Ray Tracing Method Research Articles

Influence of the spatial laser energy absorption on the molten pool dynamics in high-power laser beam welding

The spatial laser energy absorption inside the keyhole is decisive for the dynamic molten pool behaviors and the resultant weld properties in high-power laser beam welding (LBW). In this paper, a numerical simulation of the LBW process, considering the 3D transient heat transfer, fluid flow, and keyhole dynamics, is implemented, in which the free surface is tracked by the volume-of-fluid algorithm. The underlying laser-material interactions, i.e., the multiple reflections and Fresnel absorption, are considered by an advanced ray-tracing method based on a localized level-set strategy and a temperature-dependent absorption coefficient. The laser energy absorption is analyzed from a time-averaged point of view for a better statistical representation. It is found for the first time that a significant drop in the time-averaged laser energy absorption occurs at the focus position of the laser beam and that the rest of the keyhole region has relatively homogeneous absorbed energy. This unique absorption pattern may lead to a certain keyhole instability and have a strong correlation with the detrimental bulging and narrowing phenomena in the molten pool. The influence of different focus positions of the laser beam on the keyhole dynamics and molten pool profile is also analyzed. The obtained numerical results are compared with experimental measurements to ensure the validity of the proposed model.

Critical review and experimental validation of radiative transfer models for semitransparent media containing large gas bubbles

Many materials manufacturing, photobiochemical, and photoelectrochemical processes involve radiation transfer through foams and bubbly fluids. Controlling and optimizing these processes require accurate predictions of radiation transfer through semitransparent media. Previously developed models treated the heterogeneous media as homogeneous plane-parallel slabs with some effective radiation characteristics while radiation transfer was governed by the one-dimensional radiative transfer equation (RTE). Unfortunately, their accuracy and range of validity remains unclear for lack of comparison with one another or against the same set of experimental data. This study aims to critically review and assess the validity of these models both numerically and experimentally. First, predictions of the transmittance and reflectance of heterogeneous slabs containing large randomly distributed bubbles were compared with those obtained from Monte Carlo ray-tracing (MCRT) method based on geometric optics. A new hybrid model was proposed that predicts the effective scattering coefficient and asymmetry factor using the Lorenz–Mie theory and the effective absorption coefficient as the volume-weighted sum of the bubbles and medium absorption coefficients and solves the RTE using the Monte Carlo method. Its predictions showed excellent agreement with those by the MCRT method for a wide range of bubble volume fractions (0%–30%) as well as slab thicknesses (2–40 mm) and medium absorption coefficients (0.1–100 m−1). Second, microcomputed X-ray tomography scans were performed on a fused silica sample containing bubbles with mean radius of 480 μm to retrieve the exact locations, diameters, and total volume fraction of bubbles. Here also, predictions of the hybrid model using the retrieved data agreed well with experimental measurements of the spectral normal-hemispherical reflectance and transmittance of the sample for wavelengths between 0.4 and 3 μm when silica ranges from weakly absorbing to absorbing.

An improved curved grating demultiplexer based on silicon-on-insulator platform

This article proposes two basic principles to address the astigmatism problem of traditional Rowland gratings. Ray tracing method is employed to analyze the correlation between the optical performance of gratings and the structural parameters, and further, optimize the grating structure. Using the proposed principles, we design a 1×4 demultiplexer with an ultracompact footprint of 97 × 73 μm2, which is suitable of the coarse wavelength division multiplexing (CWDM) system, where the wavelength spacing is 10 nm. The numerical calculation results show that the channel crosstalk between the four channels of the device is less than −40 dB, the insertion loss is between −1.35 dB and −1.80 dB, and the channel uniformity is better than 0.45 dB. The structure proposed curved grating in this article offers broad applications in high-density integrated photonic circuits.

Simulation of GHz ultrasonic wave piezoelectric instrumentation for Fourier transform computation

The recent emerging alternative to classic numerical Fast Fourier transform (FFT) computation, based on GHz ultrasonic waves generated from and detected by piezoelectric transducers for wavefront computing (WFC), is more efficient and energy-saving. In this paper, we present comprehensive studies on the modeling and simulation methods for ultrasonic WFC computation. We validate the design of the WFC system using ray-tracing, Fresnel diffraction (FD), and the full-wave finite element method (FEM). To effectively simulate the WFC system for inputs of 1-D signals and 2-D images, we verified the design parameters and focal length of an ideal plano-concave lens using the ray-tracing method. We also compared the analytical FFT solution with our Fourier transform (FT) results from 3-D and 2-D FD and novel 2-D full wave FEM simulations of a multi-level Fresnel lens with 1-D signals and 2-D images as inputs. Unlike the previously reported WFC system which catered only for 2-D images, our proposed method also can solve the 1-D FFT effectively. We validate our proposed 2-D full wave FEM simulation method by comparing our results with the theoretical FFT and Fresnel diffraction method. The FFT results from FD and FEM agree well with the digitally computed FFT, with computational complexity reduced from O(N^2 logN) to O(N) for 2-D FFT, and from O(NlogN) to O(N) for 1-D FFT with a large number of signal sampling points N.

