Wavefront Curvature Research Articles

Matched field processing accounting for complex Earth structure: method and review

SUMMARYMatched field processing (MFP) is a technique to locate the source of a recorded wavefield. It is the generalization of plane-wave beamforming, allowing for curved wave fronts. In the standard approach to MFP, simple analytical Green’s functions are used as synthetic wavefields that the recorded wavefields are matched against. We introduce an advancement of MFP by utilizing Green’s functions computed numerically for Earth structure as synthetic wavefields. This allows in principle to incorporate the full complexity of elastic wave propagation without further manual considerations, and through that provide more precise estimates of the recorded wavefield’s origin. We call this approach numerical MFP (nMFP). To demonstrate the applicability and potential of nMFP, we present two real data examples, one for an earthquake in Southern California, and one for secondary microseism activity in the Northeastern Atlantic and Mediterranean Sea. In addition, we explore and clarify connections between localization approaches for the ambient seismic field, real world limitations, and identify key areas for future developments. To increase the adoption of MFP in the seismological community, tutorial code is provided.

Experimental visualization of sphere-induced oblique detonation in a non-uniform mixture

To the best of our knowledge, this study is the first to adopt an experimental approach for addressing the theoretical properties of sphere-induced oblique detonation in a non-uniform mixture. A stratified H2/O2–3Ar mixture was supplied with a concentration gradient normal to the launching direction of a two-stage light gas gun. High-speed schlieren images were taken to study the morphologies of oblique detonation. The waiting time after the H2 injection until the launch was varied to investigate the effect of the concentration gradient. Oblique detonations were successfully formed in every condition considered with curved wave fronts and Chapman-Jouguet detonations were partially achieved. However, stronger concentration gradients induced several critical structures, such as local quenching and a Straw-Hat structure. Also interestingly, a part of the detonation front in the region where the Chapman-Jouguet solution does not exist propagated relative to the projectile, whereas the rest remained steady. Moreover, analysis of several relevant physical length scales indicated that the nondimensional diameter, which is critical for initiating detonation in a uniform mixture, could be a valid criterion near the projectile, but not far from it. Instead, the wave curvature determined the local structures of oblique detonation, which quantitatively explained the velocity deficit and emergence of the critical structures. We believe the findings of this study will benefit the understanding of non-uniformly premixed detonation in a propagating form owing to its analogy to an oblique detonation.

Slow Conduction Corridors and Pivot Sites Characterize the Electrical Remodeling in Atrial Fibrillation.

This study aimed to evaluate the progression of electrophysiological phenomena in a cohort of patients with paroxysmal atrial fibrillation (PAF) and persistent atrial fibrillation (PsAF). Electrical remodeling has been conjectured to determine atrial fibrillation (AF) progression. High-density electroanatomic maps during sinus rhythm of 20 patients with AF (10 PAF, 10 PsAF) were compared with 5 healthy control subjects (subjects undergoing ablation of a left-sided accessory pathway). A computational postprocessing of electroanatomic maps was performed to identify specific electrophysiological phenomena: slow conductions corridors, defined as discrete areas of conduction velocity<50cm/s, and pivot points, defined as sites showing high wave-front curvature documented by a curl module >2.5 1/s. A progressive decrease of mean conduction velocity was recorded across the groups (111.6 ± 55.5cm/s control subjects, 97.1 ± 56.3cm/s PAF, and 84.7 ± 55.7cm/s PsAF). The number and density of slow conduction corridors increase in parallel with the progression of AF (8.6 ± 2.2 control subjects, 13.3 ± 3.2 PAF, and 20.5 ± 4.5 PsAF). In PsAF the atrial substrate is characterized by a higher curvature of wave-front propagation (0.86 ± 0.71 1/s PsAF vs 0.74 ± 0.63 1/s PAF; P = 0.003) and higher number of pivot points (25.1 ± 13.8 PsAF vs 9.5 ± 6.7 PAF; P< 0.0001). Slow conductions: corridors were mostly associated with pivot sites tending to cluster around pulmonary veins antra. The electrical remodeling hinges mainly on corridors of slow conduction and higher curvature of wave-front propagation. Pivot points associated to SC corridors may be the major determinants for functional localized re-entrant circuits creating the substrate for maintenance of AF.

