Three-dimensional Ray Tracing Research Articles

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.

Enhanced Dissipation of Internal Tides in a Mesoscale Baroclinic Eddy

Abstract The dissipation of low-mode internal tides as they propagate through mesoscale baroclinic eddies is examined using a series of numerical simulations, complemented by three-dimensional ray tracing calculations. The incident mode-1 internal tide is refracted into convergent energy beams, resulting in a zone of reduced energy flux in the lee of the eddy. The dissipation of internal tides is significantly enhanced in the upper water column within strongly baroclinic (anticyclonic) eddies, exhibiting a spatially asymmetric pattern, due to trapped high-mode internal tides. Where the eddy velocity opposes the internal tide propagation velocity, high-mode waves can be trapped within the eddy, whereas high modes can freely propagate away from regions where eddy and internal wave velocities are in the same direction. The trapped high modes with large vertical shear are then dissipated, with the asymmetric distribution of trapping leading to the asymmetric distribution of dissipation. Three-dimensional ray tracing solutions further illustrate the importance of the baroclinic current for wave trapping. Similar enhancement of dissipation is also found for a baroclinic cyclonic eddy. However, a barotropic eddy is incapable of facilitating robust high modes and thus cannot generate significant dissipation of internal tides, despite its strong velocities. Both energy transfer from low to high modes in the baroclinic eddy structure and trapping of those high modes by the eddy velocity field are therefore necessary to produce internal wave dissipation, a conclusion confirmed by examining the sensitivity of the internal tide dissipation to eddy radius, vorticity, and vertical scale. Significance Statement The oceanic tides drive underwater waves at the tidal frequency known as internal tides. When these waves break, or dissipate, they can lead to mixing of oceanic heat and salt which impacts the ocean circulation and climate. Accurate climate predictions require computer models that correctly represent the distribution of this mixing. Here we explore how an oceanic eddy, a swirling vortex of order 100–400 km across, can locally enhance the dissipation of oceanic internal tides. We find that strong ocean eddies can be hotspots for internal tide dissipation, for both clockwise and anticlockwise rotating vortices, and surface-enhanced eddies are most effective at internal tide dissipation. These results can improve climate model representations of tidally driven mixing, leading to more credible future predictions.

Three-dimensional raytrace modeling of the New England seamounts acoustics experiment

The 2023 New England Sea Mounts Acoustics (NESMA) experiment took place from April to June at the Atlantis II Seamount Complex. One goal NESMA seeks to address is to further the understanding of acoustic propagation around prominent bathymetric features and associated diffraction and refraction effects. The bathymetry of the experimental site exhibits extreme variability with a difference in elevation of three kilometers from the abyssal plane to the peaks of the seamounts and slopes upwards of 15°, which has a significant influence on bottom-interacting acoustic propagation. As part of the experiment, multiple broadband impulsive sound sources were deployed around the seamounts, including explosive charges, seismic air-gun, and rupture induced cavitation events. Three-dimensional ray trace models of the experiment are presented for comparison with the measured acoustic receptions. Model results are primarily concerned with signals received on three single-channel acoustic recorders deployed on the abyssal plane near the seamounts. Comparisons provide insight into variation in the structure of the measured arrivals associated with varying ray paths refracted around and between the seamounts for different source positions. The influence of geotechnical properties on the measured signals is also assessed through modeling. [Work supported by ONR.]

High luminescence efficiency in Er3+-doped chalcogenide fiber with square inner-cladding

High-purity chalcogenide glasses and optimal fiber structure design are essential to enhance fluorescence lifetime and pump absorption efficiency in a chalcogenide-based fiber laser. Here, Er3+-doped As2S3 glasses, with a low –OH concentration of only 0.023 cm−1 (0.01 ppm), were prepared by the novel purification method, and the 4I11/2 level lifetime of purified glasses was increased successfully from 2.3 ms in unpurified glass to 4.8 ms in the purified glass. Furthermore, a special chalcogenide preform with square inner double cladding (S-DCF) was designed and fabricated via a novel extrusion-stacking method for the first time. Compared with circle inner double cladding fiber and single cladding fiber, the pump absorption efficiency is increased by 2–5 times, which fits well with the simulation result by the three-dimensional ray tracing method. All the results mentioned above demonstrated that the elimination of –OH and the optimized structure of S-DCF can improve the luminescence efficiency apparently and promote the development of mid-infrared fiber laser based on Er3+-doped chalcogenide glass.

