Local Phase Shifts Research Articles

Numerical investigation of the aerodynamic benefits of wing-wing interactions in a dragonfly-like flapping wing

Numerical simulations are performed to investigate the aerodynamic benefits of wing-wing interactions on a dragonfly-like flapping wing while hovering, at a value of Reynolds number Re set to 630. The local phase shift ψ and wing spacing L* (L/c) are varied to observe their influence on aerodynamic performance. The results show that the aerodynamic benefits due to interactions are strongly dependent on both ψ and L*. The wing-wing interactions are beneficial for the in-phase stroking pattern at ψ = 0° when 1.2 ≤ L* ≤ 2.3, while it is extremely detrimental for the counter stroking pattern at ψ = 180° when 1.2 ≤ L* ≤ 2.3; these benefits and drawbacks are dependent on the timing of the interactions. The best case, when ψ = 0° and L* = 2.1, can increase the time-averaged vertical force coefficient $$\overline{C_v}$$ up to ∼10 % in comparison to the without-interaction case. Two unsteady flow features namely the “enhanced dipole structure” and the “in-sync of wake capture and wing-wing interactions” are observed that increase the vertical force generation in hovering dragonflies. The overall downward momentum imparted by the wing is larger for ψ = 0° in comparison to ψ = 180° as the wake has high vertical velocities due to the constructive role played by wing-wing interactions.

High-efficiency anomalous reflection of acoustic waves with a passive-lossless metasurface

We present the theoretical, numerical and experimental investigations on the high-efficiency anomalous reflection by a passive-lossless acoustic metasurface (AM). In contrast to the conventional AM, the direction of the reflected waves is controlled by the nonlinear local phase shifts in the passive-lossless AM rather than by the linear modulation. Closed-end tubes are designed to realize the passive-lossless AM. A considerable improvement of 31% in the overall efficiency is confirmed in the passive-lossless AM compared to that based on generalized reflection law when the incident and reflected angles are 0° and 75° respectively. Experimental results are in accord with finite element simulations and theoretical analyses. This advance in the proposed AM may pave a way for realizing more complex functionalities such as focusing, self-bending, and vortex generation.

Inversion of Nearshore X-Band Radar Images to Sea Surface Elevation Maps

A new method to invert X-band radar images for linear shoaling conditions is proposed. The commonly used approach for this type of inverse problems is the Fourier transform. Unlike in deep water conditions, in the shoaling region, waves are modulated both in terms of wavelength and amplitude. However, Fourier analysis assumes spacial and temporal periodicity, and homogeneity limiting its applicability to this region. In order to overcome these limitations, a wavelet based technique is developed. The proposed technique treats every spatial radar image within the time sequence individually, so no information on the dispersion relation is required. For validation purposes, surface elevation range-time shoaling realizations based on the mild slope equation are prepared. A radar imaging model including tilt and shadowing modulations, speckle noise, and the radar equation is applied to these realizations to provide modeled grazing incidence radar images. The inversion process starts with the application of the continuous wavelet transform independently for each spacial image. The procedure continues with employing a successive range independent modulation transfer function to the wavelet spectra in the wavenumber domain. Then, after a phase shift correction, an inverse continuous wavelet transform is applied. The procedure is finalized by a calibration of the retrieved maps. After the calibration, a thorough comparison between the original and the reconstructed surface elevations is performed. It shows high efficiency of the proposed method in treating wave number and amplitude modulated signals, as well as in addressing local phase shifts due to tilt modulation and noise contamination. The new inversion method is proven to have high accuracy in inhomogeneous conditions. It shows high potential to be implemented for individual wave reconstruction using real aperture radars.

Projective symmetries and induced electromagnetism in metric-affine gravity

We present a framework in which the projective symmetry of the Einstein–Hilbert action in metric-affine gravity is used to induce an effective coupling between the Dirac lagrangian and the Maxwell field. The effective U(1) gauge potential arises as the trace of the non-metricity tensor Qμaa and couples in the appropriate way to the Dirac fields to in order to allow for local phase shifts. On shell, the obtained theory is equivalent to Einstein–Cartan–Maxwell theory in presence of Dirac spinors.