Characterizing the temporal rotation and radial twist of the interference pattern of vortex beams

We experimentally and theoretically characterize the temporal rotation and radial twist of the interference pattern of a vortex beam with its conjugate copy. To quantitatively study the temporal rotation and radial twist, we controllably modify the conjugate beam to obtain a frequency or wavefront curvature difference using a movable Mach–Zehnder interferometer. The effects of the physical parameters (i.e., the topological charge, frequency difference and wavefront curvature difference of the vortex beams) on the temporal rotation as well as radial twist are systematically explored. We further measure two parameters, the rotation velocity Ω and twist coefficient α, respectively, to characterize the degree of the temporal rotation and radial twist of the interference pattern. The theory of the interference model on vortex beams has good agreement with the experimental results. This work is helpful for study on the detailed structure of the interference pattern and manipulation of matter with superimposed vortex beams.

Evolution characteristics of generalized Hermite-cosine-Gaussian solitons in optical nonlinear medium with spatial nonlocality

The evolution characteristics of Hermite-cosine-Gaussian beams in optical nonlinear medium with spatial nonlocality are investigated theoretically in detail. We obtain a series of analytical expressions to describe the evolution characteristics of Hermite-cosine-Gaussian beams in nonlocal medium, such as the expressions of the evolutionary propagation, the beam spot size, the statistical wavefront curvature, the critical energy etc. The results show that the statistical spot size of Hermite-cosine-Gaussian beam can remain unchanged or change periodically according to different initial incident energy. However, the transverse intensity mode of Hermite-cosine-Gaussian beam always presents periodic transformation. This is consistent with high-order temporal solitons, so the evolution of Hermite-cosine-Gaussian beams can also be called generalized solitons or breathers. The influences of initial incident energy and cosine parameters on the evolution characteristics of Hermite-cosine-Gaussian beams are analyzed in detail. Through numerical simulation, some typical evolution characteristics are shown graphically.

A Global Centroid Single Force Catalog of P‐Wave Microseisms

AbstractP‐wave microseisms are excited by ocean swell activities. The recent development of an ocean wave model allows us to compare them quantitatively. For the comparison, a single force at a centroid location can characterize the seismic excitation. A beamforming method is feasible for locating the centroids efficiently. However, the required plane wave assumption reduces the accuracy for a large aperture array. The lack of information on the wavefront curvature also makes P and PP phases indistinguishable. To utilize information on the curvature, we developed the auto‐focusing method as a natural extension of beamforming: (a) We estimated the slowness vector and the wavefront curvature by a grid‐search method, which maximizes the beam power. (b) We iteratively update the values based on the perturbation theory. (c) Based on the classified phase according to the wavefront curvature and the slowness, we locate the centroid from the slowness vector with corrections for a global 3‐D P‐wave velocity structure. We also infer the centroid‐single‐force (CSF) from the beam power. We applied this method to the vertical components of seismic records at approximately 780 Hi‐net stations in Japan from 2004 to 2020. We also compare the CSF catalog with a synthetic CSF catalog based on a numerical ocean wave model: WAVEWATCH III. Both catalogs generally show similar temporal‐spatial patterns of centroids. The amplitudes of CSF are consistent with each other, although the seismic signal‐to‐noise ratio limits the detected events. The ocean wave model cannot explain significant activities in the Gulf of Carpentaria.

Propagation-invariant high-dimensional orbital angular momentum states

Photonic states encoded in spatial modes of paraxial light fields provide a promising platform for high-dimensional quantum information protocols and related studies, where several pioneering theoretical and experimental demonstrations have paved the path for future technologies. Crucially, critical issues encountered in free-space propagation still represent a major challenge. This is the case of asynchronous diffraction between spatial modes with different modal orders, which experience variations in their transverse structure upon free-space propagation. Here we address this issue by proposing an encoding method based on the use of Laguerre–Gaussian modes of the same modal order N to define a N + 1 dimensional space. Noteworthy, such modes endowed with orbital angular momentum (OAM) experience the same propagation aberrations featuring an identical Gouy phase and wavefront curvature. We demonstrate our proposal experimentally by using time-correlated-single-photon imaging combined with a digital propagation technique. Importantly, our technique allows to eliminate, without the use of imaging systems, all issues related to asynchronous diffraction, providing an accessible way to generate propagation-invariant OAM qudits for quantum optical protocols.