Application of layer view factor method in high temperature thermal storage packed bed

This study provides a comprehensive evaluation of radiation effects on the thermal behavior of a packed bed using a discrete model for heat transfers integrating a novel method called Layer View Factor for view factors estimation, which significantly decreases computational time by less than 9000 times compared to the parallel ray tracing method. The model is validated and strongly aligned with experimental data at 823K, with a maximum mean bias and root mean square errors of ±4.5K and 10K, respectively. Analyses of temperature profiles and thermocline lengths for charging, discharging, and stand-by processes at a charge temperature of 1473K were performed, finding a thermal flattening effect with radiation, leading to lower peak temperatures and quicker thermocline length evolutions. Notably, the stand-by process exhibited the largest impact, with a maximum temperature difference of up to 100K compared to the non-radiation case. Moreover, analysis of the temperature and energy of discharge found that the maximum discharge temperature drops below 90% of the charge temperature when radiation is included. Finally, efficiency analysis of the processes showed differences of up to 2% between having or not the radiation effect, aiming its role as a redistribution mechanism in the packed bed’s temperature.

A spot-specific range uncertainty framework for robust optimization of proton therapy treatments.

An accurate estimation of range uncertainties is essential to exploit the potential of proton therapy. According to Paganetti's study, a value of 2.4% (1.5 standard deviation) is currently recommended for planning robust treatments with Monte Carlo dose engines. This number is based on a dominant contribution from the mean excitation energy of tissues. However, it was recently shown that expressing tissues as a mixture of water and "dry" material in the CT calibration process allowed for a significant reduction of this uncertainty. We thus propose an adapted framework for pencil beam scanning robust optimization. First, we move towards a spot-specific range uncertainty (SSRU) determination. Second, we use the water-based formalism to reduce range uncertainties and, potentially, to spare better the organs atrisk. The stoichiometric calibration was adapted to provide a molecular decomposition (including water) of each voxel of the CT. The SSRU calculation was implemented in MCsquare, a fast Monte Carlo dose engine dedicated to proton therapy. For each spot, a ray-tracing method was used to propagate molecular I-values uncertainties and obtain the corresponding effective range uncertainty. These were then combined with other sources of range uncertainties, according to Paganetti's study of 2012. The method was then assessed on three head-and-neck patients. Two plans were optimized for each patient: the first one with the classical 2.4% flat range uncertainty (FRU), the second one with the variable range uncertainty. Both plans were then compared in terms of target coverage and OAR mean dose reduction. Robustness evaluations were also performed, using the SSRU for both plans in order to simulate errors as realistically aspossible. For patient 1, it was found that the median SSRU was 1.04% (1.5 standard deviation), yielding, therefore, a very large reduction from the 2.4% FRU. All three SSRU plans were found to have a very good robustness level at a 90% confidence interval while sparing OAR better than the classical plan. For instance, in nominal cases, average reductions in the mean dose of 15.7, 8.4, and 13.2% were observed in the left parotid, right parotid, and pharyngeal constrictor muscle, respectively. As expected, the classical plans showed a higher but unnecessary level ofrobustness. Promising results of the SSRU framework were observed on three head-and-neck cases, and more patients should now be considered. The method could also benefit to other tumor sites and, in the long run, the variable part of the range uncertainty could be generalized to other sources of uncertainty in order to move towards more and more patient-specifictreatments.

Challenges in dynamic heat source modeling in high-power laser beam welding

The amount of absorbed energy in the keyhole as well as its spatial and temporal distribution is essential to model the laser beam welding process. The recoil pressure, which develops because of the evaporation process induced by the absorbed laser energy at the keyhole wall, is a key determining factor for the macroscopic flow of the molten metal in the weld pool during high-power laser beam welding. Consequently, a realistic implementation of the effect of laser radiation on the weld metal is crucial to obtain reliable and accurate simulation results. In this paper, we discuss manyfold different improvements on the laser-material interaction, namely, the ray tracing method, in the numerical simulation of the laser beam welding process. The first improvement relates to locating the exact reflection points in the ray tracing method using a so-called cosine condition in the determination algorithm for the intersection of reflected rays and the keyhole surface. A second correction refers to the numerical treatment of the Gaussian distribution of the laser beam, whose beam width is defined by a decay of the laser intensity by a factor of 1/e2, thus ignoring around 14% of the total laser beam energy. In the third step, the changes in the laser radiation distribution in the vertical direction were adapted by using different approximations for the converging and the diverging regions of the laser beam, thus mimicking the beam caustic. Finally, a virtual mesh refinement was adopted in the ray tracing routine. The obtained numerical results were validated with experimental measurements.

