Wavefront Curvature Research Articles

Multitask convolutional neural network for acoustic localization of a transiting broadband source using a hydrophone array.

A multitask convolutional neural network (CNN) is trained to localize the instantaneous position of a motorboat throughout its transit past a wide aperture linear array of hydrophones located 1 m above the sea floor in water 20 m deep. A cepstrogram database for each hydrophone and a cross-correlogram database for each pair of adjacent hydrophones are compiled for multiple motorboat transits. Cepstrum-based and correlation-based feature vectors (along with ground-truth source bearing and range data) form the inputs to train three CNNs so that they can predict the instantaneous source range and bearing for other "unseen" motorboat transits. It is shown that CNNs operating on multi-sensor cepstrum-based feature maps are able to predict the instantaneous range and bearing of a transiting motorboat, even when the source is near an endfire direction. Also, multi-sensor generalised cross correlation-based feature maps are able to predict the range and bearing of a transiting motorboat in the presence of interfering multipath arrivals. When compared with the cepstrum-only CNN, cross correlation-only CNN, and the conventional model-based method of passive ranging by wavefront curvature, the combined cepstrum-cross correlation CNN is shown to provide superior source localization performance in a multipath underwater acoustic environment.

Selection of a Raman beam waist in atomic gravimetry

The laser beam waist has an impact both in the sensitivity and systematic effects present in gravimetry and atom interferometry in general. In this paper we consider how different effects contribute to both aspects in order to make a better selection of the radius of the Raman beam given a particular laser power available. A large beam waist reduces systematic effects coming from wavefront curvature and Gouy phase contributions and improves the fringe contrast due to reduced intensity gradients. On the other hand, a large waist gives a smaller Rabi frequency, which lowers the sensitivity by reducing the fraction of atoms in the selected velocity range. Considering all contributions, we find that systematic effects usually have a dominant role in selecting a beam waist.

Study on the Velocity Analysis Method of Low SNR Seismic Data

When the signal to noise ratio of seismic data is very low, velocity spectrum focusing will be poor., the velocity model obtained by conventional velocity analysis methods is not accurate enough, which results in inaccurate migration. For the low signal noise ratio (SNR) data, this paper proposes to use partial Common Reflection Surface (CRS) stack to build CRS gathers, making full use of all of the reflection information of the first Fresnel zone, and improves the signal to noise ratio of pre-stack gathers by increasing the number of folds. In consideration of the CRS parameters of the zero-offset rays emitted angle and normal wave front curvature radius are searched on zero offset profile, we use ellipse evolving stacking to improve the zero offset section quality, in order to improve the reliability of CRS parameters. After CRS gathers are obtained, we use principal component analysis (PCA) approach to do velocity analysis, which improves the noise immunity of velocity analysis. Models and actual data results demonstrate the effectiveness of this method.

LIPSS manufacturing with regularity control through laser wavefront curvature

Laser-Induced Periodic Surface Structures (LIPSS) manufacturing is a convenient laser direct-writing technique for the fabrication of nanostructures with adaptable characteristics on the surface of virtually any material. In this paper, we study the influence of 1D laser wavefront curvature on nanoripples spatial regularity, by irradiating stainless steel with a line-focused ultrafast laser beam emitting 120 fs pulses at a wavelength of 800 nm and with 1 kHz repetition rate. We find high correlation between the spatial regularity of the fabricated nanostructures and the wavefront characteristics of the laser beam, with higher regularity being found with quasi-plane-wave illumination. Our results provide insight regarding the control of LIPSS regularity, which is essential for industrial applications involving the LIPSS generation technique.

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics, we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schrödinger equation. The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method. Taking advantage of the analytical expression, we analyze the influences of various physical parameters on the breathing wave propagation, including the propagation loss and the input power on the beam width, the beam intensity, and the wavefront curvature. Also, the corresponding analytical solutions are obtained. The validity of the analysis results is verified by numerical simulation. This study provides some new insights for investigating beam propagation in lossy nonlinear media

Multi-focal Shack–Hartmann wavefront sensing with self-interference Chinese Taiji-lenslet array

Shack–Hartmann wavefront sensor (SHWS) is a traditional method of obtaining the phase information of the incident light. As a classical method, SHWS has the merit of simple structure, good usability, real-time monitoring and wide waveband. Traditional SHWS depends mainly on a lenslet array which can split the incident wavefront and produce an array of distorted foci, which reflect the change of wavefront curvature under test. Compared to the mono-focal lenslet in SHWS, here self-interference Chinese Taiji lenslet have been introduced into the wavefront sensing in order to improve the precision of the centroid position by means of multiple foci. Wavefront sensing experiments on self-interference Taiji-lenslet array with bi- and quad-foci were sequentially carried out to verify the validity of our proposed method. More foci-splitter would bring more accuracy. Taiji lens can also be designed with amplitude modulation such as Taiji sieve, which is very suitable for wavefront measurement in the region of short wavelength, especially EUV and soft X-ray.

