Variation Of Phase Difference Research Articles

Kuramoto Model of Nonlinear Coupled Oscillators as a Way for Understanding Phase Synchronization: Application to Solar and Geomagnetic Indices

We apply a Kuramoto model of nonlinear coupled oscillators to the simulation of slow variations of the phase difference between sunspot number [R I ] and geomagnetic indices [aa and ζ]. The Kuramoto model is described for the particular case of two oscillators connected by symmetric coupling with quasi-stationary behavior, and its properties are investigated. By solving an inverse problem, we reconstruct the evolution of the couplings between pairs of indices [R I and aa, R I and ζ, aa and ζ], and interpret these in terms of the physics of the solar dynamo. The de-correlation between R I and geomagnetic indices found in Solar Cycle 20 by Le Mouel et al. (J. Geophys. Res. 117, A09103, 2012) is successfully reproduced by the Kuramoto model and corresponds to the alternation of the leading oscillator. Application of the Kuramoto model to the cross-correlations [C(R I ,ζ) and C(aa,ζ)] for ζ-indices computed in eight geomagnetic stations shows the latitudinal dependence of the mean phase difference. We discuss these results in terms of the solar-wind contribution to local geomagnetic indices [ζ].

SU‐E‐J‐50: Does a Breathing Surrogate From a Point On the Abdominal Skin Represent the Organ Motion in Thorax for Phase‐Based 4D CT Sorting?

Purpose:This work aims (1) to determine the validity of the current practice of the phase‐based 4DCT sorting (abdomen signal) for thorax scans; (2) to assess the potential benefit of utilizing the 3D surface breathing surrogate of chest area for phase‐based 4DCT sorting.Methods:Dynamic 3D surface images over the chest and abdomen were acquired using 3D‐suface‐camera‐system (VisionRT Ltd., London, UK) for a total of 10 patients. The vertical motions of five regions‐of‐interest (ROIs): abdomen, mid‐sternum, lower‐, middle‐, and upper‐ ipsilateral‐chest were tracked. Based on our previous work, the main source of motion artifact is the variation‐of‐phase‐differences (VPD) between the breathing surrogate and the organ motion during scanning. Thus, we utilize VPD as a quantitative index of the variation of the resulting 4DCT images. The average VPD over a 60 second time‐period was calculated for each of the abdomen and ROI combination. A simulation study with a wire phantom was designed to demonstrate the resulting 4DCT images.Results:Simulation showed significant image distortion or motion artifacts when VPD is larger than 5% of breathing period. The average VPDs of individual ROIs of each patient indicates that 75%, 59% and 22% cases have VPD larger than 5%, 10% and 15% of period each cycle between the selected ROI and the abdominal motions patterns, respectively (10.1±6.0 %, minimum 1.0% to maximum 23.9 %). Overall, patients with less 3‐second breathing‐period present VPD larger than 10%. The correlations between the abdomen and individual chest ROIs motions as well as the motions among chest ROIs are highly case‐dependent.Conclusion:Abdominal motion does not represent the chest motions for some of the patients. This results in motion artifacts in the phase‐based 4DCT. Utilizing the surface surrogate of the chest region can potentially improve phase‐based 4DCT sorting for thorax 4DCT scan, especially for fast breathing patients.

Synchronization of two electrically coupled inspiratory pacemaker neurons

Synchronization is considered to be a crucial mechanism that maintains respiratory rhythm. For understanding the effect of electrical coupling on the transition of the firing patterns and synchronization, we coupled two inspiratory pacemaker neurons together, and studied various synchronous behaviors between them. We firstly compared the bifurcation diagrams between the coupled neurons and single neuron, and found that the coupled neurons had a more complicated bifurcation mode. By increasing the coupling strength, the regular variation of phase differences was illustrated so that asynchronous and some synchronous states could be observed. These synchronous states were also shown in detail by phase portraits and firing series. In addition, we explored the ranges of different synchronous states, which attributed to different ranges of membrane capacitance and coupling strength.