Convergence of strong shock waves in an ideal gas with dust particles

In this paper, the authors study the problem of an imploding strong cylindrical/spherical shock wave collapsing at the axis/center of a cylindrical/spherical piston that is filled with a dusty gas of uniform density. The dusty gas is assumed to be a mixture of an ideal gas and a large number of dust particles. The dust particles are of a micrometric size and uniformly distributed in the mixture. A mathematical model using a system of hyperbolic partial differential equations is presented for the considered problem. The perturbation series method is used to solve the implosion problem, providing a global solution and yielding accurately the results of Guderley's local similarity solution, which holds only in the neighborhood of the axis/center of implosion. The values of all possible real similarity exponents and the corresponding amplitudes are determined in the vicinity of the shock collapse by extending the flow variables and shock location in the Taylor series in time t. Furthermore, the obtained values of similarity exponents have been compared with the existing results and numerical results obtained by the other methods. The effects of the adiabatic exponent γ, the wavefront curvature α, and various dusty gas parameters such as σ, Kp, and G0 on the shock trajectory and flow variables have been graphically analyzed.

Formation mechanism of coherent rainbows (II)

When white light laser is focused on liquids, colorful interference rings with different shapes, i.e. “coherent rainbows” can be seen. The formation mechanism of such coherent rainbows is described as follows. The laser heating changes the local temperature distribution of the liquid, which affects the refractive index locally and thus the optical path difference, i.e. thermal lens effect which may cause the laser to go off at large angles. The curvature of the laser wavefront and the convection and bubbles in the liquid can also play some roles as reported here. The wave front curvature results in the asymmetry of the coherent rainbows in the near of the focal point because the wave front curvature in front of the focal point is negative and the wave front curvature in the rear of the focal point is positive. The coherent rainbow has an oval shape with up-down asymmetry because convection in the locally heated liquid leads to an asymmetric temperature distribution. We construct a function including wave front curvature and thermal lens effect, and obtain the relationship between the size of the coherent rainbows and the position of the sample. As a result of the liquid instability induced by the laser heating, the temperature distribution in the liquid is no longer axisymmetric, thus, the focal length of the transverse and longitudinal thermal concave lens are no longer the same. The fitting results accord well with the experimental observations that the coherent rainbows change faster (slower) in front of (rear) the focal point and the longitudinal and transverse dimension of the coherent rainbow are different. Many tiny bubbles are generated in water in the center of the laser beam, forming a local “black barrier” which explains the observation that there are diffraction rings and Poisson-type bright spots in the dark area of the coherent rainbows. The coherent rainbows can be observed in many liquids where the shape and number of rings of coherent rainbows depend on liquid properties such as density, viscosity and thermal conductivity.

A Two-Step Wide-Scene Polar Format Algorithm for High-Resolution Highly-Squinted SAR

Traditional polar format algorithm (PFA) is widely used in high-resolution and highly-squinted (HRHS) synthetic aperture radar (SAR) systems, because of its unique decoupling ability for any squint angle. However, the image size limit in traditional PFA, affected by the wavefront curvature, is too small to meet the modern wide-scene requirements. To break the limit, a new two-step PFA is proposed in this letter. It uses PFA twice. The first PFA is to obtain a coarse focused big image, from which a number of subimages can be filtered out. Each subimage could be recovered to the original phase history domain and reprocessed by another modified PFA, i.e., second PFA, to get a precisely focused subimage. The final full-image can be obtained easily by mosaicking subimages together. This two-step approach is derived in detail and could obviously enlarge the valid PFA scene. It is validated by simulated and real data.

An Efficient mmW Frequency-Domain Imaging Algorithm for Near-Field Scanning 1-D SIMO/MIMO Array

In recent years, millimeter-wave (mmW) 3D imaging technology for scanning 1D single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) array has been extensively studied due to its unique advantages in near-field applications. However, current imaging algorithms for this kind of scheme are not satisfactory, either of low quality since irrational approximations are introduced, or too slow as the back projection method is employed. In this paper, an efficient frequency-domain imaging algorithm is developed to fetch up these shortages. The precise spectral expression of the echo signal within SIMO data is derived through spherical-wave decomposition and fast Fourier transform (FFT) operations. By properly approximating the nonlinear phase, the wavefront curvature is compensated after employing a 1D Stolt interpolation, and then the reflectivity map of the target can be obtained through several multiplications and inverse FFT operations. Image reconstruction for a MIMO array can be realized by coherently summing up all the SIMO focusing results. Both simulation analysis and experimental results demonstrate the effectiveness of the proposed algorithm in imaging quality and computational efficiency.

Spatiotemporal couplings through a nonlinear phase in broadband optical parametric amplification.

Optical parametric chirped-pulse amplification (OPCPA) is prone to undesired spatiotemporal couplings. This Letter studies a family of OPCPA couplings resulting from the nonlinear phase shift induced by frequency-dependent phase mismatch. These OPCPA couplings manifest as pulse-front deformation, transversely varying pulse duration, and spectrally varying wavefront curvature, which are directly linked with the phase-mismatch dispersion terms. The numerical study in this Letter also reveals that the focused signal intensity severely degrades with increasing signal bandwidth and pump depletion.

