel calibration approach for determining the mapping relationship between the depth map and the phase difference in fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and hence perfectly describes the mapping between the depth map and the phase-difference distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. A least-squares estimation algorithm with linear computation is deduced to retrieve the related parameters and to reconstruct the mapping function. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.

Dynamic holographic endoscopy?ex vivo investigations of malignant tumors in the human stomach

Laser holographic interferometry is based on the superimposition of the holograms of different motional states of an object on a single holographic storing medium. Using a combination of holographic interferometry and endoscopic imaging, we tried to detect areas of focally disturbed tissue elasticity in gastric cancer preparations. By connecting a mobile electronic speckle pattern interferometry (ESPI) camera system (light source: double frequency Nd:YAG laser, lambda = 532 nm) to different types of endoscopes, ex vivo experiments were performed on ten formalin fixed human stomachs, nine containing adenocarcinomas and one with a gastric lymphoma. Linking the endoscopic ESPI camera complex to a fast image processing system, the method of double pulse exposure image subtraction was applied at a video frame rate of 12.5 Hz. Speckle correlation patterns and corresponding phase difference distributions resulting from gastric wall deformation by gentle touch with a guide wire were analyzed. Tumor-free gastric areas showed high-contrast concentric fringes around the point of stimulation. In contrast, fringe patterns and filtered phase difference distributions corresponding to the areas of malignancy in all the cases were characterized by largely parallel lines, indicating that stimulation of rigid tumor tissue primarily led to tilting. Our ex vivo investigations of malignant gastric tumors show that the application of dynamic holographic endoscopy makes it possible to distinguish areas of malignancy from surrounding healthy tissue based on the differences in tissue elasticity.

Deformation measurement by phase-shifting digital holography

The out-of-plane displacement of a cantilever is measured by phase-shifting digital holography. From four phase-shifted holograms of a cantilever recorded by a CCD image sensor, a complex amplitude at each pixel of the CCD plane is obtained using the conventional phase-shifting method. The complex amplitude of a cantilever is reconstructed from the complex amplitude of the CCD plane using the Fresnel diffraction integral. The phase difference distribution on the cantilever before and after deformation, i.e., the out-of-plane displacement distribution, is calculated. In order to decrease the effect of speckle noise, a new method using divided holograms is proposed. The theory and experimental results are shown.

Parameter-optimized digital holographic microscope for high-resolution living-cell analysis

A parameter-optimized off-axis setup for digital holographic microscopy is presented for simultaneous, high-resolution, full-field quantitative amplitude and quantitative phase-contrast microscopy and the detection of changes in optical path length in transparent objects, such as undyed living cells. Numerical reconstruction with the described nondiffractive reconstruction method, which suppresses the zero order and the twin image, requires a mathematical model of the phase-difference distribution between the object wave and the reference wave in the hologram plane. Therefore an automated algorithm is explained that determines the parameters of the mathematical model by carrying out the discrete Fresnel transform. Furthermore the relationship between the axial position of the object and the reconstruction distance, which is required for optimization of the lateral resolution of the holographic images, is derived. The lateral and the axial resolutions of the system are discussed and quantified by application to technical objects and to living cells.

Two-wavelength method for endoscopic shape measurement by spatial phase-shifting speckle-interferometry

A two-wavelength method for endoscopic topography reconstruction is introduced that can be applied to out-of-plane sensitive electronic-speckle-pattern interferometry systems based on rigid endoscope imaging systems. The surface measurement is performed by detection of the phase-difference distribution affected by a change in the applied laser wavelength. Furthermore, the off-axis endoscopic illumination geometry is taken into account by an approximation. Experimental results of the characterization of the endoscopic surface reconstruction technique and the measurement accuracy obtained are described and discussed. Finally, the applicability of the method is demonstrated with results from the topographic reconstruction of a free-form surface.

Role of across-muscle motor unit synchrony for the coordination of forces

Evidence from five-digit grasping studies indicates that grip forces exerted by pairs of digits tend to be synchronized. It has been suggested that motor unit synchronization might be a mechanism responsible for constraining the temporal relationships between grip forces. To evaluate this possibility and quantify the effect of motor unit synchrony on force relationships, we used a motor unit model to simulate force produced by two muscles using three physiological levels of motor unit synchrony across the two muscles. In one condition, motor units in the two muscles discharged independently of one another. In the other two conditions, the timing of randomly selected motor unit discharges in one muscle was adjusted to impose low or high levels of synchrony with motor units in the other muscle. Fast Fourier transform analysis was performed to compute the phase differences between forces from 0.5 to 17 Hz. We used circular statistics to assess whether the phase differences at each frequency were randomly or non-randomly distributed (Rayleigh test). The mean phase difference was then computed on the non-random distributions. We found that the number of significant phase-difference distributions increased markedly with increasing synchronization strength from 18% for no synchrony to 65% and 82% for modest and strong synchrony conditions, respectively. Importantly, most of the mean angles clustered at very small phase difference values (approximately 0 to 10 degrees), indicating a strong tendency for forces to be exerted in a synchronous fashion. These results suggest that motor unit synchronization could play a significant functional role in the coordination of grip forces.

