Local Phase Variations Research Articles

Bohmian analysis of dark solutions in interfering Bose–Einstein condensates: The dynamical role of underlying velocity fields

In the last decades, the experimental research on Bose–Einstein interferometry has received much attention due to promising technological implications. This has thus motivated the development of numerical simulations aimed at solving the time-dependent Gross–Pitaevskii equation and its reduced one-dimensional version to better understand the development of interference-type features and the subsequent soliton dynamics. In this work, Bohmian mechanics is considered as an additional tool to further explore and analyze the formation and evolution in real time of the soliton arrays that follow the merging of two condensates. An alternative explanation is thus provided in terms of an underlying dynamical velocity field, directly linked to the local phase variations undergone by the condensate along its evolution. Although the reduced one-dimensional model is considered here, it still captures the essence of the phenomenon, rendering a neat picture of the full evolution without diminishing the generality of the description. To better appreciate the subtleties of free versus bound dynamics, two cases are discussed. First, the soliton dynamics exhibited by a coherent superposition of two freely released condensates is studied, discussing the peculiarities of the underlying velocity field and the corresponding flux trajectories in terms of both the peak-to-peak distance between the two initial clouds and the addition of a phase difference between them. In the latter case, an interesting correspondence with the well-known Aharonov-Bohm effect is found. Then, the recurrence dynamics displayed by the more general case of two condensates released from the two opposite turning points of a harmonic trap is considered in terms of the distance between such turning points. In both cases, it is presumed that the initial superposition state is generated by splitting adiabatically a single condensate with the aid of an optical lattice, which is then turned off. Nonetheless, although the lattice does not play any active role in the simulations, the parameters defining the initial states are in compliance with it, which helps in the interpretation and understanding of the results observed.

A Bohmian trajectory analysis of singular wave functions

The Schrödinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time evolution. We resort to the notion of quantum Bohmian trajectories to relate this singular behavior to local phase variations, which generate an underlying velocity field responsible for driving the quantum flux toward the singular region.

Exploring the dynamics of finite-energy Airy beams: a trajectory analysis perspective.

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the truncation and hence the propagation properties displayed by the designed beams, here we resort to a new perspective based on a trajectory methodology, complementary to the density plots more commonly used to study the intensity distribution propagation. We consider three different aperture functions, which are convoluted with an ideal Airy beam. As it is shown, the corresponding trajectories reveals a deeper physical insight about the propagation dynamics exhibited by the beams analyzed due to their direct connection with the local phase variations undergone by the beams, which is in contrast with the global information provided by the usual standard tools. Furthermore, we introduce a new parameter, namely, the escape rate, which allow us to perform piecewise analyses of the intensity distribution without producing any change on it, e.g., determining unambiguously how much energy flux contributes to the leading maximum at each stage of the propagation, or for how long self-accelerating transverse propagation survives. The analysis presented in this work thus provides an insight into the behavior of finite-energy Airy beams, and therefore is expected to contribute to the design and applications exploiting this singular type of beams.

Focusing Coherent Light through Volume Scattering Phantoms via Wavefront Shaping.

Manipulating the wavefront of coherent light incident on scattering media to enhance the imaging depth, sensitivity, and resolution is a common technique in biomedical applications. Local phase variations cause changes in the interference and can be used to create a focus inside or behind a scattering medium. We use wavefront shaping (WFS) to force constructive interference at an arbitrary location. The amount of light transmitted into a given region strongly depends on the scattering and absorption characteristics. These are described by their respective coefficients μs and μa and the scattering phase function. Controlling the scattering and absorption coefficients, we study the behavior of wavefront shaping and the achievable intensity enhancement behind volume scattering media with well-defined optical properties. The phantoms designed in this publication are made of epoxy resin. Into these epoxy matrices, specific amounts of scattering and absorbing particles, such as titanium dioxide pigments and molecular dyes, are mixed. The mixture obtained is filled into 3D-printed frames of various thicknesses. After a precise fabrication procedure, an integrating sphere-based setup characterizes the phantoms experimentally. It detects the total hemispherical transmission and reflection. Further theoretical characterization is performed with a newly developed hybrid PN method. This method senses the flux of light into a particular angular range at the lower boundary of a slab. The calculations are performed without suffering from ringing and fulfill the exact boundary conditions there. A decoupled two-path detection system allows for fast optimization as well as sensitive detection. The measurements yield results that agree well with the theoretically expected behavior.