Optical ray-tracing simulation method for the investigation of radiance non-uniformity of an integrating sphere

The paper deals with possibilities and limits of optical simulations of extended uniform light sources. Optical simulations of ideal and real light sources are performed using optical ray-tracing software which is capable to simulate non-imaging systems such as Lambertian disc and integrating spheres. The simulation methodology is validated by comparing the developed simulation model with a real experiment previously performed in optical laboratory. The comparison is made on the radiance uniformity measurement and simulation results of a general purpose integrating sphere rather than on less convenient and more frequent irradiance uniformity measurements. The aim is to develop a reliable simulation method for the investigation of radiance non-uniformity of any real extended uniform light source.

Identification and extraction of lateral target signals in tunnel geological prediction with the Karhunen-Loéve beamforming method

Before the construction of a tunnel, effective and accurate advanced prospecting techniques are required to detect unexpected geological heterogeneity around the tunnel. However, because the data collected during tunnel advance prediction include waves reflected from different directions and a large amount of environmental noise, the seismic records collected are extremely complex, and it is difficult to extract the target signals from the lateral area of the tunnel effectively. The beamforming method can create a focused wave front through the stack of the wavefield, improving the data quality of the target signal. This paper incorporates the Karhunen-Loéve method in the beamforming procedure to extract the lateral signal of the tunnel. First, the test principle of Karhunen-Loéve beamforming (KLBF) based on the tunnel seismic prediction (TSP) observation system is discussed, and the corresponding delay parameters are estimated according to different application conditions. In addition, ray tracing and three-dimensional wave equation methods are used to carry out numerical simulation research on the models of faults, karst caves and underground rivers. Finally, the corresponding KLBF method can be used to improve the quality of effective signals by different delay time calculation methods, which can better identify and extract the lateral reflected signals.

Synchrotron emitting Komissarov torus around naked singularities

From a theoretical perspective, matter accretion processes around compact objects are highly relevant as they serve as a natural laboratory to test general relativity in the strong field regime. This enables us to validate fundamental concepts such as the no-hair theorem, the cosmic censorship hypothesis, and the existence of alternative solutions to Einstein’s equations that mimic the effects of black holes. In this study, we analyze the emission spectra of geometrically thick accretion disks, referred to as Polish doughnuts, around naked singularities described by the q-metric. To begin, we revisit the construction of equilibrium configurations of magnetized tori in this spacetime and evaluate the role of the deformation parameter over these configurations. Once we have systematically studied the disks in this spacetime, we use the OSIRIS code to perform a backward ray-tracing method, resulting in the first simulations of the intensity map and emission profiles of magnetized tori within this metric. Furthermore, we validate the effect of both the quadrupole moment and the angular momentum on observable quantities such as flux and intensity for optically thin and thick disks, since for values of q < 0, which correspond to objects with prolate deformation, and which in turn, are constructed with higher values of angular momentum, the emission spectrum exhibits higher intensity than that obtained for Schwarzschild’s spacetime. Hence, we find a first differential feature that distinguishes tori formed around naked singularities from those around static black holes.

Research on Propagation Characteristics Based on Channel Measurements and Simulations in a Typical Open Indoor Environment

At present, it is difficult to obtain the indoor propagation loss quickly and accurately by directly using measurements in the millimeter wave band. To solve this problem, in this paper, a ray tracing method suitable for indoor scenes based on geometric optics theory, the uniform theory of diffraction and image theory is presented; the space-alternation generalized expectation-maximization (SAGE) algorithm is used to analyze the measured data and the multipath information of the wireless channel is analyzed; three deep learning models are used to predict the path loss at different receiving distances based on 1600 sets of path loss data. The results show that the comparison between the ray tracing and experimental results shows a good agreement. Moreover, the root-mean-square error (RMSE) and mean absolute error (MAE) of the long short-term memory (LSTM) network are the smallest, and the LSTM has a better fitting effect on the propagation loss sequences predicted at more distant locations when compared with the recurrent neural network (RNN) and gate recurrent unit (GRU) methods, which can better reflect the propagation trend. This provides theoretical support for the layout of base stations and network optimization in typical open indoor environments.