Freeform optical system design with differentiable three-dimensional ray tracing and unsupervised learning.

Optical systems have been crucial for versatile applications such as consumer electronics, remote sensing and biomedical imaging. Designing optical systems has been a highly professional work due to complicated aberration theories and intangible rules-of-thumb, hence neural networks are only coming into this realm until recent years. In this work, we propose and implement a generic, differentiable freeform raytracing module, suitable for off-axis, multiple-surface freeform/aspheric optical systems, paving the way toward a deep learning-based optical design method. The network is trained with minimal prior knowledge, and it can infer numerous optical systems after a one-time training. The presented work unlocks great potential for deep learning in various freeform/aspheric optical systems, and the trained network could serve as an effective, unified platform for generating, recording, and replicating good initial optical designs.

Design of coupling system for Cassegrain antenna array

An optical fiber coupling system consisting of a plano-convex lens array and a coupling lens array is designed for a Cassegrain antenna array. The vector theory of reflection and refraction is used to simulate the three-dimensional ray tracing of the optical system and the spot diagrams are used to analyze optical system aberrations. The mode field matching theory is used to analyze the coupling efficiency of the optical system. The simulation results show that the central coupling system for 1550 nm has the maximum coupling efficiency of 70.92%, and the average coupling efficiency of the seven sets of coupling systems is 70.89%. This paper will provide engineers or designers with a design method of the coupling system for the antenna array.

Modelling approaches to predict light absorption in gas-liquid flow photosensitized oxidations

The photosensitized production of singlet oxygen is a benchmark reaction for characterizing flow photoreactors. Light absorption is the driving force of the photooxidation reaction and modelling represents a fast and cost-efficient method for its prediction and optimization. In this study, we report two models of photon absorption in single- and two-phase flow. Firstly, a three-dimensional ray tracing model was developed and validated by experimental 9,10-dimethylanthracene (DMA) photooxidation in presence of Rose Bengal. By comparing the simulated and experimental DMA conversion, the flow and illumination conditions affected by mass transfer limitations in liquid and gas–liquid Taylor flows were identified. Furthermore, the ray tracing model was used to compare the light absorption in Taylor, annular, and two bubbly flow configurations. At a low attenuation coefficient of 2.3 cm−1 a minor difference between flow patterns was observed irrespective of liquid hold-up. At the same liquid hold-up and between 26 cm−1 and 200 cm−1, the relative volumetric absorbed photon flux strongly depends on the flow pattern. Secondly, the ray tracing model was used as reference to develop a simplified absorption model which only requires the geometry and optical properties of the multiphase flow. The novel predictive method is based on the geometrical approximation of the optical pathlength in the liquid slugs, the liquid film and the liquid volume next to the bubble caps. As it requires minimum computational power and provides good accuracy, the geometry-based model has the potential to assist future automated optimization of gas–liquid photooxidations.

Numerical Simulation of Ionospheric Disturbances Due to Rocket Plume and Its Influence on HF Radio Waves Propagation

In this paper, the ionospheric disturbances of CO2, which is released by rocket exhaust plumes, was simulated. The effect of this disturbance on the propagation of high-frequency (HF) radio waves at different incident frequencies was also simulated by using three-dimensional digital ray tracing technique. The results show that CO2 can effectively dissipate the background electrons and form ionospheric holes after being released in the ionosphere. At the peak height of ionospheric electron density (about 300 km), the electrons are dissipated fastest and the radius of ionospheric hole is also largest. This is due to the fact that the diffusion coefficient of CO2 usually increases with height while the electron density just increases before reaching its peak height and then decreases with height, and the chemical reaction rate between ions and CO2 also becomes largest at the peak height of electron density (about 300 km). Around 100 s after the release of CO2, when the radio waves at a frequency of 8 MHz pass through the ionosphere with an elevation range of 85~95°, the “secondary focusing effect” can occur, and we believe that this is due to the reflection of HF shortwaves on the walls of the ionospheric holes. With time going on, this phenomenon disappears at 300 s and only one focus is left at this time. For the HF shortwaves at same incident frequency, the focusing effect of waves displays a weakening trend with time increasing, and the height of focus center also ascends gradually. At the same time after CO2 releasing, with the increasing of radio waves frequency, the focusing effect also becomes weaker and the focus center displays an ascending trend.