Trajectory analysis of phase effects associated with truncated Airy beams

Airy wave packets constitute a very peculiar type of structured light: during their propagation, their transverse profile undergoes a self-accelerating displacement while it remains shape invariant. They are thus the only non-dispersive beam-type solution to the Helmholtz paraxial equation in free space. Such properties are possible by virtue of their infinite power content. However, experimentally, Airy beams can only be reproduced in an approximate manner, with a limited extension and hence a finite power content. To this end, differentcutoffprocedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In this Communication, we present and discuss our latest advances in the analysis of the effects that convolving an Airy beam with different aperture functions have on their propagation properties. More specifically, we make use of a trajectory-based methodology, which allows us to analyze and explain the beam propagation in terms of trajectories directly connected with the beam local phase variations.

Analysis of phase errors introduced by single-shot color phase-shifting profilometry on colored objects

We aim to report an error analysis on single-shot profilometry when projecting a composite colored fringe pattern onto a surface containing different colors. Several studies have analyzed white surfaces using profilometry; however, when color is incorporated, new considerations must be taken into account. In this work, it is found theoretically and corroborated experimentally that each color introduces local phase variations that render in phase errors with a severity that is related to the crosstalk matrix of the projector–camera system. It is also shown that the phase errors are phase-shifting dependent and could be reduced with appropriate phase recovery algorithms. Experimental results are presented and compared with those obtained using a standard temporal four-step phase-shifting method.

Partial Fourier reconstruction of complex MR images using complex-valued convolutional neural networks.

To provide a complex-valued deep learning approach for partial Fourier (PF) reconstruction of complex MR images. Conventional PF reconstruction methods, such as projection onto convex sets (POCS), uses low-resolution image phase information from the central symmetrically sampled k-space for image reconstruction. However, this smooth phase constraint undermines the phase estimation accuracy in presence of rapid local phase variations, causing image artifacts and limiting the extent of PF reconstruction. Using both magnitude and phase characteristics in big complex image datasets, we propose a complex-valued deep learning approach with an unrolled network architecture for PF reconstruction that iteratively reconstructs PF sampled data and enforces data consistency. We evaluate our approach for reconstructing both spin-echo and gradient-echo data. The proposed method outperformed the iterative POCS PF reconstruction method. It produced better artifact suppression and recovery of both image magnitude and phase details in presence of local phase changes. No noise amplification was observed even for highly PF reconstruction. Moreover, the network trained on axial brain data could reconstruct sagittal and coronal brain and knee data. This method could be extended to 2D PF reconstruction and joint multi-slice PF reconstruction. Our proposed method can effectively reconstruct MR data even at low PF fractions, yielding high-fidelity magnitude and phase images. It presents a valuable alternative to conventional PF reconstruction, especially for phase-sensitive 2D or 3D MRI applications.

Automatic and robust phase aberration compensation for digital holographic microscopy based on minimizing total standard deviation

A totally automatic and robust phase aberration compensation method is proposed for digital holographic microscopy. The correction needs no manual operation or prior knowledge of the recording setup. As the phase aberrations are modeled with orthogonal polynomials, not only phase curvature but also high order aberrations could be corrected with a single hologram. The polynomial coefficients are obtained in an optimization procedure by minimizing the total standard deviation, i.e., the sum of local standard deviation of the compensated phase map. Since both the global and the local phase variations are considered, the proposed method is more accurate and robust than the state-of-the-art numerical methods with the existence of abrupt edges and phase noise. The effectiveness of the proposed method is validated with numerical simulation and the experimental results of mouse osteoblastic MC3T3-E1 living cells and USAF 1951 resolution target.

An improved local phase variation attribute and its application in channels detection

Instantaneous phase is a commonly used attribute for structural and stratigraphic feature characterization. The conventional calculation method is to construct the complex-valued seismic trace, then get the ratio of the imaginary part to the real part and finally compute the antitangent of the ratio as the instantaneous phase attribute. In this way, the phase result at one time sample point is the total phase rotation from the beginning of the trace to this point, which means the traditional instantaneous phase is cumulative. Furthermore, the phase obtained by arctangent is usually entangled, which makes it more difficult to apply to seismic interpretation. To address the two issues above, we proposed a new way to calculate the improved local phase variation attributes. Firstly, we calculate traditional instantaneous phase and unwrap it. Then we set a time window on the unwrapped phase to compute the local phase variation by using some difference methods. Finally, we slide the time window on the whole trace to obtain the final phase variation attributes. This strategy turns the whole cumulative value into local variational value, which makes the obtained local phase variation nearly zero in the continuous region but changed greatly at the interface or the abnormal structure areas. Tested by the numerical model and the real data, the proposed attributes have a good application effect in channel detection, which provides a train of thought to seismic structure interpretation with phase attributes.