X-ray vacuum diffraction at finite spatiotemporal offset

We study the nonlinear QED signature of x-ray vacuum diffraction in the head-on collision of optical high-intensity and x-ray free-electron laser pulses at finite spatiotemporal offsets between the laser foci. The high-intensity laser driven scattering of signal photons outside the forward cone of the x-ray probe constitutes a prospective experimental signature of quantum vacuum nonlinearity. Resorting to a simplified phenomenological ad hoc model, it was recently argued that the angular distribution of the signal in the far-field is sensitive to the wavefront curvature of the probe beam in the interaction region with the high-intensity pump. In this work, we model both the pump and probe fields as pulsed paraxial Gaussian beams and reanalyze this effect from first principles. We focus on vacuum diffraction both as an individual signature of quantum vacuum nonlinearity and as a potential means to improve the signal-to-background separation in vacuum birefringence experiments.

Characteristics of Spiral Patterns Formed by Coaxial Interference between Two Vortex Beams with Different Radii of Wavefront Curvatures

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs’ difference between two vortex beams, and the twist direction relates to the sign of TCs’ difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence.

Using gravitational wave parallax to measure the Hubble parameter with pulsar timing arrays

We demonstrate how pulsar timing arrays (PTAs) can, in principle, yield a purely gravitational wave (GW) measurement of the luminosity distance and comoving distance to a supermassive black hole binary source, hence providing an estimate of the source redshift and the Hubble constant. The luminosity distance is derived through standard measurement of the chirp mass, which for the slowly evolving binary sources in the PTA band can be found by comparing the frequency of GW-timing residuals at the Earth compared to those at distant pulsars in the array. The comoving distance can be measured from GW-timing parallax caused by the curvature of the GW wavefronts. This can be detected for single sources at the high-frequency end of the PTA band out to Gpc distances with a future PTA containing well-timed pulsars out to $\mathcal{O}(10)$ kpc, when the pulsar distance is constrained to less than a GW wavelength. Such a future PTA, with $\gtrsim 30$ pulsars with precise distance measurements between 1 and 20~kpc, could measure the Hubble constant at the tens of percent level for a single source at $0.1 \lesssim z \lesssim 1.5$. At $z \lesssim 0.1$, the luminosity and comoving distances are too similar to disentangle, unless the fractional error in the luminosity distance measurement is decreased below 10%. At $z\gtrsim 1.5$, this measurement will likely be restricted by a signal-to-noise ratio threshold. Generally, clarification of the different types of cosmological distances that can be probed by PTAs, and their relation to pulsar distance measurements is important for ongoing PTA experiments aimed at detecting and characterizing GWs.

Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves

The lateral or transverse resolution of single-point interferometers for vibration measurement is especially critical for microelectromechanical systems (MEMS) vibrating up to the gigahertz range. In this regime, the acoustic wavelengths are typically in the range of the size of the laser focus. Thus, a successful vibration measurement requires distinct knowledge about the lateral resolution limit and its dependencies with instrumentation parameters. In this paper, we derive an analytic approximation formula, which allows for estimation of the systematic measurement deviation of the vibration amplitude and, thus, a definition of the lateral resolution limit of single-point interferometers for vibration measurement. Further, a compensation and an optimum numerical aperture are proposed the reduce the measurement deviation. For this, the model includes a laser-interferometer microscope of Mach-Zehnder type with Gaussian laser beams considering the Gouy effect and wavefront curvature. As a measurement scenario, an unidirectional surface acoustic wave (SAW) is regarded. The theoretic findings have been validated in the experiment with a representative vibration measurement on a SAW filter at 433,{mathrm {MHz}} with our heterodyne laser-Doppler interferometer with offset-locked semiconductor lasers. The provided formulas help instrument designers and users to choose suitable instrument parameters, especially the numerical aperture of the utilized microscope objective.