Evaluating Structural Details' Influence on Elastic Wave Propagation for Composite Structures via Ray Tracing.

This study presents a novel method based on ray tracing for analyzing wave propagation in composites specifically tailored for structural health monitoring applications. This method offers distinct advantages over the commonly used finite element method mainly in computational resource utilization, which has become a limiting factor for these kinds of analyses. The ray tracing method is evaluated against a number of example cases representing structural details such as thickness changes, stringers, or simulated damage, and the significance of ray tracing to study wave propagation under these conditions and how it can serve as a valuable tool for structural health monitoring are highlighted. This model has been developed as part of a complete SHM framework with the intention of being an efficient and simple way to calculate wave propagation and therefore it could be used as a way to determine relevant damage indicators or train an artificial intelligence model.

Symmetric gradient-index media reconstruction.

Ray tracing in gradient-index (GRIN) media has been thoroughly studied and several ray tracing methods have been proposed. Methods are based on finding the ray path given a known GRIN. In recent decades, the inverse problem, which consists of finding the GRIN distribution for a given light ray path, has been gaining attention. Given that it is not an easy task, the methods proposed in the literature vary in degrees of difficulty. In this work, an alternative method is presented to derive symmetric GRIN distributions whose implementation can be considered the simplest to date. Since it is based on invariants, which result from the symmetries of the system as stated by Fermat's principle, it is an exact numerical method, i.e., the physical system is not approximated. The robustness of the method permits the reconstruction of the GRIN distribution from a ray propagating in three-dimensions. In order to demonstrate its operation, different known symmetric GRIN media are reconstructed using rays that propagate in two and three dimensions.

Investigation into the effect of multiple line dipoles magnetic field through LS-3 parabolic trough solar system

This paper simulates the LS-3 parabolic trough solar collector with Monte Carlo Ray Tracing and computational fluid dynamics methods. The heat flux is non-uniform around the absorber tube. Therefore, multiple line dipoles magnetic field location can effect on solar collector performance. There is no article that has investigated the effect of this parameter in the parabolic trough solar collector. Also, this collector is simulated for the first time for June 21 and December 21, and the heat flux distribution for it is provided by the Monte Carlo Ray Tracing method. The multiple line dipoles magnetic field leads to a decrease in the maximum temperature of the absorber tube wall by 2.3 %. The magnetic field intensity also affects the solar collector's performance. If the magnetic flux density is equal to 100 G, 75 G and 50 G, then the value of Performance Evaluation Criteria is equal to 1.47, 1.43 and 1.39, respectively. Finally, the magnetic field location affects the Nusselt number but does not affect the Darcy friction factor. For example, if the multiple dipoles magnetic field are placed at angles of 0, 30, 60, and 90°, then the Nusselt number ratio is 1.50, 1.42, 1.44, and 1.65, respectively.

Solar Dish Concentrator: A Case Study at the Energy Center Rooftop

Concentrating solar technology plays a role, albeit a niche role compared to commercial solar systems (photovoltaics and thermal collectors). Within the context of sustainable development and within the green transition phase, it could be a respectable player. The main purpose of this study is to create and validate a model that approximates the temperature trend of a receiver installed in a CSP (concentrated solar plant). A method to approximate optical and thermal performance is discussed. The paraboloid installed in the Energy Center (Turin, Italy) was taken as a reference, creating a model that could simulate real operating conditions. The Monte Carlo (MC) method for ray tracing was adopted developing two models. The first model sets the maximum reflectivity of the paraboloid and neglects the loss of “limb darkening,” while the second one sets a reflectivity of 80%. Once the incident flux was obtained, the optical performance was analytically calculated and compared to the value provided by the manufacturer. The thermal performance was also studied, reproducing the dimensions of the receiver consisting of a sintered alumina tube placed at a focal distance from the paraboloid. Two configurations were analyzed: one neglecting the losses due to radiation and natural convection, the other one including the losses due to radiation and considering the atmospheric wind condition. Finally, the model was validated by comparing the obtained temperatures with those measured by thermocouples placed on the receiver. Analyzing two random days in the year 2020, an average error of 7% and 2% was obtained.

Microwave lens ray tracing method as a tool for optimizing the parameters of beamforming circuits of antenna arrays

In the paper, a microwave lens tracing method is studied, which takes into account the influence of the beam-forming circuit elements on the amplitude distribution of the field over the antenna array aperture and multiple reflections of rays inside the lens cavity. An approach has been used that makes it possible to simulate the structure of microwave lenses and take into account the effect of mutual bonds inside the lens body. The proposed procedures are aimed at reducing time costs in the design of lens-type beam-forming circuits in antenna arrays of radio electronic equipment in the microwave-EHF wavelength ranges. The results of comparison of the ray tracing method and electrodynamic modeling of microwave lenses have been presented.