Contribution of the retinal contour to the peripheral optics of human eye

Understanding the relationship between the retinal contour and peripheral aberrations is fundamental for exploring the mechanism of myopia progression. Not much has been known about how the retinal expansion can affect peripheral aberrations across the two-dimensional visual field. This study aims to quantify and analyze the changes in the lower- and higher-order aberrations across the visual field induced by retinal expansion, and to understand how this relationship can be influenced by axial astigmatism and the misalignments in the ocular components. Retinal expansion was represented by translating retinal points along the chief rays in the vitreous humor. A realistic eye model was constructed incorporating astigmatism, misalignments and other irregular features based on measurement data. Three-dimensional ray tracing was performed on this model and its two symmetric versions to analyze the changes of axial and peripheral aberrations induced by retinal expansion. The results show that spherical equivalent refraction changes the most during retinal expansion with the rate of −4 to −3 D/mm, which is around 10 times larger than the plus cylinder power. Axial astigmatism determines the retinal impacts on peripheral astigmatism, and unique patterns were found near the two peripheral field locations with zero cylinder power. Ocular misalignments mainly affect higher-order aberrations, especially third-order coma. For most optical features, the impacts of retinal expansion are stronger for larger eccentricity. The impacts of retinal expansion on the lower- and higher-order aberrations have been systematically characterized for the two-dimensional visual field, showing unique patterns in the presence of astigmatism and ocular misalignments.

Aperture total internal reflection (A-TIR) for contact angle measurement

Recently, aperture total internal reflection (A-TIR) was proposed to characterize the microdroplet patterns, such as the coverage fraction of the droplet, by placing the aperture just in front of the detector in classical total internal reflection (TIR). However, the reflection from the curved liquid-air interface was simulated using simple two-dimensional modeling, causing inaccuracy in A-TIR measurement. In addition, the reflectance dependency on the aperture size and the working distance of the aperture was not investigated, hindering its applications. In this study, the simulation based on three-dimensional (3-D) ray tracing with Fresnel equation modeling was successfully developed and verified to explain the internal reflection from the curved droplet liquid-air interface. With this developed 3-D modeling, A-TIR characteristics were explored using the parameters of the aperture size and the working distance of the aperture as well as the droplet surface coverage fraction, which shows a good agreement between the experiment and the simulation. Furthermore, it was for the first time demonstrated that the droplet contact angle can be effectively determined by obtaining the droplet thickness from the analytic quadratic solution by subtracting the measured reflectance at the two different sized apertures and using the spherical profile relation. Low contact angles in the range of 1∼ 15° were determined experimentally for the micro- and macro-sized droplets with a droplet diameter of 70 ∼ 7000 µm by the measured thickness of 1 ∼ 450 µm using A-TIR and compared with Fizeau interferometry and side-view imaging to show a good agreement. The simulation shows that A-TIR can be a new optical diagnostic tool to measure the contact angles 0 ∼ 90° regardless of the droplet diameter by adjusting the aperture size and the working distance. In addition, A-TIR can effectively determine the small contact angles less than 5°, even ultrasmall contact angles less than 1° for the submicron thickness, not requiring the complicated microscope setup. Thus, we can observe a sessile droplet's drastic contact angle change during wetting phenomena from 90° to 0° on the same A-TIR setup. Additionally, A-TIR can be used for a single or an array of micro or nanodroplets with a microscope objective by reducing the laser beam size and scanning methodology.

The effect of canopy architecture on the patterning of "windflecks" within a wheat canopy.

Under field conditions, plants are subject to wind-induced movement which creates fluctuations of light intensity and spectral quality reaching the leaves, defined here as windflecks. Within this study, irradiance within two contrasting wheat (Triticum aestivum) canopies during full sun conditions was measured using a spectroradiometer to determine the frequency, duration and magnitude of low- to high-light events plus the spectral composition during wind-induced movement. Similarly, a static canopy was modelled using three-dimensional reconstruction and ray tracing to determine fleck characteristics without the presence of wind. Corresponding architectural traits were measured manually and in silico including plant height, leaf area and angle plus biomechanical properties. Light intensity can differ up to 40% during a windfleck, with changes occurring on a sub-second scale compared to ~5min in canopies not subject to wind. Features such as a shorter height, more erect leaf stature and having an open structure led to an increased frequency and reduced time interval of light flecks in the CMH79A canopy compared to Paragon. This finding illustrates the potential for architectural traits to be selected to improve the canopy light environment and provides the foundation to further explore the links between plant form and function in crop canopies.