Cyclic Continuous Max-Flow: A Third Paradigm in Generating Local Phase Shift Maps in MRI.

Sensitivity to phase deviations in MRI forms the basis of a variety of techniques, including magnetic susceptibility weighted imaging and chemical shift imaging. Current phase processing techniques fall into two families: those which process the complex image data with magnitude and phase coupled, and phase unwrapping-based techniques that first linearize the phase topology across the image. However, issues, such as low signal and the existence of phase poles, can lead both methods to experience error. Cyclic continuous max-flow (CCMF) phase processing uses primal-dual-variational optimization over a cylindrical manifold, which represent the inherent topology of phase images, increasing its robustness to these issues. CCMF represents a third distinct paradigm in phase processing, being the only technique equipped with the inherent topology of phase. CCMF is robust and efficient with at least comparable accuracy as the prior paradigms.

Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

Phase demodulation from a single carrier-frequency fringe pattern is becoming increasingly important particularly in areas of optical metrology such as dynamic interferometry, deflectometry and profilometry. The Fourier transform (FT) method and the spatial-carrier phase-shifting technique (SCPS) are two popular and well-established approaches to demodulation. However FT has the drawback of significant edge errors because of the Gibbs effect, whilst detuning errors for the local phase shift occur when SCPS is applied. A novel demodulation method based on pixel-level Lissajous figure and ellipse fitting (PLEF) is presented in this paper. Local demodulation in the spatial domain makes PLEF more flexible than the FT method, without spectral leakage. Based on a more adaptable approach, account is taken of variations in illumination and phase distribution over a few neighboring pixels. The mathematic demodulation model is of interest and has been demonstrated via simulation. Theoretical phase extraction error is as low as 10−4 rad. Experiments further corroborate the effectiveness of the proposed method. In conclusion, various influencing factors, e.g. variations of background/modulation, phase amplitude, carrier frequency, additive noise that may affect the precision of PLEF are discussed in detail.

Acoustic metasurfaces for scattering-free anomalous reflection and refraction

Manipulation of acoustic wavefronts by thin and planar devices, known as metasurfaces, has been extensively studied, in view of many important applications. Reflective and refractive metasurfaces are designed using the generalized reflection and Snell's laws, which tell that local phase shifts at the metasurface supply extra momentum to the wave, presumably allowing arbitrary control of reflected or transmitted waves. However, as it has been recently shown for the electromagnetic counterpart, conventional metasurfaces based on the generalized laws of reflection and refraction have important drawbacks in terms of power efficiency. This work presents a new synthesis method of acoustic metasurfaces for anomalous reflection and transmission that overcomes the fundamental limitations of conventional designs, allowing full control of acoustic energy flow. The results show that different mechanisms are necessary in the reflection and transmission scenarios for ensuring perfect performance. Metasurfaces for anomalous reflection require non-local response, which allows energy channeling along the metasurface. On other hand, for perfect manipulation of anomalously transmitted waves, local and non-symmetric response is required. These conclusions are interpreted through appropriate surface impedance models which are used to find possible physical implementations of perfect metasurfaces in each scenario. We hope that this advance in the design of acoustic metasurfaces opens new avenues not only for perfect anomalous reflection and transmission but also for realizing more complex functionalities, such as focusing, self-bending or vortex generation.

Asymptotic linear stability of Benney–Luke line solitary waves in 2D

In this paper, we study transverse linear stability of line solitary waves to the two-dimensional Benney–Luke equation which arises in the study of small amplitude long water waves in 3D. In the case where the surface tension is weak or negligible, we find a curve of resonant continuous eigenvalues of the linearized operator in a neighborhood of . Time evolution of these resonant continuous eigenmodes is described by a 1D damped wave equation in the transverse variable and it gives a linear approximation of the local phase shifts of modulating line solitary waves. In exponentially weighted space whose weight function increases in the direction of the motion of the line solitary wave, the other part of solutions to the linearized equation decays exponentially as .