Image-guided ray tracing and its applications

Eikonal solvers have important applications in seismic data processing and inversion, the so-called image-guided methods. To this day, in image-guided applications, the solution of the eikonal equation is implemented using partial-differential-equation solvers, such as fast-marching or fast-sweeping methods. We have found that alternatively, one can numerically integrate the dynamic Hamiltonian system defined by the image-guided eikonal equation and reconstruct the solution with image-guided rays. We evaluate interesting applications of image-guided ray tracing to seismic data processing, demonstrating the use of the resulting rays in image-guided interpolation and smoothing, well-log interpolation, image flattening, and residual-moveout picking. Some of these applications make use of properties of the ray-tracing system that are not directly obtained by eikonal solvers, such as ray position, ray density, wavefront curvature, and ray curvature. These ray properties open space for a different set of applications of the image-guided eikonal equation, beyond the original motivation of accelerating the construction of minimum distance tables. We stress that image-guided ray tracing is an embarrassingly parallel problem that makes its implementation highly efficient on massively parallel platforms. Image-guided ray tracing is advantageous for most applications involving the tracking of seismic events and imaging-guided interpolation. Our numerical experiments using synthetic and real data sets indicate the efficiency and robustness of image-guided rays for the selected applications.

Aberrations in (3+1)-dimensional Bragg diffraction using pulsed Laguerre-Gaussian laser beams

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Gaussian beam envelope, studied with (3+1)D numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular-, Gaussian-, Blackman- and hyperbolic secant pulses. For the latter, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\pi$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)D numerical simulations for pulsed Gaussian beams, as well as experimental data and find very good agreement, considering a mixture of Bose-Einstein condensate and thermal cloud.

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.

Photonic nanojet generation under converging and diverging beams

In practical applications of the photonic nanojet (PNJ), a microscope objective can be used to illuminate a microsphere. Under such conditions, it is difficult to determine the absolute position of the sphere with respect to the focal point of the incident beam. A small change in the axial position of the sphere can change the form of the incident wavefront from diverging to converging and will significantly influence the evolution of PNJ. In our paper, we report a systematic study of the PNJ properties, including the effective focal length and the full-width at half maximum (FWHM) by changing the source curvature. We treat the cases of diverging and converging wavefronts with different NAs (from 0.1 to 0.8) and sphere diameters (from 1.6 λ to 33 λ ). We demonstrate that for a diverging source curvature, the effective focal length and FWHM of the PNJ increase as a function source NA for all the sphere diameters. By further increase of the source NA, for a NA of 0.8, the PNJ can be found only for sphere diameters less than 16 λ (refractive index n = 1.5 ). At larger diameters, the microsphere behaves like a diffractive–refractive lens, collimating the light and showing aberrations. For the converging source, the effective focal length and FWHM tend to decrease as a function of source NA, the PNJ localizing inside the sphere for N A > 0.2 . Also, the PNJ shows similar behavior with respect to the NA of a converging source and sphere refractive index under plane wave illumination. Finally, we compare our theoretical 2D simulation results with 3D sphere geometries for diameters of 1.6 λ and 8.3 λ ; we find similar behavior for converging and diverging source wavefront curvatures.

On the validity of the planar wave approximation to compute synthetic seismograms of teleseismic body waves in a 3-D regional model

SUMMARYInjection methods are a very efficient means to compute synthetic seismograms of short-period teleseismic body waves in 3-D regional models. The principle is to inject an incident teleseismic wavefield inside a regional 3-D Cartesian spectral-element grid. We have developed an opern-source package that allows us to inject either an incident plane wave, computed with a frequency–wavenumber method, or the complete wavefield, computed in a spherically symmetric reference earth model with AxiSEM. The computations inside the regional spectral-element grid are performed with SPECFEM3D_Cartesian. We compare the efficiency and reliability of the two injection methods for teleseismic P waves, considering a wide range of epicentral distance and hypocentral depths. Our simulations demonstrate that in practice the effects of wave front and Earth curvature are negligible for moderate size regional domains (several hundreds of kilometres) and for periods larger than 2 s. The main differences observed in synthetic seismograms are related to secondary phases that have a different slowness from the one of the reference P phase.