Stabilization of atmospheric turbulence-distorted video containing moving objects using the monogenic signal

The motion of moving objects in turbulence-distorted videos is affected by both the atmospheric turbulence fluctuations and the objects’ own movements. Therefore, simultaneous video stabilization and preservation of the moving objects is a challenging task. Using the monogenic signal, we propose a fast two-stage approach to mitigate these erratic motions in videos and preserve the moving objects. In the first stage, each frame of a video is represented by the monogenic signal, which is used to model the turbulence-induced random brightness scintillation and local wiggles through local monogenic amplitude and phase. Then, a low-pass filter is employed to attenuate the high spatial frequency of local monogenic amplitude and phase variations to remove turbulence-induced distortions and obtain stable background frames. In the second stage, a two-step mask generating scheme is proposed to preserve the moving objects. Firstly, the coarse masks of the moving objects are obtained using the difference images between distorted frames and stable background frames. The coarse masks are then refined through analyzing the difference images of the local monogenic amplitude and phase between distorted frames and stable background frames. Finally, the stable video frames containing moving objects are reconstructed from the refined masks and the stable background frames. Experimental results show that the proposed approach is efficient and provides stabilized video and preservation of moving objects simultaneously in atmosphere turbulent conditions.

Nature and evolution of incommensurate charge order in manganites visualized with cryogenic scanning transmission electron microscopy

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge-lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ([Formula: see text]93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale ([Formula: see text]6 pm to 11 pm) transverse displacements, suggesting that charge-lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

Comparative analysis of nanometric inspection methods in fringeless speckle pattern interferometry.

In digital speckle pattern interferometry, fringeless speckle pattern interferograms are obtained when the object field deformation is insufficient to produce local phase variations higher than 2π. Therefore, the use of the well-known phase recovery algorithms based on fringe processing is not adequate. In this work, distinct algorithms based on the application of a straightforward arccosine function to a filtered interferogram and the correlation of intensity images and implicit smoothing splines are proposed, analyzed, and compared for the fast inspection of nanometric displacement fields, avoiding the acquisition of several images. In addition, three different methods for the normalization of fringeless speckle pattern interferograms are proposed. The Structural Similarity Index is used to assess the performance of the tested methods by means of numerical simulations under different illuminations, signal-to-noise ratios, phase excursions, and mean speckle size conditions. The analysis shows that the phase recovered by the methods based on the arccosine function and correlation are appropriate for a fast inspection solution. The implicit smoothing spline outperforms other methods in almost all conditions.

Video stabilization in atmosphere turbulent conditions based on the Laplacian-Riesz pyramid.

Video stabilization in atmosphere turbulent conditions is aimed at removing spatiotemporally varying distortions from video recordings. Conventional shaky video stabilization approaches do not perform effectively under turbulent circumstances due to the erratic motion common to those conditions. Using complex-valued image pyramids, we propose a method to mitigate this erratic motion in videos. First, each frame of a video is decomposed into different spatial frequencies using the Laplacian pyramid. Second, a Riesz transform is adopted to extract the local amplitude and the local phase of each sub-band. Next, low-pass filters are designed to attenuate the local amplitude and phase variations to remove turbulence-induced distortions. Experimental results show that the proposed approach is efficient and provides stabilizing video in atmosphere turbulent conditions.

Real valued diffusion-weighted imaging using decorrelated phase filtering.

Because of the intrinsic low signal-to-noise ratio in diffusion-weighted imaging (DWI), magnitude processing often causes an overestimation of the signal's amplitude. This results in low-estimation accuracy of diffusion models and reduced contrast because of a superposition of the image signal and the noise floor. We adopt a new phase correction (PC) technique that yields real valued diffusion data while maintaining a Gaussian noise distribution. We conduct simulations of the noise propagation in the echo-planar imaging reconstruction chain to determine the spatial noise correlation in the image. Using the correlation pattern, optimized filter kernels are derived to estimate the true phase of the signal in each voxel. Furthermore, we adopt an outlier detection technique to replace the real value by the magnitude in case of substantial signal loss resulting from incorrect PC. The benefits of our method are demonstrated on Monte Carlo simulations, DWI data acquired from healthy volunteer experiments, estimated parameters of the diffusion kurtosis imaging model, and the model-free diffusion spectrum imaging technique. The improved PC approach significantly reduces the noise bias and only slightly increases the sensitivity to local phase variations. PC can enhance the usefulness of higher b-values, allowing deeper insights into tissue microstructure. Magn Reson Med 77:559-570, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Numerical investigations into effects of three-dimensional wake patterns on unsteady aerodynamic characteristics of a circular cylinder at Re=1.3×105

