Seismic ray-tracing calculation based on parabolic travel-time interpolation

A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.

Accuracy of optimized Sirius ray-tracing method in intraocular lens power calculation

AIM:To evaluate the accuracy and predictability of ray tracing-assisted intraocular lens(IOL) calculation function in Sirius internal software and further improve the accuracy by optimizing the calculation of predicted lens position(PLP).METHODS:This retrospective study recruited 52 eyes of 49 patients.All of the cases with cataract had undergone phacoemulsification combined with IOL implantation.SRK-T,Haigis formula,and Sirius ray-tracing method were all used for each eye’s IOL calculation.The mean absolute value of prediction error(prediction error=predicted refraction-postoperative refraction) was defined as mean absolute prediction error(MAPE) and was determined for each method.Calculation of PLP was optimized by effective lens position(ELP).Optimized PLP was entered to Sirius internal software again to verify whether the method was improved.RESULTS:Compared with SRK-T and Haigis formulas,less accuracy was shown in Sirius ray-tracing method(P=0.001).The ELP of the IOL moved forward compared to PLP(P<0.001).The MAPE of the ELP-inputted Sirius ray-tracing method was reduced.ELP and PLP were well correlated.Taking ELP as y and PLP given by Sirius soft as x,a linear regression formula y=0.1637 x+3.1741 was concluded(R^(2)=0.1066,P=0.018).It was shown that the optimized Sirius ray-tracing method(optimized PLP entered),compared with SRK-T and Haigis formulas,worked with the same accuracy(P=0.038).CONCLUSION:The original Sirius ray tracing method is not satisfactory enough.However,in normal eyes,the optimized Sirius ray-tracing method in IOL calculation was as accurate as SRK-T and Haigis formulas.

Fast algorithm and numerical simulation for ray-tracing in 3D structure

Beginning with the method of whole path iterative ray-tracing and according to the positive definiteness of the coefficient matrix of the systems of linear equations, a symmetry olock tridiagonal matrix was decomposed into the product of block bidiagonal triangular matrix and its transpose by means of Cholesky decomposition. Then an algorithm for solving systems of block bidiagonal triangular linear equations was given, which is not necessary to treat with the zero elements out of banded systems. A fast algorithm for solving the systems of symmetry block tridiagonal linear equations was deduced, which can quicken the speed of ray-tracing. Finally, the simulation based on this algorithm for ray-tracing in three dimensional media was carried out. Meanwhile, the segmentally-iterative ray-tracing method and banded method for solving the systems of block tridiagonal linear equations were compared in the same model mentioned above. The convergence condition was assumed that the L-2 norm summation for mk, 1 and mk. 2 in the whole ray path was limited in 10-6. And the calculating speeds of these methods were compared. The results show that the calculating speed of this algorithm is faster than that of conventional method and the calculated results are accurate enough. In addition, its precision can be controlled according to the requirement of ray-tracing.

Three-dimensional ray-tracing simulation of fast magnetoacoustic waves in a stratified solar atmosphere

In the solar atmosphere, there exist two frequently-observed phenomena, Moreton waves and EIT(extreme-ultraviolet imaging telescope) waves, whose physical nature is still under debate. In this work, we perform a three-dimensional ray-tracing simulation for the propagation of fast magnetoacoustic waves. We build a stratified solar atmosphere model and take partial ionization into consideration to give an exact description of chromosphere and transition region. The calculated result is compared with a flare event observation in which both Moreton waves and EIT waves were present. In agreement with observations, the calculated wavefront show different kinematical characteristics in different propagation directions during different times.Moreton waves and EIT waves have higher propagation speeds near the active region where the magnetic field strength is strong. The result suggests that both Moreton waves and EIT waves of this event can be interpreted as the fast magnetoacoustic waves propagating at different heights in the solar atmosphere.

Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method

The internal quantum efficiency（IQE） of the light-emitting diodes can be calculated by the ratio of the external quantum efficiency（EQE） and the light extraction efficiency（LEE）.The EQE can be measured experimentally,but the LEE is difficult to calculate due to the complicated LED structures.In this work,a model was established to calculate the LEE by combining the transfer matrix formalism and an in-plane ray tracing method.With the calculated LEE,the IQE was determined and made a good agreement with that obtained by the ABC model and temperature-dependent photoluminescence method.The proposed method makes the determination of the IQE more practical and conventional.

