Ray Tracing Algorithm Research Articles

Comprehensive and strict validation of neutral atmosphere ray tracing algorithms and some improvements for space geodetic radio signals

This study presents a more thorough and rigorous method for the validation of atmospheric ray tracing algorithms used for computing the path delays of space geodetic microwave signals. Romberg integration through a hypothetical atmospheric structure, e.g. the US standard atmosphere, is recommended to derive the reference values of slant total delay (STD) and geometric delay (GD) for validations. Enlighten by the validation results, simplification for the ray tracing algorithm APM-3D and revision for the piecewise linear (PWL) method are proposed and both are proved to be valid. Comparison results show that in a spherically symmetric atmosphere (one-dimensional (1D) media), if the atmosphere is vertically stratified with sufficient height layers, all 1D, two-dimensional (2D), and three-dimensional (3D) ray tracing algorithms tested yield identical STDs and GDs with reference values at an elevation angle of 5°; while with limited height layers, the revised PWL method exhibits better performance than other 1D algorithms considered. The 2D and 3D algorithms are further compared using realistic 3D atmosphere from ERA5 reanalysis data, and it indicates mm to cm level of differences in GDs; while the STD differences range between <0.1 mm to cm level, depending on weather condition and whether shooting is implemented during the tracing. Both STD and GD discrepancies become larger under severe weather, and the magnitude of 2D-3D difference is found to be consistent with the azimuthal variation of STDs. In comparison of results obtained without shooting, shooting procedure tends to decrease the STD differences but has little impact on the differences in GD. The simplified APM-3D can replace the original version with 10−5 mm level of agreements in STD.

Temporal vectorized visibility for direct illumination of animated models

Direct illumination rendering is an important technique in computer graphics. Precomputed radiance transfer algorithms can provide high quality rendering results in real time, but they can only support rigid models. On the other hand, ray tracing algorithms are flexible and can gracefully handle animated models. With NVIDIA RTX and the AI denoiser, we can use ray tracing algorithms to render visually appealing results in real time. Visually appealing though, they can deviate from the actual one considerably. We propose a visibility-boundary edge oriented infinite triangle bounding volume hierarchy (BVH) traversal algorithm to dynamically generate visibility in vector form. Our algorithm utilizes the properties of visibility-boundary edges and infinite triangle BVH traversal to maximize the efficiency of the vector form visibility generation. A novel data structure, temporal vectorized visibility, is proposed, which allows visibility in vector form to be shared across time and further increases the generation efficiency. Our algorithm can efficiently render close-to-reference direct illumination results. With the similar processing time, it provides a visual quality improvement around 10 dB in terms of peak signal-to-noise ratio (PSNR) w.r.t. the ray tracing algorithm reservoir-based spatiotemporal importance resampling (ReSTIR).

Error compensation for near optical coaxial phase measuring deflectometry with refraction error model

Phase measuring deflectometry (PMD) is a key measurement technology for specular surfaces form measurement. Compared with conventional PMD techniques, the near optical coaxial PMD (NCPMD) can achieve compact configuration, light weight and reducing measurement error caused by shadows of the surface structures through utilizing a plate beamsplitter. However, the introduction of the plate beamsplitter will affect the measurement accuracy of the NCPMD system. The refraction of the plate beamsplitter needs to be considered. In this work, a virtual system of NCPMD was established, and an error model of the NCPMD system by considering the refraction influence of the plate beamsplitter was presented to analyze the shape reconstruction error caused by the plate beamsplitter. Moreover, the calibration method of the beamsplitter and the ray tracing algorithm to achieve error compensation of the beamsplitter were proposed. The proposed error compensation method can effectively improve the measurement accuracy of NCPMD system which has been confirmed by surface measurement experiments.

Ultra-short time-echo based ray tracing for transcranial focused ultrasound aberration correction in human calvaria.