In contrast with a wide range of applications concerning flows around a circular cylinder at upper subcritical Reynolds numbers (Re), there is no systematic understanding about the fundamentals of so-called random flow patterns, and their effects on intermittent modulations in the time history of pressure or force, and the decrease in their spanwise correlations. This paper employed the large-eddy simulation (LES) technique to predict flows past a circular cylinder at Re=1.3×105 and to provide images based on flow visualization that can clarify the physical mechanism responsible for these outcomes. A reasonably sufficient spanwise length was adopted for the numerical model by taking into consideration the effect of aspect ratios (the spanwise length to the diameter). We found that even at such high Res, a three-dimensional pattern of vortical field is present in the wake resulting in total force modulation and weak spanwise correlation, e.g., obvious oblique shedding. The whole development process of the three-dimensional wake is exhibited as a universal. The results revealed that local phase variations in primary vortex shedding are the starting points of three-dimensional wake patterns, which are induced by the “irregular” streamwise vortex. The three-dimensional near wake following local phase variations is associated with a successive evolution composed of certain stages in order. Quantitative analyses based on the time series of sectional lift coefficients show that intermittent increase in primary shedding periods and sectional lift streak divisions are closely related to local phase variations and vortex division in the development process of the three-dimensional pattern. In addition to the phase difference along the span, the three-dimensional pattern also weakens vortex shedding in cross sections perpendicular to the axis of the cylinder, resulting in modulation of the sectional lift coefficient.

Multivariate Functional Halfspace Depth

This article defines and studies a depth for multivariate functional data. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape, and phase variation. We study both population and finite sample versions. The multivariate sample of curves may include warping functions, derivatives, and integrals of the original curves for a better overall representation of the functional data via the depth. We present a simulation study and data examples that confirm the good performance of this depth function. Supplementary materials for this article are available online.

Imaging the electro-kinetic response of biological tissues with phase-resolved optical coherence tomography

AbstractIn this study, the electro-kinetic phenomena (EKP) induced in biological tissue by external electric field, while not directly visible in optical coherence tomography (OCT) images, were detected by analyzing their textural speckle features. During application of a low-frequency electric field to the tissue, speckle patterns changed their brightness and shape depending on the local tissue EKP. Since intensities of OCT image speckle patterns were analyzed and discussed in our previous publications, this work is mainly focused on OCT signal phase analysis. The algorithm for extracting local spatial phase variations from unwrapped phases is introduced. The detection of electrically induced optical changes manifest in OCT phase images shows promise for monitoring the fixed charge density changes within tissues through their electro-kinetic responses. This approach may help in the identification and characterization of morphology and function of healthy and pathologic tissues.

Effect of Process Variables on Microstructural Features during Solidification of AM60B Magnesium Alloy

In this study, commercial AM60B magnesium alloy was studied under different solidification conditions to understand the influence of cooling rate, thermal gradient, growth velocity, Niyama criterion, solidification time and mold dimensions on microstructural features such as secondary and tertiary dendrite arm spacing, grain size, porosity, pore shape and size, local morphological and phase variations. Porosity, grain size and dendrite arm spacing were measured as functions of the process variables. It was realized that the process of mold filling and solidification are simultaneous in nature and they significantly affect the microstructure development trends and its dependency on the process parameters. A significant effect, of the above mentioned, was found on the obtained porosity values and their variation along the casting. The results clearly indicate that rate of filling, nature of flow of liquid and shape of the mold greatly affect the solidification process and thereby the microstructure.

Multivariate Functional Halfspace Depth

A multivariate depth for functional data is defined and studied. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape and phase variation. Both population and finite sample versions are studied. The multivariate sample of curves may include warping functions, derivatives and integrals of the original curves for a better overall representation of the functional data via the depth. A simulation study and data example confirm the good performance of this depth function.

Laser-induced preferential domain nucleation in hafnium-doped congruent lithium niobate crystal

The focused visible laser-induced preferential domain nucleation effect is investigated in 3 mol% hafnium-doped congruent lithium niobate crystal. The local phase variation is in-situ monitored during laser-induced preferential domain nucleation. The variations of phase distributions are reconstructed by digital holographic interferometry. The nucleation field decreases exponentially with increasing irradiation intensity. The space charge field along the z direction is thought to be an important mechanism for the laser-induced preferential domain nucleation. Laser-induced hafnium-doped congruent lithium niobate crystals appear to be a promising candidate for further development of ferroelectric domain engineering.