Ultra-Low-Power Wide Range Backscatter Communication Using Cellular Generated Carrier.

With the popularization of Internet-of-things (IoT) and wireless communication systems, a diverse set of applications in smart cities are emerging to improve the city-life. These applications usually require a large coverage area and minimal operation and maintenance cost. To this end, the recently emerging backscatter communication (BC) is gaining interest in both industry and academia as a new communication paradigm that provides high energy efficient communications that may even work in a battery-less mode and, thus, it is well suited for smart city applications. However, the coverage of BC in urban area deployments is not available, and the feasibility of its utilization for smart city applications is not known. In this article, we present a comprehensive coverage study of a practical cellular carrier-based BC system for indoor and outdoor scenarios in a downtown area of a Helsinki city. In particular, we evaluate the coverage outage performance of different low-power and wide area technologies, i.e., long range (LoRa) backscatter, arrow band-Internet of Things (NB-IoT), and Bluetooth low energy (BLE) based BC at different frequencies of operation. To do so, we carry out a comprehensive campaign of simulations while using a sophisticated three-dimensional (3D) ray tracing (RT) tool, ITU outdoor model, and 3rd generation partnership project (3GPP) indoor hotspot model. This study also covers the energy harvesting aspects of backscatter device, and it highlights the importance of future backscatter devices with high energy harvesting efficiency. The simulation results and discussion provided in this article will be helpful in understanding the coverage aspects of practical backscatter communication system in a smart city environment.

A study about signal variation with minor receiver displacement in a meeting room at 60\xa0GHz: measurements and simulations

The aim of this work is to study the impact of small receiver displacement on a signal propagation in a typical conference room environment at a millimeter wave frequency of 60 GHz. While channel measurements provide insights on the propagation phenomena, their use for the wireless system performance evaluation is challenging. Whereas, carefully executed three-dimensional ray tracing (RT) simulations represent a more flexible option. Nevertheless, a careful validation of simulation methodology is needed. The first target of this article is to highlight the benefits of an in-house built three-dimensional RT tool at 60 GHz and shows the effectiveness of simulations in predicting different characteristics of the channel. To validate the simulation results against the measurements, two different transmitter (Tx) positions and antenna types along with ten receiver (Rx) positions are considered in a typical conference room. In first system configuration, an omnidirectional antenna is placed in the middle of the table, while in the second system configuration a directed horn antenna is located in the corner of the meeting room. After validating the simulation results with the measurement data, in the second part of this work, the impact of a small change, i.e., 20 cm in the receiver position, is studied. To characterize the impact, we apply as performance indicators the received power level, root mean square delay spread (RMS-DS) and RMS angular spread (RMS-AS) in azimuth plane. The channel characteristics are considered with respect to the direct orientation (DO), i.e., the Rx antenna is directed toward the strongest incoming path. Different antenna configurations at the Tx and Rx side are applied to highlight the role of antenna properties on the considered channel characteristics. Especially, in the second system configuration the impact of different antenna half power beamwidth on different considered channel characteristics is highlighted through acquired simulation results. The validation of results shows the RMS error of only 2–3 dB between the measured and simulated received power levels for different Tx configurations in the direction of DO. Results indicate that only a small change of the Rx position may result a large difference in the received power level even in the presence of line-of-sight between the Tx and Rx. It is found that the STD of received power level across the room increases with the decrease in HPBW of the antenna. As can be expected, directed antennas offer lower value of RMS-DS and RMS-AS compared with isotropic antenna.