Reflective plasmonic waveplates based on metal–insulator–metal subwavelength rectangular annular arrays

We propose and present a quarter-wave plate using metal–insulator–metal (MIM) structure with sub-wavelength rectangular annular arrays (RAA) patterned in the upper Au film. It is found that by manipulating asymmetric width of the annular gaps along two orthogonal directions, the reflected amplitude and phase of the two orthogonal components can be well controlled via the RAA metasurface tuned by the MIM cavity effect, in which the localized surface plasmon resonance dip can be flattened with the cavity length. A quarter-wave plate has been realized through an optimized design at 1.55μm, in which the phase difference variation of less than 2% of the π/2 between the two orthogonal components can be obtained in an ultra-wide wavelength range of about 130nm, and the reflectivity is up to ∼90% within the whole working wavelength band. It provides a great potential for applications in advanced nanophotonic devices and integrated photonic systems.

Nonlinear Rabi oscillations in a Bose-Einstein condensate

For a Bose-Einstein condensate in a trap with oscillating barriers, in the resonance approximation, evolution equations are derived. Their analytical solution reveals the existence of two fundamentally different types of nonlinear conservative Rabi oscillations: (i) with periodic temporal variation of moduli and phase difference of levels' amplitudes of probability, and (ii) with monotonic temporal variation of the phase difference. It is shown that the two types can be realized for the same parameters of the scheme, but for different initial conditions. Analytical predictions are confirmed by numerical solution to the Gross-Pitaevskii equation.

New-Type Biosensor Based on Multiple Total-Internal Reflections in Heterodyne Interferometry

In this paper, a novel biosensor based on multiple total-internal reflections (MTIRs) in heterodyne interferometry (HI) is proposed. The biosensor is made of an elongated prism. As a heterodyne optical light source transmits through the new-type biosensor, it will undergo multiple total-internal reflections (MTIRs). Thus we can obtain the text signal at the output. The phase difference variation due to the different refractive indices of the tested media can be obtained by a Lock-In-amplifier (LIA). By some numerical calculations, we can achieve the related parameters of the tested medium. The resolution of the sensor can reach 4×10-7 refractive index unit (RIU). The electro-optical biosensor has some merits, easy operation, in real-time measurement, and high stability, etc.

GPS phase difference variation statistics: A comparison between phase scintillation index and proxy indices

Scintillated GPS phase observations are traditionally characterized by the phase scintillation index, derived from specialized GPS receivers usually tracking at 50Hz. Geodetic quality GPS receivers, on the other hand, are normally tracking at frequencies up to 1Hz. However, availability of continuously operating geodetic receivers both in time and geographical location are superior to scintillation receiver’s coverage in many parts of the world. This motivates scintillation studies using regional and global geodetic GPS networks. Previous studies have shown the usefulness of GPS estimated total electron content variations for detecting ionospheric irregularities. In this paper, collocated geodetic and scintillation receivers are employed to compare proxy indices derived from geodetic receivers with the phase scintillation index during quiet and moderately disturbed ionospheric conditions. Sensitivity of the phase scintillation indices at high latitude stations to geomagnetic activity is discussed. Global mapping of ionospheric disturbances using proxy indices from real-time 1Hz GPS stations are also presented.

A Measuring Method of Track Irregularity for High-Speed Railway Based on Dual-Frequency Laser Interference Technique

A new measuring method of track irregularity for high-speed railway is proposed by using dual-frequency laser interference technique. The linear deviation between the phase-locked gauging head and the center line of the railway route can be calculated by comparing the phase difference variation of the laser beat signal in the test ray path and the reference ray path when the portable track inspection car is moving forward along the track. While we use laser ranging technique to measure gauge, after processing data, the static irregularity of track will be acquired by changing straightness deviation of phase-locked gauging head into straightness deviation of left-right two tracks. The method is different from the existing techniques for detecting high-speed railway irregularity, such as the inertial reference method, the measuring method of chord and the method of laser alignment; it utilized the accuracy of the time to accomplish the high-precision measurement of the space and achieved innovation in theory.

Absolute distance measurement using frequency-sweeping heterodyne interferometer calibrated by an optical frequency comb

We present a frequency-sweeping heterodyne interferometer to measure an absolute distance based on a frequency-tunable diode laser calibrated by an optical frequency comb (OFC) and an interferometric phase measurement system. The laser frequency-sweeping process is calibrated by the OFC within a range of 200 GHz and an accuracy of 1.3 kHz, which brings about a precise temporal synthetic wavelength of 1.499 mm. The interferometric phase measurement system consisting of the analog signal processing circuit and the digital phase meter achieves a phase difference resolution better than 0.1 deg. As the laser frequency is sweeping, the absolute distance can be determined by measuring the phase difference variation of the interference signals. In the laboratory condition, our experimental scheme realizes micrometer accuracy over meter distance.