M3SC:A Generic Dataset for Mixed Multi-Modal(MMM)Sensing and Communication Integration

The sixth generation(6G)of mobile communication system is witnessing a new paradigm shift,i.e.,integrated sensing-communication system.A comprehensive dataset is a prerequisite for 6G integrated sensing-communication research.This paper develops a novel simulation dataset,named M3SC,for mixed multi-modal(MMM)sensing-communication integration,and the generation framework of the M3SC dataset is further given.To obtain multimodal sensory data in physical space and communication data in electromagnetic space,we utilize Air-Sim and WaveFarer to collect multi-modal sensory data and exploit Wireless InSite to collect communication data.Furthermore,the in-depth integration and precise alignment of AirSim,WaveFarer,andWireless InSite are achieved.The M3SC dataset covers various weather conditions,multiplex frequency bands,and different times of the day.Currently,the M3SC dataset contains 1500 snapshots,including 80 RGB images,160 depth maps,80 LiDAR point clouds,256 sets of mmWave waveforms with 8 radar point clouds,and 72 channel impulse response(CIR)matrices per snapshot,thus totaling 120,000 RGB images,240,000 depth maps,120,000 LiDAR point clouds,384,000 sets of mmWave waveforms with 12,000 radar point clouds,and 108,000 CIR matrices.The data processing result presents the multi-modal sensory information and communication channel statistical properties.Finally,the MMM sensing-communication application,which can be supported by the M3SC dataset,is discussed.

A Rigorous Analysis of Vehicle-to-Vehicle Range Performance in a Rural Channel Propagation Scenario as a Function of Antenna Type and Location via Simulation and Field Trails

Vehicle-to-Everything(V2X) communications will be an essential part of the technology in future autonomous drive decision systems.A fundamental procedure is to establish a robust communication channel between end-to-end devices.Due to the antenna placed at different positions on vehicles,the existing cellular electro-magnetic(EM) wave propagation modelling does not fit properly for V2X direct communication application.In order to figure out a feasible understanding of this problem,this paper focuses on the propagation channel analysis in a rural Vehicle-to-Vehicle(V2V) scenario for vehicular communication with antenna position experiments at different heights.By adopting the ray-tracing algorithm,a rural scenario simulation model is built up via the use of a commercial-off-the-shelf(COTS) EM modelling software package,that computes the path loss received power and delay spread for a given propagation channel.Next,a real-world vehicle measurement campaign was performed to verify the simulation results.The simulated and measured receiver power was in good agreement with each other,and the results of this study considered two antenna types located at three different relative heights between the two vehicles.This research provides constructive guidance for the V2V antenna characteristics,antenna placement and vehicle communication channel analysis.

In uence of Particle Size on Laser Absorption and Scanning Track Formation Mechanisms of Pure Tungsten Powder During Selective Laser Melting

A three-dimensional laser absorption model based on ray tracing was established to describe the coupled interaction of a laser beam with particles in the powder layers of pure tungsten(W)material processed by selective laser melting(SLM).The influence of particle size on the powder-to-laser absorptivity and underlying absorption behavior was investigated.An intrinsic relationship between the absorption,distribution of absorbed irradiance within the powder layers,and surface morphology and geometric characteristics(e.g.,contact angle,width and height of tracks,and remelted depth)of the laser scanning tracks is presented here.Simulation conclusions indicate that the absorptivity of the powder layers considerably exceeds the single powder particle value or the dense solid material value.With an increase in particle size,the powder layer absorbs less laser energy.The maximum absorptivity of theWpowder layers reached 0.6030 at the particle size of 5 lm.The distribution of laser irradiance on the particle surface was sensitive to particle size,azimuthal angle,and the position of the powder particles on the substrate.The maximum irradiance in the powder layers decreased from 1.117×10^–3 to 0.85×10^–3W·μm^-2 and the contour of the irradiance distribution in the center of the irradiated area gradually contracted when the particle size increased from 5 to 45 lm.An experimental study on the surface morphologies and cross-sectional geometric characteristics of SLM-fabricated W material was performed,and the experimental results validated the mechanisms of the powder-to-laser-absorption behavior that were obtained in simulations.This work provides a scientific basis for the application of the ray-tracing model to predict the wetting and spreading ability of melted tracks during SLM additive manufacturing in order to yield a sound laser processability.

Implementation Framework and Validation of Cluster-Nuclei Based Channel Model Using Environmental Mapping for 6G Communication Systems

With the research of the upcoming sixth generation(6 G) systems, new technologies will require wider bandwidth, larger scale antenna arrays and more diverse wireless communication scenarios on the future channel modeling. Considering channel model is prerequisite for system design and performance evaluation of 6 G technologies, we face a challenging task: how to accurately and efficiently model 6 G channel for various scenarios? This paper tries to answer it. Firstly, the features of cluster-nuclei(CN) and principle of cluster-nuclei based channel model(CNCM) are introduced. Then, a novel modeling framework is proposed to implement CNCM,which consists four steps: propagation environment reconstruction, cluster-nuclei identification, multipath parameters generation, and channel coefficients generation. Three-dimensional environment with material information is utilized to map CN with scatterers in the propagation pathway. CN are identified by geometrical and electric field calculation based on environmental mapping, and multipath components within CN are calculated by statistical characteristics of angle, power and delay domains. Finally, we present a three-level verification structure to investigate the accuracy and complexity of channel modeling comprehensively. Simulation results reveal that CNCM can perform higher accuracy than geometrybased stochastic model while lower complexity compared with ray-tracing model for practical propagation environment.