Unraveling the Origin of Low Optical Efficiency for Quantum Dot White Light-Emitting Diodes From the Perspective of Aggregation-Induced Scattering Effect

Quantum dots (QDs) are promising materials for various optoelectronic applications. However, the efficiency of QD white light-emitting diodes (QD-white-LEDs) is not at the desired level, particularly when the QD concentration in the silicone matrix is high and the corresponding mechanism has not been fully elucidated. In this study, we experimentally and theoretically investigated the aggregation-induced scattering (AIS) effect of QDs in silicone and unraveled the origin of low efficiency for QD-white-LED devices. Three-dimensional finite-difference time domain and ray tracing simulations were carried out to establish the AIS model for QDs. Results indicate that the AIS effect is stronger for higher QD concentrations and leads to a larger effective aggregate size (EAS), which was confirmed by comparing with the experimental results of QD-silicone films. Furthermore, we found that the AIS effect causes a significant reduction in the radiant efficiencies of QD-white-LEDs when the EAS exceeds 50 particles, which is validated by fabricated devices. According to the spectral energy analysis, the low efficiency of QD-white-LEDs can be attributed to a strong AIS effect at high QD concentrations, causing severe backscattering and reabsorption loss. This study is also important for nondestructive testing the degree of aggregation demonstrated by QDs in a silicone matrix and for precisely modeling QD-white-LEDs.

Identification of the infrasound signals emitted by explosive eruption of Mt. Shinmoedake by three-dimensional ray tracing.

Mt. Shinmoedake, a part of the Mt. Kirishima cluster of volcanoes in Kyushu, Japan, erupted on 10 March 2018. Our infrasound sensor network located at a distance of more than 200 km from the source detected signals emitted by an explosive eruption of Mt. Shinmoedake. The arrival time of the signals is divided into three time intervals. To reveal how the observed infrasound signals propagated from the source to the sensors, we carry out three-dimensional ray tracing on the basis of the Hamilton equations including the vertical profiles of the temperature and wind around the ray path. We present formulas for calculating travel time and distance of infrasound from a source to an observation site and its turning altitude in the atmosphere. We have identified four kinds of signals, namely, the waves propagated in the troposphere undergoing multiple refraction and those refracting from the stratosphere, the mesosphere, and the lower thermosphere. Brief discussion is devoted to some of the unidentified signals.

3D deterministic ray tracing method for massive MIMO channel modelling and parameters extraction

Geometric stochastic method and deterministic ray tracing method are two common methods of modelling massive multiple-input multiple-output (MIMO) channels. The former has high computational efficiency but a large number of input parameters need to be extracted from measurements for different environments. Conversely, the latter is more suitable for a specific environment but consumes a lot of computing costs. In this study, a novel three-dimensional (3D) deterministic ray tracing method for massive MIMO channel modelling is proposed. The computational efficiency can be improved in two aspects compared with conventional deterministic ray tracing methods. Firstly, substantial intersection tests used in determining the propagation paths of rays are replaced with the adjacency relationships between tetrahedrons. Secondly, the process of ray tracing is independent of the location of a receiving antenna and therefore repeated ray tracing process is unnecessary for different elements of receiving antenna array. The proposed method is also used as a substitute for measurements to extract input parameters for geometric stochastic channel models. The accuracy of the proposed method in massive MIMO channel modelling and parameters extraction is verified by comparing the results with measurements and other existing channel models.

Assessment of InSAR tropospheric signal correction methods

Tropospheric signals are considered as one of the most important performance limitations to compute the deformations caused by earthquake, subsidence, volcano, and so on using interferometric synthetic aperture radar (InSAR) technique. Various correction methods have been proposed to reduce the effect of these signals in displacement fields in previous research works. Different types of correction methods are used to estimate the tropospheric signal on InSAR observations. For this purpose, meteorological data derived from ERA-Interim (ERA-I) data, Weather Research and Forecasting (WRF) model, and Advanced Synthetic Aperture Radar/ENVISAT acquisitions are used. ERA-I reanalysis data and a locally run WRF model are also used to compute the tropospheric corrections with integral of the air refractivity method, which is called integration method. Also, the ability of ray tracing techniques to reduce the effect of the tropospheric signal in unwrapped interferogram is compared with integration method. To carry out a comprehensive study, the effects of correction methods are studied in two different areas. The results of the ray tracing methods have a significant difference with the results obtained from integration method and are more efficient when the weather condition between two satellite acquisitions is more different. The results show that the three-dimensional ray tracing method can reduce the root-mean-square error of the results up to 4.8 cm compared to the integration methods.

