Wavefront Curvature Effects Research Articles

Curvature-mediated source and sink effects on the genesis of premature ventricular complexes in long QT syndrome.

Premature ventricular complexes (PVCs) are spontaneous excitations occurring in the ventricles of the heart that are associated with ventricular arrhythmias and sudden cardiac death. Under long QT conditions, PVCs can be mediated by repolarization gradient (RG) and early afterdepolarizations (EADs), yet the effects of heterogeneities or geometry of the RG or EAD regions on PVC genesis remain incompletely understood. In this study, we use computer simulation to systematically investigate the effects of the curvature of the RG border region on PVC genesis under long QT conditions. We show that PVCs can be either promoted or suppressed by negative or positive RG border curvature depending on the source and sink conditions. When the origin of oscillation is in the source region and the source is too strong, a positive RG border curvature can promote PVCs by causing the source area to oscillate. When the origin of oscillation is in the sink region, a negative RG border curvature can promote PVCs by causing the sink area to oscillate. Furthermore, EAD-mediated PVCs are also promoted by negative border curvature. We also investigate the effects of wavefront curvature and show that PVCs are promoted by convex but suppressed by concave wavefronts; however, the effect of wavefront curvature is much smaller than that of RG border curvature. In conclusion, besides the increase of RG and occurrence of EADs caused by QT prolongation, the geometry of the RG border plays important roles in PVC genesis, which can greatly increase the risk of arrhythmias in cardiac diseases.NEW & NOTEWORTHY The effects of the curvature or geometry of the repolarization gradient region and wavefront curvature on the genesis of premature ventricular complexes are systematically investigated using computer modeling and simulation. Premature ventricular complexes can be promoted by either positive or negative curvature of the gradient region depending on the source and sink conditions. The underlying mechanisms of the curvature effects are revealed, which provides mechanistic insights into arrhythmogenesis in cardiac diseases.

Complex far fields and optical singularities due to propagation beyond tight focusing: combined effects of wavefront curvature and aperture diffraction

All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the interface or scatterer particle under consideration, and the other is the diffraction caused by the finite lens aperture. In the present paper we explore these phenomena in detail by considering a rigorous simulated model and an appropriate experimental setup. We hence demonstrate the complicated intensity profiles and optical singularity characteristics of the observed far field. Then we describe ways to minimize these deviations in a general experiment. But more importantly, our analysis proves that these deviations by themselves are significant optical phenomena of fundamental interest. The observed complex field profiles have similarities to standard diffraction-limited tight focal fields, though our field detection is different from the standard schemes. This indicates the relevance of these complex fields to a larger class of systems involving wavefront curvature and aperture diffraction. The detailed analysis and results of the present paper already serve as core explorations of these optical phenomena; and we also suggest future research directions where these system aspects can be purposefully created and explored further.

Two-stage Correction for Wavefront Curvature Effects of PFA in Focusing Non-ideal Circular SAR Data

Two-stage Correction for Wavefront Curvature Effects of PFA in Focusing Non-ideal Circular SAR Data

Evolution and dynamics of spatial self-phase modulation in pyrromethene 567 for all-optical photonic diode applications

Spatial self-phase modulation has emerged as a novel and ubiquitous nonlinear optical effect, revealing potential application in all-optical devices for signal processing. The work investigates the evolution and dynamics of SSPM patterns in pyrromethene 567 (PM 567). A temperature-dependent refractive index gradient which induces a phase shift in the incident beam is responsible for the formation of spatial self-phase modulation. The non-linear response of PM 567 in different solvents and concentrations is investigated and tabulated. The effect of wavefront curvature, path length, and mechanical chopper on the formation of the SSPM patterns was studied. To our knowledge, an optical-diode-based unidirectional generation of spatial self-phase modulation in dyes has been reported for the first time. Simply cascading PM 567 dissolved in DMSO and Methanol having distinct nonlinear optical responses, an all-optical diode for unidirectional light propagation based on spatial self-phase modulation in PM 567 was achieved. The work reveals the potential application of PM 567 for achieving spatial asymmetry in light propagation based on SSPM in photonic devices for all-optical signal processing.

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy.

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust. Soc. Am. 150, 2566 (2021)] is extended to include leading order effects of wavefront curvature by assuming that the motion is quasiplanar, which is consistent with other paraxial model equations in nonlinear acoustics. The material is modeled using a general expansion of the strain energy density to fourth order in strain that comprises thirteen terms defining the elastic moduli. Equations of motion for the transverse displacement components are obtained using Hamilton's principle. The coupled equations of motion describe diffraction, anisotropy of the wave speeds, quadratic and cubic plane wave nonlinearity, and quadratic nonlinearity associated with wavefront curvature. Two illustrative special cases are investigated. Spatially varying shear vertical wave motion in the fiber direction excites a quadratic nonlinear interaction unique to transversely isotropic soft solids that results in axial second harmonic motion with longitudinal polarization. Shear horizontal wave motion in the fiber plane reveals effects of anisotropy on third harmonic generation, such as beam steering and dependence of harmonic generation efficiency on the propagation and fiber directions.