Non-stationary local thermoacoustic phase relationships in a gas turbine combustor

A framework is presented for analyzing the local instantaneous phase difference between non-stationary heat release rate and pressure oscillations that is appropriate for use in high-pressure liquid-fueled combustors. High-speed OH* chemiluminescence images were used as a qualitative marker of the heat release rate, from which the local phase shift relative to the pressure was calculated using the Hilbert transform technique. Two types of behavior were observed during time sequences with constant amplitude pressure oscillations. For the first behavior, a region with out-of-phase pressure and heat release rate oscillations moved upstream along the nozzle shear layer towards the nozzle. For the second behavior, transitions occurred between out-of-phase oscillations in a region along the centerline and a toroidal region close to the nozzle. For time periods with increasing amplitude pressure fluctuations, in-phase heat release rate and pressure oscillations developed throughout the upstream portion of the combustor. These in-phase oscillations could extend along the burner centerline and towards the downstream portion of the combustor. This behavior is reversed during time periods with decreasing amplitude pressure oscillations; the upstream portion of the combustor transitions to featuring regions with out-of-phase oscillations.

Susceptibility‐weighted imaging using inter‐echo‐variance channel combination for improved contrast at 7 tesla

To implement and optimize a new approach for susceptibility-weighted image (SWI) generation from multi-echo multi-channel image data and compare its performance against optimized traditional SWI pipelines. Five healthy volunteers were imaged at 7 Tesla. The inter-echo-variance (IEV) channel combination, which uses the variance of the local frequency shift at multiple echo times as a weighting factor during channel combination, was used to calculate multi-echo local phase shift maps. Linear phase masks were combined with the magnitude to generate IEV-SWI. The performance of the IEV-SWI pipeline was compared with that of two accepted SWI pipelines-channel combination followed by (i) Homodyne filtering (HPH-SWI) and (ii) unwrapping and high-pass filtering (SVD-SWI). The filtering steps of each pipeline were optimized. Contrast-to-noise ratio was used as the comparison metric. Qualitative assessment of artifact and vessel conspicuity was performed and processing time of pipelines was evaluated. The optimized IEV-SWI pipeline (σ = 7 mm) resulted in continuous vessel visibility throughout the brain. IEV-SWI had significantly higher contrast compared with HPH-SWI and SVD-SWI (P < 0.001, Friedman nonparametric test). Residual background fields and phase wraps in HPH-SWI and SVD-SWI corrupted the vessel signal and/or generated vessel-mimicking artifact. Optimized implementation of the IEV-SWI pipeline processed a six-echo 16-channel dataset in under 10 min. IEV-SWI benefits from channel-by-channel processing of phase data and results in high contrast images with an optimal balance between contrast and background noise removal, thereby presenting evidence of importance of the order in which postprocessing techniques are applied for multi-channel SWI generation. 2 J. Magn. Reson. Imaging 2017;45:1113-1124.

Lead–Lag Relationship Using a Stop-and-Reverse-MinMax Process

The intermarket analysis, in particular the lead–lag relationship, plays an important role within financial markets. Therefore, a mathematical approach to be able to find interrelations between the price development of two different financial instruments is developed in this paper. Computing the differences of the relative positions of relevant local extrema of two charts, i.e., the local phase shifts of these price developments, gives us an empirical distribution on the unit circle. With the aid of directional statistics, such angular distributions are studied for many pairs of markets. It is shown that there are several very strongly correlated financial instruments in the field of foreign exchange, commodities and indexes. In some cases, one of the two markets is significantly ahead with respect to the relevant local extrema, i.e., there is a phase shift unequal to zero between them.