Physiology-like crystalline lens modelling for children

Understanding the age-dependent properties of the crystalline lenses of children is fundamental in studying the mechanism of myopic development and progression. A more realistic lens structure has more power for predicting the optical properties of the crystalline lenses. In this manuscript, a new lens model is proposed to predict the age-dependent change in the crystalline lens for children aged 6 to 15 years old. The lens model has the capability of involving most parameters measurable on the in vivo human lens. Moreover, the discrepancy of refractive indices at the equatorial edge and anterior and posterior vertices of the external lens surface is explained systematically. The analysis shows that this discrepancy has a significant role on the optical performance of the lens. The age-dependent properties are modelled based on available experimental data. The relationship between structural and optical performance is investigated with three-dimensional ray-tracing. The contributions of each parameter to the optical power and spherical aberration are revealed. The study has highlighted the importance of building physiology-like crystalline lens structure since some parameters ignored by previous studies can have a great optical impact.

Dosimetry modeling of focused kV x‐ray radiotherapy for wet age‐related macular degeneration

Wet (neovascular) age-related macular degeneration (AMD) is the leading cause of blindness in the United States. The mainstay treatment requires monthly intravitreal injection of anti-vascular endothelial growth factor (anti-VEGF) drugs, associated with multiple visits, high cost, and the risk of procedural injury and infection. Anti-VEGF drugs inhibit the formation of neovasculature but do not directly attack it. Radiotherapy can destroy neovasculature and potentially also inhibit wet-AMD associated inflammation and fibrosis not addressed by VEGF inhibitors. However, the current collimation-based radiotherapy device uses fixed 4mm beams, which are prone to overtreat or undertreat the choroidal neovascularization (CNV) lesions because of their various sizes and shapes. This simulation study evaluates personalized conformal treatment with focused kV radiation using cutting-edge polycapillary x-ray optics. Simulation of the polycapillary optics was achieved via Monte Carlo (MC)-based three-dimensional (3D) geometric ray tracing. Phase-space files modeling the focused photons were generated. The method was previously verified by phantom measurements. The ultrasmall ~0.2mm beam focal spot perpendicular to the beam direction enables spatially fractionated grid therapy, which has been shown to preferentially damage abnormal neovascular blood vessels vs normal ones. Geant4-based MC simulations of scanning while rotating beam delivery were performed to conformally treat three clinical cases of large, medium, and small CNV lesions with regular and grid deliveries. Dose delivery uncertainties due to positioning errors were analyzed, including ±0.75mm displacement in the three orthogonal directions and ±5° vertical/horizontal rotation of the eyeball. The simulated CNV treatments by 60-kVp focused x-ray beams show highly conformal delivery of dose to the lesion plus margin (0.75mm) with sharp dose fall-offs and controllable spatial modulation patterns. The 90%-10% isodose penumbra is <0.5mm. With a prescription dose of 16Gy to the lesions, the critical structure doses are well below the tolerance. The average CNV dose varies within 10% (mostly within 4%) due to 0.75-mm linear displacements and 5-degree gaze angle rotation of the eyeball. Focused kV technique allows personalized treatment of CNV lesions and reduces unwanted radiation to adjacent healthy tissue. The simulated dose distribution is superior to currently available techniques.

Simulated high frequency ray paths considering traveling ionospheric disturbances

This study presents a modified version of a classical 3-D numerical ray tracing code [originally by Jones and Stephenson (A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere. Office of Telecommunications Report 75–76, US Government Printing Office, Washington, DC, 1975)], now linked to ionosphere, neutral atmosphere, Earth’s magnetic field, and traveling ionospheric disturbances (TIDs) models. This method is applied to study the effect of TIDs on radio waves by simulating the waves’ propagation in a disturbed ionosphere. A 3-D cubic interpolation method is implemented in the ray tracing code to solve discontinuities and guarantee the ray tracing validity and accuracy under all conditions. Changes of the ground range distance (R) and the bearing angle (σ) are assessed for various simulated ray paths. A Pedersen ray case is also shown, for which small changes of signal frequency lead to enhanced variations. The study of HF ray path variations in terms of various TIDs characteristics and under different background ionospheric conditions and transmitter locations and radiation pattern can contribute to the mitigation of TIDs effects, either helping to improve existing methods or to develop new ones. The 3-D ray tracing code described and implemented in this work may well work for this purpose.