Magnetic resonance guided transcranial focused ultrasound holds great promises for treating neurological disorders. This technique relies on skull aberration correction which requires computed tomography (CT) scans of the skull of the patients. Recently, ultra-short time-echo (UTE) magnetic resonance (MR) sequences have unleashed the MRI potential to reveal internal bone structures. In this study, we measure the efficacy of transcranial aberration correction using UTE images.&#xD;Approach. We compare the efficacy of transcranial aberration correction using UTE scans to CT based correction on four skulls and two targets using a clinical device (Exablate Neuro, Insightec, Israel). We also evaluate the performance of a custom ray tracing algorithm using both UTE and CT estimates of acoustic properties and compare these against the performance of the manufacturer's proprietary aberration correction software. &#xD;Main results. UTE estimated skull maps in Hounsfield units (HU) had a mean absolute error of 242 ± 20 HU (n=4). The UTE skull maps were sufficiently accurate to improve pressure at the target (no correction: 0.44 ± 0.10, UTE correction: 0.79 ± 0.05, manufacturer CT: 0.80 ± 0.05), pressure confinement ratios (no correction: 0.45 ± 0.10, UTE correction: 0.80 ± 0.05, manufacturer CT: 0.81 ± 0.05), and targeting error (no correction: 1.06 ± 0.42 mm, UTE correction 0.30 ± 0.23 mm, manufacturer CT: 0.32 ± 0.22) (n=8 for all values). When using CT, our ray tracing algorithm performed slightly better than UTE based correction with pressure at the target (UTE: 0.79 ± 0.05, CT: 0.84 ± 0.04), pressure confinement ratios (UTE: 0.80 ± 0.05, CT: 0.84 ± 0.04), and targeting error (UTE: 0.30 ± 0.23 mm, CT: 0.17 ± 0.15). &#xD;Significance. These 3D transcranial measurements suggest that UTE sequences could replace CT scans in the case of MR guided focused ultrasound with minimal reduction in performance which will avoid ionizing radiation exposure to the patients and reduce procedure time and cost.&#xD.

ANN and CFD driven research on main performance characteristics of solar chimney power plants: Impact of chimney and collector angle

Solar energy systems operate directly connected to the sun. Solar chimney power plants are privileged systems that can provide power output even in cloudy weather and during hours when there is no sun. The design and sizing of this system, which researchers focused on after its first application in the 1980s, is very effective on its performance. In this study, the collector slope and chimney slope that give maximum power output for the Manzanares pilot plant are investigated with a 3D CFD model. Simulations made using the RNG k-e turbulence model and the DO (discrete ordinates) solar ray tracing algorithm provide results that are in high compatibility with experimental data and literature. It is understood that the system provides maximum power at 0.6° collector slope and 1.5° chimney divergence angle. It is seen that the system, which gives a power output of approximately 46 kW in the reference case, exceeds the power output by 4.5 times and reaches 216.853 kW in the design that includes the collector and chimney slope. The effects of the main elements of the system on the performance are also included by changing the collector radius and chimney height while preserving these inclination angles. More than the power output in the reference case, 49.233 kW, can be achieved with the inclined design, with a collector radius of 73.2 m and a chimney height of 155.68 m. Although the effect of increasing the chimney height on power output continues after 1.2 floors, its effect decreases. In the study, it is seen that increasing the chimney height and changing the collector radius provide a greater increase in power output. Furthermore, the scope extends to the incorporation of an Artificial Neural Network (ANN) model, presenting a novel approach to predicting SCPP system performance. The findings ascertain the utilisation of 9 neurons in the hidden layer of the ANN, demonstrating a precise alignment with the study data.

A Calculation Method for the Hyperspectral Imaging of Targets Utilizing a Ray-Tracing Algorithm

This paper proposes a hyperspectral imaging simulation method based on a ray-tracing algorithm. The algorithm combines calculations based on solar and atmospheric visible light radiation as well as the spectral bidirectional reflection distribution function (BRDF) of the target surface material and can create its own scenarios for simulation calculations on demand. Considering the presence of multiple scattering between the target and background, using the ray-tracing algorithm enables the precise computation of results involving multiple scattering. To validate the accuracy of the algorithm, we compared the simulated results with the theoretical values of the visible light scattering intensity from a Lambertian sphere. The relative error obtained was 0.8%. Subsequently, a complex scene of engineering vehicles and grass was established. The results of different observation angles and different coating materials were calculated and analyzed. In summary, the algorithm presented in this paper has the following advantages. Firstly, it is applicable to geometric models composed of any triangular mesh elements and accurately computes the effects of multiple scattering. Secondly, the algorithm combines the spectral BRDF information of materials and improves the efficiency of multiple scattering calculations using nonuniform sampling. The computed hyperspectral scattering data can be applied to simulate airborne or space-borne remote sensing data.