Geometric Theory for the Design of Multielement Optical Systems

To establish a theoretical basis for providing a better design method of multielement optical systems, we have developed a third-order geometric theory of a plane-symmetric multielement optical system that consists of a planar light source, an arbitrary number of ellipsoidal gratings, and an image plane. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas, coma, spherical aberration, and resultant aberration are discussed. To make the theory practical, we determine the aberration coefficients numerically, rather than analytically, with the aid of ray tracing that takes into account the angular distribution of rays originating from a given light source. A merit function is defined so as to represent closely the variance of the spots formed when an infinite number of rays are traced and to take into account the dimensions of the source and the last optical element. The theory is also applicable to mirror-grating or mirror systems.

Retrieval of Vertical Distribution of Tropospheric Refractivity through Ground-Based GPS Observation

In the present reported study, the vertical distributions of local atmospheric refractivity were retrieved from ground- based GPS observations at low elevation angles. An improved optimization method was implemented at altitudes of 0-10 km to search for a best-fit refractivity profile that resulted in atmospheric delays most similar to the delays calculated from the observations. A ray-tracing model was used to simulate neutral atmospheric delays corresponding to a given refractivity profile. We initially performed a ＂theoretical retrieval＂, in which no observation data were involved, to verify the optimization method. A statistical relative error of this ＂theoretical retrieval＂ （-2% to 2%） indicated that such a retrieval is effective. In a practical retrieval, observations were obtained using a dual-frequency GPS receiver, and its initial value was provided by CIRA86aQ_UoG data. The statistical relative errors of the practical retrieval range from -3% to 5% were compared with co-located radiosonde measurements, Results clearly revealed diurnal variations in local refractivity prc,files, The results also suggest that the general vertical distribution of refractivity can be derived with a high temporal resolution. However, further study is needed to describe the vertical refractivity gradient clearly.

EUV Optical Design -Reflective and Diffractive Optics

This article describes the task of optical designers to achieve a better design. This is followed by some discussions on the necessity of total design that takes all the elements into account from its light source to the final image plane. Methods are given to simulate rays from a bending magnet and an undulator, surface figure errors, and thermal deformations. Some examples are given for an undulator beamline and an EUVL optical system, together with tolerance estimates of the figure error and thermal deformation.

Property of slice square polycapillary x-ray optics

A geometrical description of square polycapillary x-ray optics and the basic theory of the transmission of x-rays are presented. A method of numerical calculation is developed based on ray-tracing theory. The method simulates the intensity distribution of x-rays propagating through slice square polycapillary x-ray optics. The simulation results are compared with the experimental results.

Light scattering by a spherical particle with multiple densely packed inclusions

This paper calculates light scattering by a spherical water particle containing densely packed inclusions at a visible wavelength 0.55 μm by a combination of ray-tracing and Monte Carlo techniques. While the individual reflection and refraction events at the outer boundary of a sphere particle are considered by a ray-tracing program, the Monte Carlo routine simulates internal scattering processes. The main advantage of this method is that the shape of the particle can be arbitrary, and multiple scattering can be considered in the internal scattering processes. A dense-medium light-scattering theory based on the introduction of the static structure factor is used to calculate the phase function and asymmetry parameters for densely packed inclusions. Numerical results of the single scattering characteristics for a sphere containing multiple densely packed inclusions are given.

Group Velocity of Anisotropic Waves-Part Ⅱ: Conservative Properties

It has been argued in Part I that traditional expression of multidimensional group velocity used in meteorology is only applicable for isotropic waves. While for anisotropic waves, it cannot manifest propagation of waves group along the trajectory of a reference wave point, and varies with rotation of coordinates. The general mathematical expression of group velocity which may be used also for anisotropic waves has been derived in Part I. It will be proved that the mean wave energy, momentum and wave action density are all conserved as a wave group propagates at the general group velocity. Since general group velocity represents the movement of a reference point in either isotropic or anisotropic wave trains, it may be used to define wave rays. The variations of wave parameters along the rays in a slowly varying environment are represented by ray-tracing equations. Using the general group velocity, we may derive the anisotropic ray-tracing equations, which give the traditional ray-tracing equations for isotropic waves.