Optical strain sensor based on diffraction grating and surface plasmon resonance heterodyne interferometer

We designed an optical sensor for measuring a tensile strain by using a diffraction grating and a surface plasmon resonance (SPR) interferometer, and analyzed the periodic nonlinearity effect and the thermal effects in the sensor. As a heterodyne light beam strikes a grating, the +1st order diffraction beam generates and then enters into a SPR apparatus at the resonance angle. A tensile force applied to the grating will introduce a significant phase-difference variation between p- and s-polarizations of the light emerging from SPR apparatus. The variation used to determine the strain can be precisely measured with heterodyne interferometric technique. The feasibility of our method was demonstrated with a measurement resolution of 0.52mɛ and a sensitivity of 0.58°/mɛ in a dynamic range of 10mɛ. The sensor provides the advantages of low temperature sensitivity, high stability against air fluctuation, a simple structure, rapid measurement, and straightforward operation.

Novel liquid crystal multistage circular polarization switch for three-dimensional laser pico projectors

Crosstalk is one of the most important factors affecting the image quality of polarization switching three-dimensional (3D) projectors. The variation in the phase difference of a polarization switch owing to dispersion degrades crosstalk performance. We propose a novel multistage circular polarization switch comprising liquid crystal devices using a ferroelectric liquid crystal (FLC) in-plane fast switch and a thick nematic liquid crystal (NLC) retarder. In this paper, we present a proof-of-concept model of a 3D laser pico projector using a scanning MEMS head in combination with the polarization switch. We also evaluate the crosstalk and 3D performance of the projector.

Measurement of air refractive index based on surface plasmon resonance and phase detection

A method for refractive index of air measurement is presented based on surface plasmon resonance (SPR) and phase detection using a dual-frequency laser interferometer. Theoretical analyses indicate that the phase-difference variation of the measurement signal versus the reference signal is linear with refractive index of air (RIA) fluctuation, and the calculation formula of RIA is derived. The structure design of the self-adaptive SPR sensor greatly reduces the measurement error resulting from the incident angle shift and improves the sensitivity. The experiments show that measurement uncertainty of 10(-6) order has been achieved when phase detection precision is 0.1°. The phenomenon of sudden phase variation during air pumping and air filling, which is caused by temperature fluctuation, is discussed.

Measurement of small displacement based on surface plasmon resonance heterodyne interferometry

Abstract This paper proposes an optical method for measuring small displacements using the surface plasmon resonance (SPR) heterodyne interferometry. A heterodyne light beam reflected by a mirror passes through a hemisphere glass and then enters into a surface plasmon resonance apparatus at the resonant angle. A small displacement of the mirror will introduce a phase-difference variation between p - and s -polarizations of the light emerging from the SPR apparatus. The phase-difference variation can be precisely measured with the heterodyne interferometric technique, and the associated displacement can be estimated. The feasibility of this method was verified by experiment, and the displacement measurement resolution of about 1.4 nm over a traveling range of 6 μm was achieved. Our method of measurement has the merits of both common-path interferometry and heterodyne interferometry.

Heterodyne grating interferometer based on a quasi-common-optical-path configuration for a two-degrees-of-freedom straightness measurement

We present a heterodyne grating interferometer based on a quasi-common-optical-path (QCOP) design for a two-degrees-of-freedom (DOF) straightness measurement. Two half-wave plates are utilized to rotate the polarizations of two orthogonally polarized beams. The grating movement can be calculated by measuring the phase difference variation in each axis. The experimental results demonstrate that our method has the ability to measure two-DOF straightness and still maintain high system stability. The proposed and demonstrated method, which relies on heterodyne interferometric phase measurement combined with the QCOP configuration, has the advantages of high measurement resolution, relatively straightforward operation, and high system stability.

Applying the optical activity of cholesteric liquid crystal for measuring small wavelength differences

This work proposes a simple measurement technique based on the optical activity of cholesteric liquid crystal (CLC) and circular common-path heterodyne interferometry for measuring small wavelength differences. A circularly polarized heterodyne light passes through a CLC cell and an analyzer, generating an interference signal. When the CLC cell is properly chosen with a circular regime, it has strong optical activity. Accordingly, the phase difference between the left and right circular light of the interference signal depends strongly on the wavelength. As the wavelength changes, variations of the phase difference can be accurately detected by heterodyne interferometry. Substituting the variation of phase difference into specially derived equations, the wavelength variations can be estimated accurately. The feasibility of this method, which is applicable when the wavelength is larger than the product of the pitch and the refractive index of the CLC cell, was demonstrated; it provides the advantages of simple installation, ease of operation, and high accuracy.