Wavefront curvature restoration by a sensor based on the Talbot phenomenon under Gaussian illumination.

The present paper deals with the accuracy of wavefront curvature restoration based on pit displacement measurements in a Talbot wavefront sensor under Gaussian illumination conditions. The measurement possibilities of the Talbot wavefront sensor are theoretically investigated. A theoretical model based on the Fresnel regime is used to determine the intensity distribution in the near field, and the effect of the Gaussian field is described in terms of the spatial spectrum of the grating image. The effect of wavefront curvature on the measurement error of the Talbot sensor is discussed-particularly, the measurement of wavefront curvature is investigated.

A Modified Space-Variant Phase Filtering Algorithm of PFA for Bistatic SAR

Wavefront curvature effects grow worse in spotlight Bistatic synthetic aperture radar (BSAR) imagery when reconstructed via polar format algorithm (PFA) under the large-scale scene. The wavefront curvature error, which causes geometric distortion and defocuses to the image, is induced by the faulty hypothesis of the planar wavefront. Due to the approximated or unsegmented wavefront curvature error, conventional compensation algorithms experience different degrees of performance restriction. In this letter, the geometric distortion error and the intact defocus error are separated and analyzed for the first time. Based on the separated phase error model, a modified space-variant post-filtering (MSVPF) algorithm is proposed to correct the wavefront curvature effects of the PFA image. Two major contributions of this algorithm are as follows. First, as no high-order term is ignored in the constructed space-variant filter, the proposed algorithm can compensate for the defocus error with any order. Second, MSVPF employs a separate strategy to correct the space-variant defocus and geometric distortion, which avoids high overlap rate in subimage processing and maintains the computational efficiency of the original SVPF. The effectiveness of the proposed algorithm is demonstrated by numerical simulations.

Sediment sound speed dispersion inferences from broadband reflection coefficient measurements

The frequency dependence, or dispersion, of sound speed in marine sediments has been a topic of considerable interest and remains a research topic. While experiments on well-sorted sediments (having a narrow range of grain sizes) show promising concordance with theory, the more typical continental shelf sediments exhibit a rather wide range of grain sizes. A major experimental challenge is to measure in-situ sound speed over a sufficiently wide frequency range, such that the underlying mechanisms (e.g., viscous or friction) that control intrinsic dispersion can be isolated. Broadband 1.8-10 kHz seabed reflection measurements in the TREX13 experiment show a critical angle that is very nearly frequency independent. When effects of wavefront curvature, sound speed gradients, layering, and roughness are taken into account, this observation indicates that sediment sound speed must also be nearly independent of frequency. [Research supported by the ONR Ocean Acoustics Program.]

Probing interferometric parallax with interplanetary spacecraft

We describe an experimental scenario for testing a novel method to measure distance and proper motion of astronomical sources. The method is based on multi-epoch observations of amplitude or intensity correlations between separate receiving systems. This technique is called Interferometric Parallax, and efficiently exploits phase information that has traditionally been overlooked. The test case we discuss combines amplitude correlations of signals from deep space interplanetary spacecraft with those from distant galactic and extragalactic radio sources with the goal of estimating the interplanetary spacecraft distance. Interferometric parallax relies on the detection of wavefront curvature effects in signals collected by pairs of separate receiving systems. The method shows promising potentialities over current techniques when the target is unresolved from the background reference sources. Developments in this field might lead to the construction of an independent, geometrical cosmic distance ladder using a dedicated project and future generation instruments. We present a conceptual overview supported by numerical estimates of its performances applied to a spacecraft orbiting the Solar System. Simulations support the feasibility of measurements with a simple and time-saving observational scheme using current facilities.