GNSS signal ray-tracing algorithm for the simulation of satellite-to-satellite excess phase in the neutral atmosphere

Traditionally, GNSS space-based and ground-based estimates of tropospheric conditions are performed separately. It leads to limitations in the horizontal (e.g., a single space-based radio occultation profile covers a 300 km slice of the troposphere) and vertical resolution (e.g., ground-based estimates of troposphere conditions have spacing equal to stations’ distribution) of the tropospheric products. The first stage to achieve an integrated model is to create an effective 3D ray-tracing algorithm for the satellite-to-satellite (radio occultation) path reconstruction. We verify the consistency of the simulated data with the RO observations from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1) Data Analysis and Archive Center (CDAAC) in terms of excess phase and bending angle. The results show that our solution provides an effective RO excess phase, with a relative error varying from 35% at the height of 25–30 km (1.0–1.5 m) to 0.5% at heights 5–10 km (0.1–1 m) and 14 to 2% at heights below 5 km (2–14 m). The bending angle retrieval on simulated data attained for high-resolution ray-tracing, bias lower than 2% with respect to the observed bending angle. The optimal solution takes about 1 s for one transmitter–receiver pair with a tangent point below 5 km altitude. The high-resolution processing solution takes 3 times longer.

Radio Communication Blackout Mitigation: Analyzing Magnetic Field Effects via Ray-Tracing Analysis

Avoiding radio communication blackouts during atmospheric entry is crucial to a space mission and can be life-saving. A novel ray-tracing algorithm, called Blackout Ray Tracer (BORAT), based on a Snell’s law solver, is introduced to analyze the signal behavior during reentry using geometrical optics for nonmagnetized and magnetized plasma. The ray-tracing analysis is performed on Knapp’s case fluid simulations provided by the University of Stuttgart. The effect of an applied magnetic field on ray tracing is discussed and visualized using radiation patterns. The results suggest that a sufficiently strong magnetic field is promising to mitigate radio communication blackouts.

Deflection angle and shadow evolution from charged torus-like black hole under the effect of non-magnetic plasma and non-plasma medium

In this study, we investigate the deflection angle of a torus-like regular charged black hole in the limit approximation of a weak field to check the effects of non-magnetic plasma and non-plasma medium. Using spacetime optical geometry, we first compute the Gaussian optical curvature. We study the light deflection angle from a charged torus-like black hole using the Gibbons and Werner approach. By taking into account the well-known Keeton–Petters approach, we validate our results. Moreover, we examine the shadow of a charged torus-like black hole by using the ray-tracing algorithm under the influence of pressureless and non-magnetized plasma and study the graphical effects of cosmological constant and charge for both anti-de Sitter and de Sitter cases on the shadow of a black hole.

Bounding Volume Hierarchy-Assisted Fast SAR Image Simulation Based on Spatial Segmentation

In order to improve the simulation efficiency under the premise of ensuring the fidelity of synthetic aperture radar (SAR) simulation images, we propose a BVH-assisted fast SAR image simulation method based on spatial segmentation. The beam scanning model is established based on RD imaging geometric relation, and the bounding volume hierarchy (BVH) algorithm is used to assist in obtaining the time-varying latticed radiation and shadow areas within the radar beam, combining them with the real-time position of the sensors to complete the simulation of the electromagnetic (EM) wave transmission. The ray tracing algorithm is used to calculate the multiple backscatter fields of EM waves, including various material properties of the target surface. The SAR spatial traversal is adopted to spatially segment the latticed radiation area, and the compute unified device architecture (CUDA) kernel function is designed using the echo matrix cell method to make each cell of the target echo matrix as a subfield of the backscattering field, and the position of the echo matrix cell is traversed to obtain the target backscattering field. The target simulated echo is processed by the range Doppler (RD) imaging algorithm to obtain the SAR-simulated image. The simulation results show that compared with a CPU single-thread simulation, the simulation speed of the proposed method is significantly improved, and the SAR simulation image has high structural similarity with the real image, which fully verifies the effectiveness of the proposed method.