Anomalous propagation conditions of electromagnetic wave observed over Bosten Lake, China in July and August, 2014

Atmospheric duct is a common phenomenon over large bodies of water, and it can significantly affect the performance of many radio systems. In this paper, a two-month（in July and August, 2014） sounding experiment in ducting conditions over Bosten Lake was carried out at a littoral station（41.89°N, 87.22°E） with high resolution GPS radiosondes, and atmospheric ducts were observed for the first time in this area. During the two months, surface and surface-based ducts occurred frequently over the Lake. Strong diurnal variations in ducting characteristics were noticed in clear days. Ducting occurrence was found at its lowest in the early morning and at its highest（nearly 100%） in the afternoon. Duct strength was found increasing from early morning to forenoon, and reaching its maximum in the afternoon. But contrarily, duct altitude experienced a decrease in a clear day. Then the meteorological reasons for the variations were discussed in detail, turbulent bursting was a possible reason for the duct formation in the early morning and the prevailing lake-breeze front was the main reason in the afternoon. The propagation of electromagnetic wave in a ducting environment was also investigated. A raytracing framework based on Runge–Kutta method was proposed to assess the performance of radio systems, and the precise critical angle and grazing angle derived from the ray-tracing equations were provided. Finally, numerical investigations on the radar performance in the observed ducting environments have been carried out with high accuracy, which demonstrated that atmospheric ducts had made great impacts on the performance of radio systems. The range/height errors for radar measurement induced by refraction have also been presented, too, which shows that the height errors were very large for trapped rays when the total range was long enough.

Joint observation of the concentric gravity wave event on the Tibetan Plateau

A concentric gravity wave event was captured by a photographer in NagarzêCounty(90.28°N,28.33°E)between 02:00 and 04:00(local time)on May 11,2019.This concentric gravity wave event was also observed by the Suomi National Polar-orbiting Partnership satellite and the all-sky airglow imager at Yangbajing station(90.5°E,30.1°N).The temporal and spatial information on gravity waves from the photographs provided a rare opportunity to study the propagation of gravity waves over the Tibetan Plateau.According to wind and temperature data from the MERRA-2 reanalysis(Modern-Era Retrospective analysis for Research and Applications,Version 2)and empirical models(NRLMSISE-00[Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere]and HWM[horizontal wind model]),we inversely derived the propagation trajectory from the observed wave pattern to the source region by using the ray-tracing method.The source of the concentric gravity wave was identified as deep convection in Bangladesh(90.6°E,25.0°N).The maximum background wind speed in the propagation direction(31.05 m/s)was less than the phase speed of 53 m/s,which is consistent with the wind-filtering theory.

Propagation of Superluminous L-O Mode Waves During Geomagnetic Activities

The effect of the azimuthal angle φ of the wave vector k on the propagation characteristics of the superluminous L-O mode waves （together with a case of the R-X mode） during different geomagnetic activities using a three-dimensional （3D） ray-tracing method is investigated. This work is primarily an extension of our previous two-dimensional study in which the wave azimuthal angle was not considered. We present numerical simulations for this mode which is generated in the source cavity along a 70° night geomagnetic field line at the specific altitude of 1.5RE （where RE is the Earth＇s radius）. It is found that, as in the two-dimensional case, the trajectory of L-O mode starting in the source meridian plane （or the wave azimuthal angle φ = 180°） can reach the lowest latitude; whereas it basically stays at relatively higher latitudes starting off the source meridian plane （or φ=180°）. The results reveal that under appropriate conditions, the superluminous L-O mode waves may exist in the radiation belts of the Earth, but this remains to be supplemented by observational data.

A Novel Statistical AOA Model Pertinent to Indoor Geolocation

A novel statistical angle-of-arrival (AOA) model for indoor geolocation applications is presented. The modeling approach focuses on the arrivals of the multipath components with respect to the line-of-sight (LOS) path which is an important component especially when indoor geolocation applications are considered. The model is particularly important for indoor applications where AOA information could be utilized for tracking indirect paths to aid in precise ranging in harsh and dense multipath environments where LOS path might be blocked due to obstructions. The results have been obtained by a measurement calibrated ray-tracing (RT) tool.

Common offset ground penetrating radar data inversion based on ray theory

The authors use the common offset ground penetrating radar(GPR)data inversion based on ray theory to estimate interval velocity and to obtain the relative permittivity.In the ray-tracing based inversion,the input data are the offset distance between antennas,the velocity of the first layer,the pick-up amplitude and re-ference amplitude of each reflection layer.The thickness and velocity of each layer are calculated by this recursive method.Firstly,the horizontal homogeneous layered medium model is established,and the ideal inversion results are obtained.Subsequently,Monte Carlo method is used to establish a randomly undulating homogeneous layered medium model.The common offset GPR data for the built geological model is then simulated by finite-difference time-domain(FDTD).It proved that this ray-tracing based inversion method is feasible for the horizontal layered geological model,even the layered geological model with random undulation.Undulation,represented by RMS height and CL(correlation length),influences the inversion results.Finally,a more complex geological model--pinch-out model was established.In the pinch-out model,the pinch-out interface can be clearly identified,though there is a false anomaly,which will not significantly affect the identification of the underground medium structure.