Evaluation of time dependent neutron transport algorithms using 2D modular ray tracing MOC

Three algorithms for solving the multigroup time dependent neutron transport in two dimensions utilizing the method of characteristics (MOC) are developed in this study. These algorithms are distinguished base on the average angular flux calculation along the characteristic line (track) and the applied approximation to the angular flux time derivative. Since the calculation of the scalar flux in the characteristics method requires the average angular flux along the track, two approaches for implementation of track averaged angular flux are presented. In the first approach, the effect of the angular flux in the previous time step as an extra term added to the source is considered. Second, the average angular flux is applied similar to the common method used in the steady state form. Moreover, two states for the angular flux time derivative in implementing the transient neutron transport solution are considered. First, the angular dependency of the angular flux in time derivative is preserved. Second, isotropic scalar flux approximation is applied to the time derivative.Considering the vital role of ray tracing and improving the non-physical disturbances effect caused by ray tracing methods, the latest modular ray tracing (MRT) method is utilized for the transient calculation. For verification, the well-known TWIGL benchmark is modeled and the results are compared with MPACT and DeCART codes. Additionally, the heterogeneous benchmark problems MOXK_2G and MOXK_7G are simulated and the results are compared with DeCART and VARIANT_K codes.

Rethinking the potential productivity of crassulacean acid metabolism by integrating metabolic dynamics with shoot architecture, using the example of Agave tequilana.

Terrestrial CAM plants typically occur in hot semiarid regions, yet can show high crop productivity under favorable conditions. To achieve a more mechanistic understanding of CAM plant productivity, a biochemical model of diel metabolism was developed and integrated with 3-D shoot morphology to predict the energetics of light interception and photosynthetic carbon assimilation. Using Agave tequilana as an example, this biochemical model faithfully simulated the four diel phases of CO2 and metabolite dynamics during the CAM rhythm. After capturing the 3-D form over an 8-yr production cycle, a ray-tracing method allowed the prediction of the light microclimate across all photosynthetic surfaces. Integration with the biochemical model thereby enabled the simulation of plant and stand carbon uptake over daily and annual courses. The theoretical maximum energy conversion efficiency of Agave spp. is calculated at 0.045-0.049, up to 7% higher than for C3 photosynthesis. Actual light interception, and biochemical and anatomical limitations, reduced this to 0.0069, or 15.6 Mg ha-1 yr-1 dry mass annualized over an 8-yr cropping cycle, consistent with observation. This is comparable to the productivity of many C3 crops, demonstrating the potential of CAM plants in climates where little else may be grown while indicating strategies that could raise their productivity.

Research and Analysis of Ray Tracing Methods

In computer graphics, the study of how to build realistic scenes on the computer has been the focus of research. The dominant approach to simulating the correct light source was to use rasterization, but rasterization does not correctly simulate multiple reflections. To make virtual scenes more realistic, ray tracing was proposed to provide better results. With the rapid development of computer hardware, the use of ray tracing for rendering animation or games is becoming more and more common, and many scenes can now be rendered with ray tracing instead of rasterization for better results. This paper introduces and analyses the various methods of ray tracing in chronological order, starting with the original forward ray tracing and backward ray tracing, followed by Whitted algorithms with recursion, and then a series of methods introducing rendering formulas. And then, a few rays tracing algorithms introducing the Metropolis sampling method is mentioned. One can conclude that this method is going to be used for future optimization and development. It is significant for the development of ray tracing.

Study of the Deterministic Transmission Loss Prediction Model for Troposcatter

Troposcatter transmission loss prediction models are based mainly on ITU-R’s empirical models. However, the available troposcatter propagation models do not enable the real-time calculation of the transmission loss for a specific propagation link. Therefore, the primary purpose of this study is to develop a deterministic troposcatter transmission loss prediction model to realize the real-time calculation or prediction of the transmission loss. In this study, the turbulent scattering cross-section, the refractive turbulence structure constant and the radar equation were introduced to our approach, and the troposcatter transmission loss prediction model was established based on the geometry of the troposcatter circuit. In addition, a weighted method for taking the value of the refractive turbulence structure constant, generated from the WRF schema, was proposed, based on the ray tracing method. Furthermore, the proposed model was validated with the experimental measurement of troposcatter, which verifies the proposed model’s availability and reliability.