Tailor-joining of Ti6Al4V skin with V-shaped assembly error using enhanced PLBW scheme: Keyhole dynamics and metal bridging behavior

Building thin-walled titanium alloy skin using conventional laser beam welding (LBW) frequently suffers from undesirable seam quality due to the V-shaped notch; a typical assembly error occurs after skin rolling with a specific sheet thickness range. This work proposed an improved scheme with metal bridging capacity and liquid film stability to overcome this by executing a pulsed laser beam and spot irradiation in a flat-top mode. Welding was performed on 1.5 mm-thick Ti6Al4V sheets configured in the butt joint with a reserved notch geometry, which is 20 degrees between the groove surface. We also conducted numerical modeling and solutions concerning the heat-flow-phase dynamics using an enhanced ray tracing algorithm. Results show that the as-build weld beads, characterized by middle rippers, slight depression, and edge ridges, present superb continuity and uniformity when applying an average heat input of 40–90 J/mm and a pulse energy of 187.5–750 J. Effective metal bridging across the notch error is achieved at both pulse duration and interval phases due to not only the complete melting of welding side but also the enhanced melt film stability against the surface tension. The cooling of the weld pool starts with a sharp temperature drop at ∼3×105 K/s (on average) during the keyhole collapsing regime, then slows down due to the damped up-down oscillation of the free surface combined with the natural convection-conduction effect. The flow pattern of molten metal changes from squeezing-like to vortexes and finally to a backfilling mode, depending on the evolution of keyhole geometry. Although the keyhole dynamics differs, various process conditions regarding heat input and pulse energy yield effective metal bridging of a single weld spot and sufficient refusion between the adjacent weld spots, ensuring the well-overlapped weld bead formation.

Preliminary Implications of Viscoelastic Ray Theory for Anelastic Seismic Tomography Models

ABSTRACT The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed-form solutions of forward ray-tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray-tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide-angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray-tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near-critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre-near-critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray-tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.

Shortest-path ray tracing on self-adapting random grids

SUMMARY A new ray tracing algorithm based on the shortest path method was designed and optimized to model seismic rays. The workflow is based on Dijkstra’s algorithm to find the shortest path iteratively on self-adapting random grids. These random grids adapt from one iteration to the next, storing in memory those nodes that minimize the traveltime in each iteration, consequently automatically densifying the grid in areas with significant velocity variations. Different data structures and grid geometries were studied, and it was confirmed that using a combination of a binary heap and random grids prevents systematic errors generated by using regular grids while keeping the computational times low. Since the nodes that minimize the traveltime are stored in each iteration, the memory requirements increase logarithmically, with the initial iterations having the most significant impact on the error minimization but plateauing afterwards. It was found that, albeit this increase in memory requirements, by focusing the densification of nodes in areas close to the actual trajectory of the rays, the error minimization requires fewer iterations than other implementations based on multiple realizations of random grids (requiring less than a tenth of the number of iteration of other methods). A function to handle extreme topographic variations was also designed, which uses a boolean test to reject rays crossing the topography, making the algorithm suitable for first arrival modelling in complex topography areas, such as the required for tomographic inversion of first arrivals in thrust-belt land seismic.

A Comprehensive Survey of Isocontouring Methods: Applications, Limitations and Perspectives

This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.

Improved monte Carlo ray-tracing algorithm based on importance sampling

This paper proposes an improved ray-tracing algorithm with importance sampling (IS) to reduce the computational complexity. For multiple receiver situation, we provide improved IS including adaptive and weighted optimization.

Temporal Coherence-Based Distributed Ray Tracing of Massive Scenes.

Distributed ray tracing algorithms are widely used when rendering massive scenes, where data utilization and load balancing are the keys to improving performance. One essential observation is that rays are temporally coherent, which indicates that temporal information can be used to improve computational efficiency. In this paper, we use temporal coherence to optimize the performance of distributed ray tracing. First, we propose a temporal coherence-based scheduling algorithm to guide the task/data assignment and scheduling. Then, we propose a virtual portal structure to predict the radiance of rays based on the previous frame, and send the rays with low radiance to a precomputed simplified model for further tracing, which can dramatically reduce the traversal complexity and the overhead of network data transmission. The approach was validated on scenes of sizes up to 355 GB. Our algorithm can achieve a speedup of up to 81% compared to previous algorithms, with a very small mean squared error.