The effect of interface curvature on AVO inversion of near-critical and postcritical PP-reflections

Widely exploited in the industry, amplitude-variation-with-offset (AVO) inversion techniques are based on weak-contrast approximations of the plane-wave reflection coefficients. These approximations are valid for plane waves reflected at almost flat interfaces with weak contrasts in seismic parameters and for reflection angles below the critical angle. Regardless of the underlying assumptions, linearized coefficients provide a simple and physically adequate tool to accurately invert AVO data for seismic parameters at precritical angles. However, the accuracy of linearized coefficients drastically decreases with increasing incidence angle. Limitations occur around and beyond the critical ray, where the effect of wavefront curvature becomes prominent and thus can no more be neglected. The effective reflection coefficients generalize the plane-wave reflection coefficients for waves generated by point sources and reflected at curved interfaces. They account for the wavefront curvature and are adequate at any incidence angle. Our previous studies have shown that including the reflections around and beyond the critical angle in the AVO inversion significantly improves the accuracy of estimated parameters. However, the interface curvature also must have its contribution to the long-offset AVO inversion. We find that the interface curvature affects the energy propagation along the ray tube and the energy diffusion across the ray tube. The energy propagation along the tube is characterized by the geometrical spreading, which is strongly affected by interface curvature. The transverse diffusion is captured by the effective reflection coefficients which are less influenced by interface curvature. The long-offset AVO inversion is thus sensitive to interface curvature through a combination of several wave propagation factors.

Polar Format Algorithm Wavefront Curvature Compensation Under Arbitrary Radar Flight Path

An improved space-variant postfiltering approach to compensate for the wavefront curvature effect in polar format imagery is presented in this letter. The main contribution of this new method is the construction of a space-variant filter, which is based on exploiting the endomorphism property of the polar format transformation. The new approach provides an accurate and general solution to wavefront curvature compensation under arbitrary radar flight path. Finally, point target simulation has validated the effectiveness of the new approach.

Space-Variant Filtering for Wavefront Curvature Correction in Polar Formatted Bistatic SAR Image

An analytical expression of the phase error from wavefront curvature in bistatic spotlight-mode synthetic aperture radar (SAR) image reconstructed via polar format algorithm (PFA) is derived in this paper. The wavefront curvature effect, which arises from the unrealistic planar wavefront assumption in bistatic PFA, induces phase error terms resulting in space-variant geometry distortion and defocusing. Based on the analytical expression of the wavefront curvature error, a space-variant filtering approach is applied to compensate for it in the polar formatted bistatic SAR image. Analysis on the scene size limit after using the correction method indicates that the derived space-variant filter is capable of extending the focused scene size of bistatic PFA considerably. Point target (PT) simulation validates the approach.

Pulsar timing array observations of gravitational wave source timing parallax

Pulsar timing arrays act to detect gravitational waves by observing the small, correlated effect the waves have on pulse arrival times at Earth. This effect has conventionally been evaluated assuming the gravitational wave phasefronts are planar across the array, an assumption that is valid only for sources at distances $R\gg2\pi{}L^2/\lambda$, where $L$ is physical extent of the array and $\lambda$ the radiation wavelength. In the case of pulsar timing arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and $\lambda$ is of order pc. Correspondingly, for point gravitational wave sources closer than $\sim100$~Mpc the PTA response is sensitive to the source parallax across the pulsar-Earth baseline. Here we evaluate the PTA response to gravitational wave point sources including the important wavefront curvature effects. Taking the wavefront curvature into account the relative amplitude and phase of the timing residuals associated with a collection of pulsars allows us to measure the distance to, and sky position of, the source.

Beam transit effects in single molecule coherent diffraction

We explore how phase and amplitude gradients, which are almost inevitable in a coherent illumination probe, affect the atomic reconstruction of an isolated molecule based on diffraction intensities. By modeling the probe as a defocused Gaussian source, we show that structural distortion can be introduced in the reconstructed object if plane-wave illumination is assumed in the diffraction phase-retrieval algorithm. For the plane-wave approximation, we conclude that the standard deviation ${\ensuremath{\sigma}}_{d}$ describing the source width should be such that ${\ensuremath{\sigma}}_{d}\ensuremath{\sim}10{R}_{c}$, where ${R}_{c}$ is the nominal radius of the molecule. In a pulsed source, where diffraction data are obtained when the moving molecule is at an instantaneous location within the illumination window, the effects of wave front curvature can be reduced by defocusing the illumination. This improvement comes at the expense of a weaker diffraction signal. For the three-dimensional reconstruction of a molecule, diffraction patterns from many different orientations of identical molecules are required. Since phase-retrieval methods are inherently solving for the probe plus the molecule, irreproducibility of wave front curvature or molecule location within the probe will introduce additional degrees of freedom to the structure solution problem.