Quasioptical System for Corneal Sensing at 220–330 GHz: Design, Evaluation, and Ex Vivo Cornea Parameter Extraction

The design, simulation, and characterization of a quasioptical system for submillimeter-wave quantification of corneal thickness and water content are presented. The optics operate in the 220-330 GHz band and are comprised of two, custom aspheric, biconvex lenses in a Gaussian beam telescope configuration. The design produces broadband wavefront curvature matching to 7.5 mm radius of curvature target surfaces thus emulating a plane-wave-on-planar-media condition and enabling application of stratified medium theory to data analysis. Aspheric lens coefficients were optimized with geometric ray tracing subject to optical path length penalties and physical-optics simulations showed aspheric designs achieved wavefront coupling to spherical surfaces, superior to equivalent, canonical hyperbolic lenses. The fabricated lens system was characterized in a planar near-field scanner system and demonstrated good agreement to physical-optics simulations. An average central corneal thickness of 652 μm and free water content volume of 47% were extracted from ex vivo sheep corneas via complex s-parameters and agree with literature values. Extracted contact lens thickness and water content agreed with independently validated values. Moreover, the quasioptical system enabled observation of dynamic changes in artificial tear-film, thickness, and water content. This work elucidates two major findings related to submillimeter-wave wavefront matching on spherical surfaces, with wavelength order radii of curvature: 1) An asphere whose sag coefficients are optimized via field phase variation on a spherical surface produces coupling superior to a plano-hyperbolic lens. 2) For most feasible apertures, the Gaussian beam waist is located in the aperture near field, suggesting consideration for operating in the beam near field.

Generalized matrix transformation formalism for reflection and transmission of complex optical waves at a plane dielectric interface.

We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the incident constituent plane-wave fields to obtain the reflected and transmitted fields. This formalism, though physically equivalent to Fresnel formalism, has greater mathematical elegance and computational efficiency as compared to the latter. We utilize exact 3D electric-field expressions, which enable us to seamlessly analyze waves of miscellaneous wavefront shapes and properties using the single formalism, along with appropriately retaining the geometric phase and wavefront curvature information. We demonstrate our formalism by obtaining and analyzing the reflected and transmitted fields in a simulated Gaussian beam model.

Spatial self-phase modulation of a Gaussian beam transmitted through a ferrofluid

We report on the experimental observation of the diffraction pattern formed in the far-field region when a high-power continuous-wave laser convergent or divergent Gaussian beam passes through a cuvette with ferrofluid. Two different types of diffraction rings with opposite light-intensity distribution are shown in the far field. The difference between the diffractive patterns is attributed to the interaction of the strong spatial self-phase modulation caused by the refractive index change of the medium with wavefront curvature of the input Gaussian beam. The observed behavior of the diffraction pattern dynamics is interpreted theoretically based on the Fresnel-Kirchhoff integral. The negative polarity of nonlinear refraction can be identified by the central interference profiles and the diffraction pattern. At the same time, the self-defocusing phenomena of the ferrofluid can be determined by the type of pattern. The nonlinear refraction coefficients of the ferrofluid were estimated to be ∼-2.89×10-5cm2/W (convergent Gaussian beam) and ∼-3.53×10-5cm2/W (divergent Gaussian beam). In addition, the corresponding third-order nonlinear optical susceptibility of the sample was also estimated as ∼1.43×10-5esu and ∼1.75×10-5esu, respectively. The experimental results imply a novel potential application of ferrofluid in nonlinear phase modulation devices.

Laser planar trapping

We investigate the phenomenon of the transverse breaking of symmetry of Gaussian lasers transmitted through dielectrics, showing for which incidence conditions and beam parameters it can be observed in optical experiments. The numerical analysis, done by using the integral form of the transmitted beam at the lower interface of a dielectric prism, shows, for incidence approaching the critical region, a laser planar trapping. By using an analytic approximation for the intensity of lower transmitted beam, we model the wave front curvature by a closed expression which depends on the refractive index, on the geometrical properties of the dielectric block, and, finally, on the incidence angle of the incoming beam. The analytic formula shows an excellent agreement with the numerical analysis and it could be useful in future experimental implementations.

Ranolazine-Mediated Attenuation of Mechanoelectric Feedback in Atrial Myocyte Monolayers.