Two dimensional elastic dynamically focused beam migration in transversely isotropic (TI) media

The anisotropic ray tracing equations of elastic waves are derived for calculating the central ray's travel time, trajectory, and parameters P and Q. Based on the anisotropic ray tracing algorithm, we proposed a transversely isotropic elastic dynamically focused beam migration for two dimensional media. Based on the two dimensional Kirchhoff-Helmholtz integral of elastic waves, the elastic imaging weight coefficients are used to reduce the crosstalk noise. Then, based on the previous research, we introduced a sign function to eliminate the effect of polarity reversal in qPqSV wave migration. Through model tests, it can be found that the proposed method can process the multicomponent seismic data and image the complex structures for anisotropic media. The optimized dynamic ray tracing algorithm is superior to the conventional one in computational efficiency. Furthermore, the proposed method eliminates the limitations of the Gaussian beam imaging. This method not only does not affect the accuracy of shallow imaging, but also enhances the energy focusing and the amplitude of deep layers. The model tests have shown the accuracy and effectiveness of our proposed method.

Wireless Channel Model Based on Ray Tracing Algorithm in the Sea Environment

The maritime environment is complex and changeable, and an accurate maritime wireless channel model is particularly difficult to establish. This study investigates the sensitivity of a three-dimensional (3D) maritime ray tracing (RT) model for the use of the geometrical optics in radio channel characterizations of maritime environments. The channel measurement experiments are mainly carried out at three frequency points of 1.5, 1.8, and 2.5 GHz, and the simulation results of the model are compared and corrected with the measured received power. Analysis shows that the modified model simulation results at 1.5, 1.8, and 2.5 GHz frequency points are in good agreement with the actual measurement, and the RMS is within 7 dB. Moreover, the reverse RT algorithm has the advantages of fast calculation speed and high efficiency. The effects of the different sea conditions, frequencies, and distances on the propagation of electromagnetic waves are analyzed on the basis of this model.

GNSS-A Network Solution with Zenith Acoustic Delay Estimation

The ocean sound speed changes drastically with time and space. It is almost impossible to achieve centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning without regarding spatio-temporal variations of sound speed. Inspired by the atmospheric delay estimation, we define zenith acoustic delay (ZAD) as the zenith-direction ranging error sourced by the sound speed variations, and then it is decomposed into one temporal component and two horizontal components for the sound speed variations in time and space, respectively. We propose a network solution with the three ZAD components of each seafloor geodetic point as common parameters to be estimated, and then present a piece-wise estimation to characterize their time-varying nature. To remedy the ray bending effect this study is implemented in the context of the ray tracing algorithm based on a reference sound speed profile (SSP). Experimental tests show that the proposed network solution improves ZAD estimation and results in a better position determination as compared to the single-point positioning (SPP) solution. The proposed network solution for a single campaign can achieve a horizontal positioning precision better than 5 cm (1-sigma) for the seafloor geodetic array centroid. The temporal variation of ZAD is up to one meter while the horizontal variations vary within a few decimeters in the time domain and show an azimuthal asymmetry in space.

Numerical simulation at the micro-scale for the heat transfer modelling in the thermoplastic composites laser-assisted AFP process

Laser-assisted Automated Fibre Placement for thermoplastic composites has shown its potential to process complex shaped parts with high productivity rates but many challenges, both physical and technical, still need to be addressed in order to achieve proper in-situ consolidation. Ensuring high quality bonding of the laid tapes relies on perfect control of their thermal history throughout the process, and heat transfer has long proven essential to achieve this. Numerous heat transfer models account for optical interaction between the laser and composite at a macroscopic scale. Here, a thermo-optical model at the micro-scale is designed and differentiates the fibres from matrix domain, accounting for their respective properties. A single tape is modelled in a static configuration. Based on a composite material realistic microstructure, a ray-tracing algorithm highlights the laser heat absorption depth dependency to laser incidence angle and fibre distribution. Numerical surface temperatures are compared to experimental data obtained with a specific set-up leading to an overall accurate approximation. Finally, the microstructure model relevance is assessed with 1D homogenised models considering either ideal surface heating or a volumetric heat source. The surface heating model leads to inaccurate approximation of surface temperatures, whereas volumetric heat source absorption substantially limits temperature errors. As a result, this model gives a satisfactory compromise between model complexity, computational time and temperature prediction.