Experimental verification of spherical-wave effect on the AVO response and implications for three-term inversion

Spherical-wave offset-dependent reflectivity is investigated by measuring ultrasonic reflection amplitudes from a water/Plexiglas interface. The experimental results show substantial deviation of the measured amplitudes from the plane-wave reflection coefficients at large angles. However, full-wave numerical simulations of the point source reflection response using the reflectivity algorithm show excellent agreement with the measurements, demonstrating that the deviation from the plane-wave response is caused by the wavefront curvature. To analyze the effect of wavefront curvature on elastic inversion, we simulate the spherical-wave reflectivity at different frequencies and invert for elastic parameters by least-square fitting of the plane-wave (Zoeppritz) solution. The results show that the two-parameter inversion based on the intercept and gradient is robust, although estimation of three parameters ([Formula: see text], [Formula: see text], and density) that use the curvature of the offset variation with angle (AVA) response is prone to substantial frequency-dependent errors. We propose an alternative approach to parameter estimation, one that uses critical angles estimated from AVA curves (instead of the AVA curvature). This approach shows a significant improvement in the estimation of elastic parameters, and it could be applied to class 1 AVO responses.

Numerical study of glare spot phase Doppler anemometry

The phase Doppler anemometry has (PDA) been developed to measure simultaneously the velocity and the size of droplets. When the concentration of particles is high, tightly focused beams must be used, as in the dual burst PDA. The latter permits an access to the refractive index of the particle, but the effect of wave front curvature of the incident beams becomes evident. In this paper, we introduce a glare spot phase Doppler anemometry which uses two large beams. The images of the particle formed by the reflected and refracted light, known as glare spots, are separated in space. When a particle passes through the probe volume, the two parts in a signal obtained by a detector in forward direction are then separated in time. If two detectors are used the phase differences and the intensity ratios between two signals, the distance between the reflected and refracted spots can be obtained. These measured values provide information about the particle diameter and its refractive index, as well as its two velocity components. This paper is devoted to the numerical study of such a configuration with two theoretical models: geometrical optics and rigorous electromagnetism solution.

Numerical simulation of speckle noise in laser vibrometry

The fundamental mechanism by which speckle noise is generated in laser vibrometry before describing a new numerical simulation for prediction of speckle noise level in a real measurement is considered. Factors within the simulation include rate of change of phase within individual speckle transitions, low-pass filtering to match the frequency range of experimental data with which comparison is to be made, a track-and-hold facility for periods of low signal amplitude, and wavefront curvature effects. The simulation data provide real insight into the phase and amplitude modulation of the Doppler signal, and good agreement is found in the final comparison with experimental data from a measurement on a rotating target.

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.

Contact fluorescence imaging of reentry in monolayers of cultured neonatal rat ventricular myocytes.

We present a novel contact fluorescence imaging (CFI) approach to monitor transmembrane potentials in monolayers of cultured neonatal rat ventricular cells. We apply CFI to demonstrate, for the first time, long-term recordings as well as electrical induction and termination of reentrant activity in this in vitro model. CFI was performed in confluent cell monolayers stained with di-8-ANEPPS. An anatomic obstacle (6 x 0.5 mm) was created in the center of the monolayers. Reentry was induced with a premature stimulus after pacing at 2 Hz (both via field stimulation). Seven sustained (>3 min) reentrant episodes, anchored to the anatomic obstacle, were observed in three monolayers. Field stimulation (30 V/cm) was applied to successfully terminate 6 of the 7 reentries. Analysis of reentrant activity showed similarities with anatomic reentry in tissue preparations, such as reduced conduction velocity around the core, variable conduction velocity along the reentrant pathway due to wavefront curvature effects, and field-induced activation at the obstacle borders leading to reentry termination (cardioversion). This study demonstrates the feasibility of CFI for macroscopic optical mapping of transmembrane potentials in a single layer of cultured cells. Our results suggest that the monolayer cell culture model is an attractive complement to tissue models of reentry and cardioversion.

Location and profile of phase conjugate image with gaussian beam pumping

AbstractWhen applying phase conjugate waves to various types of image processing, the characteristics of the wavefront, generated by the nonlinear optical medium, are an important research problem. The characteristics of a phase conjugate mirror with plane wave pumping have been investigated in previous research. To perform more realistic analysis, we derive equations describing the image location of the phase conjugate mirror with fundamental mode Gaussian beams as the pumping light and calculate the phase conjugate images numerically. The relationship between the probe light and the phase conjugate image using the Fresnel diffraction formula will be formulated first. Then the image location and the image magnification factor in consideration of the wave‐front curvature of the pump light is derived. Then the characteristics of the image location are analyzed considering the change of the curvature radius of the Gaussian beam in the thickness direction of the nonlinear optical medium. The image profile of the phase conjugate mirror is found by numerical calculation. The results show for the first time the effects of wavefront curvature of the pump light on the image reconstruction capability, which is an important characteristic of the phase conjugate mirror.