Clinical validation of susceptibility-weighted cardiovascular magnetic resonance in comparison to T2 and T2* imaging for detection of intramyocardial hemorrhage following acute myocardial infarction

Background Intramyocardial hemorrhage (IMH) identified by CMR is an established prognostic marker following acute myocardial infarction (AMI), but remains relatively underused in the clinical setting. Detection of IMH by T2-weighted or T2* CMR can be limited by long breath hold times and sensitivity to artefacts, especially at 3 Tesla. Alternative methods that can detect IMH with shorter breath hold times are therefore desirable. CMR is capable of detecting differences in the magnetic susceptibility of tissues. The paramagnetic properties of hemoglobin products within IMH cause local phase shifts relative to surrounding tissue. Phase data can be filtered and combined with magnitude data to generate susceptibility weighted MR images (SW MRI). SW imaging has been shown to be highly sensitive for the detection of cerebral hemorrhage, but typically uses long echo times, resulting in prolonged image acquisition. With the larger size of IMH, we hypothesized that SW MRI may be used with shorter echo times, leading to rapid imaging with breath hold times of approximately 4 seconds. We compared the image quality and diagnostic ability of this SW MRI pulse sequence with T2-weighted and T2* CMR to detect IMH at 3T. Methods

Phase-sensitive narrowband heterodyne holography

We report on amplitude and phase imaging of out-of-plane sinusoidal surface vibration at nanometer scales with a heterodyne holographic interferometer. The originality of the proposed method is to make use of a multiplexed local oscillator to address several optical sidebands into the temporal bandwidth of a sensor array. This process is called coherent frequency-division multiplexing. It enables simultaneous recording and pixel-to-pixel division of sideband holograms, which permits quantitative wide-field mapping of optical phase-modulation depths. Additionally, a linear frequency chirp ensures the retrieval of the local mechanical phase shift of the vibration with respect to the excitation signal. The proposed approach is validated by quantitative motion characterization of the lamellophone of a musical box, behaving as a group of harmonic oscillators, under weak sinusoidal excitation. Images of the vibration amplitude versus excitation frequency show the resonance of the nanometric flexural response of one individual cantilever, at which a phase hop is measured.

Diurnal variation of rainfall in the Yangtze River Valley during the spring‐summer transition from TRMM measurements

A 12 year archive of the Tropical Rainfall Measuring Mission (TRMM) rain rate is used to document the regionality of diurnal rainfall cycle in the Yangtze River Valley (YRV). The regional rain peaks, local phase shifts, rain event's behavior, and related seasonal change from March to August are examined. In the middle reach of YRV, rainfall appears mainly in early morning and displays a distinct local shift of diurnal phase. Such features are well established at each presummer (from May to June) and result from the eastward migrating events with a late night growth in size. They are supported by the low‐level convergence that moves from the east slope of the Tibetan Plateau to the middle reach of YRV, as the deviated wind vector rotates clockwise to enhance southerlies at late night and southwesterlies in the morning. In the lower reach of YRV, however, one observes an eruption of morning rainfall with less local difference in diurnal phase. Morning rainfall is active in presummers of some years but suppressed in some others, contributing greatly to the variance of rainfall budget and resulting in anomalous wet/dry seasons. It is found to arise from a local growth of rain events rather than the migrating events from the middle reach. A majority of these organized convections prefer to form and develop in a belt‐shaped zone where the nocturnal southwesterlies of warm/moist air impinge on the Meiyu front in the lower troposphere.

Photonic generation of stable microwave signals from a dual-wavelength Al_2O_3:Yb^3+ distributed-feedback waveguide laser

We report the fabrication and characterization of a dual-wavelength distributed-feedback channel waveguide laser in ytterbium-doped aluminum oxide. Operation of the device is based on the optical resonances that are induced by two local phase shifts in the distributed-feedback structure. A stable microwave signal at ~15 GHz with a -3 dB width of 9 kHz was subsequently created via the heterodyne photodetection of the two laser wavelengths. The long-term frequency stability of the microwave signal produced by the free-running laser is better than ±2.5 MHz, while the power of the microwave signal is stable within ±0.35 dB.