Secular variation of hemispheric phase differences in the solar cycle

AbstractWe investigate the phase difference of the sunspot cycles in the two hemispheres and compare it with the latitudinal sunspot distribution. If the north‐south phase difference exhibits a long‐term tendency, it should not be regarded as a stochastic phenomenon. We use datasets of historical sunspot records and drawings made by Staudacher, Hamilton, Gimingham, Carrington, Spörer, and Greenwich observers, as well as the sunspot activity during the Maunder minimum reconstructed by Ribes and Nesme‐Ribes. We employ cross‐recurrence plots to analyse north‐south phase differences. We show that during the last 300 years, the persistence of phase‐leading in one of the hemispheres exhibits a secular variation. Changes from one hemisphere to the other leading in phase were registered near 1928 and 1968 as well as two historical ones near 1783 and 1875. A long‐term anticorrelation between the hemispheric phase differences in the sunspot cycles and the latitudinal distribution of sunspots was traced since 1750 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical models of turbulent flow in rolling motion

The flowing and heat transfer characteristics of turbulent flow in tubes and rectangular channels in rolling motion are investigated theoretically. The flowing and heat transfer models of turbulent flow in rolling motion are established. The correlations of frictional resistance coefficient and Nusselt number are derived. The results are also validated with experiments. The effects of several parameters on frictional resistance coefficient and Nusselt number are investigated. The oscillating amplitude of Nusselt number is in direct ratio with Prandtl number and rolling frequency approximately. The more the flowing velocity is, the less the effect of rolling motion on the flow is. The variation of initial phase difference between Nusselt number and rolling motion with rolling frequency is very limited.

An integrated signal conditioner for high-frequency inductive position sensors

This paper describes the design, implementation and evaluation of a signal conditioner application-specific integrated circuit (ASIC) for high-frequency inductive non-contact position sensors. These sensors employ a radio frequency technology based on an antenna planar arrangement and a resonant target, have a high inherent resolution (0.1% of antenna length) and can measure target position over a wide distance range (<0.1 mm to >10 m). However, due to the relatively high-frequency excitation (1 MHz typically) and to the specific layouts of these sensors, there is unwanted capacitive coupling between the transmitter and receiver coils; this type of distortion reduces linearity and resolution. The ASIC, which is the first generation of its kind for this type of sensor, employs a differential mixer topology which suppresses the capacitive coupling offsets. The system architecture and circuit details are presented. The ASIC was fabricated in a 0.6 µm high-voltage CMOS technology occupying an area of 8 mm2. It dissipates about 30 mA from a 24 V power supply. The ASIC was tested with a high-frequency inductive position sensor (with an antenna length of 10.8 cm). The measured input-referred offset due to transmitter crosstalk is on average about 22 µV over a wide phase difference variation (−99° to +117°) between the transmitter and demodulating signals.

Small-displacement sensing system based on multiple total internal reflections in heterodyne interferometry

A small-displacement sensing system based on multiple total internal reflections in heterodyne interferometry is proposed. In this paper, a small displacement can be obtained only by measuring the variation in phase difference between s- and p-polarization states for the total internal reflection effect. In order to improve the sensitivity, we increase the number of total internal reflections by using a parallelogram prism. The theoretical resolution of the method is better than 0.417 nm. The method has some merits, e.g., high resolution, high sensitivity, and real-time measurement. Also, its feasibility is demonstrated.

A Small-Displacement Sensor Using Total Internal Reflection Theory and Surface Plasmon Resonance Technology for Heterodyne Interferometry

A small-displacement sensor based on total-internal reflection theory and surface plasmon resonance technology is proposed for use in heterodyne interferometry. A small displacement can be obtained simply by measuring the variation in phase difference between s- and p-polarization states with the small-displacement sensor. The theoretical displacement resolution of the small-displacement sensor can reach 0.45 nm. The sensor has some additional advantages, e.g., a simple optical setup, high resolution, high sensitivity and rapid measurement. Its feasibility is also demonstrated.