S-ordered phase-sum and phase-difference distributions of entangled coherent states

The $s$-ordered phase-sum and phase-difference distributions are considered for Bell-like superpositions of two-mode coherent states. The distributions are sensitive, respectively, to the sum and difference of the phases of the entangled coherent states. They show loss of information about the entangled state and may take on negative values for some orderings $s$.

Comparison of local precipitation–SST relationship between the observation and a reanalysis dataset

We defined a grid–scale time–phase relationship between precipitation (PR) and underlying sea surface temperature (SST) as the local PR–SST relationship, and compared the spatial distribution of the relationship in the observation with that in a reanalysis dataset. An analysis using observed pentad mean data shows precipitation lagging SST for two pentads over large areas of tropical oceans. A reanalysis dataset, on the other hand, has a shorter time–phase difference between precipitation and SST than that in the observation and does not match the spatial distribution of the observed local PR–SST relationship over the tropical Indian Ocean and the tropical western Pacific. A reanalysis dataset may not capture the observed local PR–SST relationship in terms of either time–phase difference or spatial distribution because a numerical model in a data assimilation system uses SST as a lower boundary condition as well as the inhomogeneity of observations the system used.

Electronic speckle pattern shearing interferometer with a photopolymer holographic grating.

A photopolymer holographic grating is used to produce the two sheared images in an electronic speckle pattern shearing interferometer. A ground glass screen following the grating eliminates unwanted diffraction orders and removes the requirement for the CCD camera to resolve the diffraction grating's pitch. The sheared images on the ground glass are further imaged onto the CCD camera. The fringe pattern contrast was estimated to be above 90%. A validation of the system was done by comparing the theoretical phase difference distribution with the experimental data from the three-point bending test.

The derivation of direction selectivity in the striate cortex.

In the central visual pathway of binocular animals, the property of directional selectivity (DS) is first exhibited in striate cortex. In this study, we sought to determine the neural circuitry underlying the transformation from non-DS neurons to DS cortical cells. In a well established model, DS receptive fields (RFs) are derived from the sum of two non-DS inputs with 90 degrees (quadrature) spatiotemporal phase differences. We explored possible input sources for this model, which include non-DS simple cells and lateral geniculate nucleus (LGN) neurons, by examination of spatiotemporal RFs of single cells and of pairs of cells. We find that distributions of non-DS simple RFs do not match the temporal predictions of the quadrature model because of a lack of long-latency responses. The long-latency inputs could potentially arise from lagged LGN afferents. However, analysis of cell pairs indicates that DS cells receive cortical input from non-DS simple cells for both short- and long-latency components, with temporal phase differences typically <90 degrees. Furthermore, the distribution of minimum phase differences needed to generate DS cells overlaps that exhibited by non-DS simple cells. Considered together, these results are consistent with a linear model whereby DS simple cells are formed from simple-cell inputs, with temporal phase differences often less than quadrature.

BURST-ENHANCED SYNCHRONIZATION IN AN ARRAY OF NOISY COUPLED NEURONS

Stochastic phase synchronization is studied in an array of coupled neurons that are capable of exhibiting diverse bursting behaviors as a system parameter is tuned. It is found that synchronization occurs for lower coupling constants when the neurons are initially in a bursting state. Neurons not initially in a bursting state begin to exhibit bursting behavior concurrently with the onset of synchronization. The system passes through various synchronization regimes as the coupling constant is increased, with the number of spikes per burst increasing in each window of synchronization. In addition, spatial organization, measured by the distribution of local phase differences, is observed during the synchronization windows.

位相シフトディジタルホログラフィ干渉法による変形計測(OS8-2 光学的手法,OS8 実験力学の新たな発展)

Measurement of the out-of-plane displacement of a cantilever is performed by phase-shifting digital holographic interferomety. Phase-shifting method is used for the phase analysis of the hologram recorded on a CCD sensor. The complex amplitude of the reconstructed object is obtained from the complex amplitude of the CCD plane using the Fresnel diffraction algorithm. The difference of the phase distributions before and after deformation, i.e. out-of-plane displacement is calculated. In order to decrease the effect of speckle pattern, the hologram is divided into 16 parts. The phase is obtained from the phase with the maximum amplitude among the complex amplitudes obtained from all the separated holograms. As the result, by eliminating the effect of speckle, a smooth phase difference distribution is obtained.