Correlative Microscopy of Living Cells between Fluorescence and Quantitative Phase Imaging with a High Resolution Wavefront Sensor

Phase visualization of cells is used for decades, with setups such as Zernike phase contrast or Nomarski-DIC equipments. Those techniques use the fact that light passing through a sample accumulates phase shift. Nevertheless, they are quite impossible to give information on the quantitative phase shift of each pixel of the image and are commonly used only to increase contrast. We describe here the use of quadri-wave lateral shearing interferometry [1] for wavefront sensing, in order to measure quantitatively the local phase shift within a sample, with a high sensitivity.We use a high resolution wavefront sensor and we get a 300x400 sampling points on the sample, with both phase and intensity information. The method is simple and can be implemented on a conventional microscope: its native bright-field illumination system is used as the light source, and the wavefront sensor has only to be mounted on a video port, with the possibility to combine phase and fluorescence imaging.Correlative microscopy between wide-field fluorescence and optical phase on COS-7 living cells is considered, either on regular substrate or fibronectin-coated micro-patterns. The phase visualization of intracellular organelles is clearly possible with a high contrast, and targeted fluorescence allows a precise and simultaneous identification of each component. A multidimensional image is then obtained by combining those two images. Many organelles, such as mitochondria and endocytosis vesicles, can be specifically determined by their relative phase shift and shape, with a high degree of confidence. Refractive index anisotropy is also used to visualize phase shift of anisotropic components, such as cytoskeleton, with different polarizations of transmitted light.[1] Bon, Maucort, Wattellier and Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17, 13080-13094 (2009).

Tunable Photonic Microwave Filter With Single Bandpass Based on a Phase-Shifted Fiber Bragg Grating

A novel tunable photonic microwave single bandpass filter based on the optical resonance originated by a local phase shift introduced in the periodic structure of a fiber Bragg grating is proposed. Dynamic control of the phase shift is obtained employing a piezoelectric transducer in order to stretch the grating, thus changing the resonance wavelength. A photonic microwave filter is obtained by using an optical single-sideband modulation. Experimental results are provided in order to prove the concept.

Dual-Wavelength DFB Erbium-Doped Fiber Laser With Tunable Wavelength Spacing

A novel tunable dual-wavelength distributed-feedback fiber laser is presented. It is based on the optical resonances induced by two local phase shifts introduced in the periodic structure of an erbium-doped fiber Bragg grating. A dynamic control of the phase shifts, which are generated by piezoelectric transducers, permits the tunability of the wavelength spacing between the optical harmonics of the laser signal. The wavelength spacing is continuously tuned from 0.128 to 7 GHz. Moreover, a microwave carrier is created within such frequency tuning range by the heterodyne photodetection of the dual-wavelength laser signal.

Direct observation of geometric phases using a three-pinhole interferometer

We present a method to measure the geometric phase defined for three internal states of a photon (polarizations) using a three-pinhole interferometer. From the interferogram, we can extract the geometric phase related to the three-vertex Bargmann invariant as the area of a triangle formed by interference fringes. Unlike the conventional methods, our method does not involve the state evolution. Moreover, the phase calibration of the interferometer and the elimination of the dynamical phase are not required. The gauge invariance of the geometric phase corresponds to the fact that the area of the triangle is never changed by the local phase shift in each internal state.

Phase labeling using sensitivity encoding (PLUS): Data acquisition and image reconstruction for geometric distortion correction in EPI

Geometric distortion caused by magnetic field inhomogeneity is generally an inevitable tradeoff for fast MRI acquisitions using echo-planar imaging. Most of the existing distortion-correction techniques require separate scans for field maps in order to correct the distortion contained in a measurement. A drawback of these current techniques is that the field map scans and the measurement can capture different patient positions, which invalidates the stationary condition. A new method was developed in this work to correct geometric distortion by using local phase shifts derived directly from the measurement itself, without the need of extra field map scans. This self-sufficient method takes advantage of parallel imaging and k-space trajectory modification to produce multiple images from a single acquisition. The measurement is also used to derive sensitivity maps for parallel imaging reconstruction. The derived phase shifts are retrospectively applied to the measurement for correction of geometric distortion in the measurement itself. The proposed method was successfully demonstrated using experimental data from a phantom and a human brain.