Analysis of the response of human iPSC-derived cardiomyocyte tissue to ICaL block. A combined in vitro and in silico approach

The high incidence of cardiac arrythmias underlines the need for the assessment of pharmacological therapies. In this field of drug efficacy, as in the field of drug safety highlighted by the Comprehensive in Vitro Proarrhythmia Assay initiative, new pillars for research have become crucial: firstly, the integration of in-silico experiments, and secondly the evaluation of fully integrated biological systems, such as human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). In this study, we therefore aimed to combine in-vitro experiments and in-silico simulations to evaluate the antiarrhythmic effect of L-type calcium current (ICaL) block in hiPSC-CMs. For this, hiPSC-CM preparations were cultured and an equivalent virtual tissue was modeled. Re-entry patterns of electrical activation were induced and several biomarkers were obtained before and after ICaL block. The virtual hiPSC-CM simulations were also reproduced using a tissue composed of adult ventricular cardiomyocytes (hAdultV-CMs). The analysis of phases, currents and safety factor for propagation showed an increased size of the re-entry core when ICaL was blocked as a result of depressed cellular excitability. The bigger wavefront curvature yielded reductions of 12.2%, 6.9%, and 4.2% in the frequency of the re-entry for hiPSC-CM cultures, virtual hiPSC-CM, and hAdultV-CM tissues, respectively. Furthermore, ICaL block led to a 47.8% shortening of the vulnerable window for re-entry in the virtual hiPSC-CM tissue and to re-entry vanishment in hAdultV-CM tissue. The consistent behavior between in-vitro and in-silico hiPSC-CMs and between in-silico hiPSC-CMs and hAdultV-CMs evidences that virtual hiPSC-CM tissues are suitable for assessing cardiac efficacy, as done in the present study through the analysis of ICaL block.

Laser propagation in a Rindler accelerated reference frame based on matrix optics.

The Rindler space-time describing a series of accelerating observers is Ricci flat, but it still has novel optical effects. In the case of Wenzel, Kramers, and Brillouin (WKB) approximation, we derive the light paths in the Rindler frame based on the covariant wave equation and geodesic equations. Then, we use ABCD matrix optics method to explore the propagation characteristics of Rindler frame, thus link three different optical transformation scenes (geometry, gravity, and vacuum refractive index) together. Moreover, the propagation characteristics of hollow beam in Rindler space-time are described analytically. In the longitudinal direction, we demonstrate the shift and stretch effects of the dark spot of a beam, while the transverse spot size is proved to be convergence in the accelerated system, and the wavefront curvature can tend a constant twice the acceleration at the far field. Those characteristics are quite different from the ones in the flat space-time. Based on these calculations, we simply demonstrate the position uncertain relationship between the transverse beam size and the momentum, which surprisingly coincides with the derivation of quantization. We hope that we can provide one simple method to analyze the beam propagation in the accelerated frame.

Residual high-order wavefront curvature error compensation for the polar format algorithm in widefield spotlight SAR imaging

ABSTRACT Polar format algorithm (PFA) is an efficient image formation algorithm for spotlight-mode synthetic aperture radar (SAR). However, the derivation of PFA relies upon the approximation of planar wavefront, and the resulting wavefront curvature error (WCE) causes severe SAR image degradation, e.g., distortion and defocus. The distortion stems from the first-order WCE and the defocus mainly comes from the quadratic WCE. To eliminate the defocusing effects, the existing space-variant post-filtering algorithms (SVPFAs) mainly compensate the quadratic term of WCE and ignore the residual high-order terms. Actually, the residual odd-order WCE will also broaden the main-lobe of the target and the residual even-order WCE will lead to the problem of sidelobe asymmetry. To tackle these issues, this letter proposes a modified SVPFA to correct both the quadratic and the residual high-order WCE. First, based on the derivation of PFA, the accurate expression of WCE is obtained. Second, the quadratic and residual high-order WCE are separated without complicated high-order two-dimensional Taylor expansion. Finally, the WCE is corrected by phase compensation and geometric distortion correction, respectively. The effectiveness of the proposed algorithm is verified by simulation experiments.

Theoretical properties of the autocovariance of wavefront curvature induced by atmospheric turbulence and their potential for Cn2 profiling

ABSTRACT Remote measurements of optical turbulence profiles $C_\mathrm{ \mathit{ n}}^2(h)$ in the Earth atmosphere are nowadays performed from the spatial autocovariance of either scintillation or the wavefront slope. Here, I theoretically study the properties of the spatio-angular autocovariance of the wavefront curvature induced by optical turbulence, assuming the von Kármán model for the complex amplitude fluctuations. The width of the curvature autocovariance function is approximately 10 times smaller than that of the scintillation and 1000 times smaller than that of the wavefront slope. Thus, a significant enhancement of the attainable altitude resolution of turbulence profiles is expected from the spatio-angular autocovariance of the curvature. The curvature autocovariance amplitude is proportional to $C_\mathrm{ \mathit{ n}}^2(h)$ and also depends on the turbulence altitude h and on the turbulence inner scale l0. A simple procedure disentangles those dependencies and leads to $C_\mathrm{ \mathit{ n}}^2(h)$ and also to the inner scale profile l0(h).