BackgroundMechanical stretch increases Na+ inflow into myocytes, related to mechanisms including stretch-activated channels or Na+/H+ exchanger activation, involving Ca2+ increase that leads to changes in electrophysiological properties favoring arrhythmia induction. Ranolazine is an antianginal drug with confirmed beneficial effects against cardiac arrhythmias associated with the augmentation of INaL current and Ca2+ overload.ObjectiveThis study investigates the effects of mechanical stretch on activation patterns in atrial cell monolayers and its pharmacological response to ranolazine.MethodsConfluent HL-1 cells were cultured in silicone membrane plates and were stretched to 110% of original length. The characteristics of in vitro fibrillation (dominant frequency, regularity index, density of phase singularities, rotor meandering, and rotor curvature) were analyzed using optical mapping in order to study the mechanoelectric response to stretch under control conditions and ranolazine action.ResultsHL-1 cell stretch increased fibrillatory dominant frequency (3.65 ± 0.69 vs. 4.35 ± 0.74 Hz, p < 0.01) and activation complexity (1.97 ± 0.45 vs. 2.66 ± 0.58 PS/cm2, p < 0.01) under control conditions. These effects were related to stretch-induced changes affecting the reentrant patterns, comprising a decrease in rotor meandering (0.72 ± 0.12 vs. 0.62 ± 0.12 cm/s, p < 0.001) and an increase in wavefront curvature (4.90 ± 0.42 vs. 5.68 ± 0.40 rad/cm, p < 0.001). Ranolazine reduced stretch-induced effects, attenuating the activation rate increment (12.8% vs. 19.7%, p < 0.01) and maintaining activation complexity—both parameters being lower during stretch than under control conditions. Moreover, under baseline conditions, ranolazine slowed and regularized the activation patterns (3.04 ± 0.61 vs. 3.65 ± 0.69 Hz, p < 0.01).ConclusionRanolazine attenuates the modifications of activation patterns induced by mechanical stretch in atrial myocyte monolayers.

Propagation dynamics of tripole breathers in nonlocal nonlinear media

We demonstrate the propagation dynamics of optical breathers in nonlinear media with a spatial nonlocality, which is governed by the nonlocal nonlinear Schrodinger equation, by employing the variational approach. Taking a tripole breather as an example, the approximate analytical solution is obtained and the physical propagation properties, such as the evolution of the critical power, the spot size, the wavefront curvature, and the intensity distribution of the breather, have been discussed in detail. The physical reasons for the evolution of the tripole breathers are analyzed by borrowing the ideas from Newtonian mechanics. It is found that the analytical results obtained by the variational approach agree well with the numerical results of the nonlocal Schrodinger equation for the strong nonlocal case, especially when the incident power approaches the critical power.

New estimation of the curvature effect for the X-ray vacuum diffraction induced by an intense laser field

Abstract Quantum electrodynamics predicts X-ray diffractions under a high-intensity laser field via virtual charged particles, and this phenomenon is called vacuum diffraction (VD). In this paper, we derive a new formula to describe VD in a head-on collision geometry of an X-ray free-electron laser (XFEL) pulse and a laser pulse. The wavefront curvature of the XFEL pulse is newly considered in this formula. With this formula, we also discuss the curvature effect on VD signals based on realistic parameters at the SACLA XFEL facility.

Propagation properties of quadrupole breather in nonlinear media with a nonlocal exponential-decay response

We investigate the propagation properties of quadrupole breather in nonlinear media with a nonlocal exponential-decay response by using the variational method and the equivalent particle method. The analytical solution of the quadrupole breather is obtained. The breather beamwidth, the wavefront curvature, the intensity pattern, and the comparisons between the analytical quadrupole breather solution and the numerical simulations of the nonlocal nonlinear Schrödinger equation in the case of highly nonlocal nonlinearity are analyzed. The results show that the analytical solution is in good agreement with the numerical simulations at near-critical power incidence. Furthermore, we find that the envelope of the difference value curve between the analytical solution and the numerical simulation can be described as a logarithmic function under different input powers. It is useful for further understanding the propagation properties of optical breathers in nonlocal nonlinear media and might be of interest to the applications in error analysis and precision measurements.

Zernike coefficients from wavefront curvature data.

The concept of curvature sensing is reviewed, and a comprehensive derivation of the curvature polynomials is given, whose inner products with the wavefront curvature data yield the Zernike aberration coefficients of an aberrated circular wavefront. The data consist of the Laplacian of the wavefront across its interior and its outward normal slope at its circular boundary. However, we show that the radial part of the curvature polynomials and their slopes at the boundary of the wavefront have a value of zero, except when the angular frequency of the corresponding Zernike polynomial is equal to its radial degree. As a result, the effect of noise on the corresponding Zernike coefficients is lower because the noisy data at the boundary of the wavefront is not used to determine their values. The use of the curvature polynomials to determine the Zernike coefficients is demonstrated with simulated noisy curvature data of an aberration function consisting of 10 Zernike coefficients, namely defocus, primary, secondary, and tertiary astigmatism, coma, and spherical aberrations.