Ray Tracing Research Articles

Truncated cylindrical array plate for mid-air imaging

Abstract Mid-air imaging, a visual display technology for augmented reality (AR) that enables multiple people to view images simultaneously without the need for special eyewear, involves the formation of real images in mid-air through various optical elements. This paper presents a novel mid-air imaging optical plate, termed the truncated cylindrical array plate (TCAP). TCAP is composed of transparent cylinders with obliquely truncated ends and mirrors, specifically designed to address issues such as stray light and limited viewing angles in existing mid-air imaging optical elements. We evaluated TCAP through computer simulations and by fabricating a prototype optical element. Ray tracing simulations and stereo matching algorithms demonstrated that mid-air images are symmetrically formed on the side opposite of the light source relative to the TCAP. Furthermore, the simulations indicated that a bright, stray-light-free mid-air image could be achieved within a horizontal viewing angle of approximately $$\pm \, 40 ^\circ $$ ± 40 ∘ . Experimental evaluation using a handcrafted prototype further confirmed the plane symmetry of mid-air image formation, validating its functionality as a mid-air imaging element. The proposed method is advantageous in systems where stray light is problematic, such as mid-air image interaction systems or optical systems utilizing mid-air imaging elements.

An open source code for modeling radio wave propagation in earth’s ionosphere

We present FARR (Finite-difference time-domain ARRay), an open source, high-performance, finite-difference time-domain (FDTD) code. FARR is specifically designed for modeling radio wave propagation in collisional, magnetized plasmas like those found in the Earth’s ionosphere. The FDTD method directly solves Maxwell’s equations and captures all features of electromagnetic propagation, including the effects of polarization and finite-bandwidth wave packets. By solving for all vector field quantities, the code can work in regimes where geometric optics is not applicable. FARR is able to model the complex interaction of electromagnetic waves with multi-scale ionospheric irregularities, capturing the effects of scintillation caused by both refractive and diffractive processes. In this paper, we provide a thorough description of the design and features of FARR. We also highlight specific use cases for future work, including coupling to external models for ionospheric densities, quantifying HF/VHF scintillation, and simulating radar backscatter. The code is validated by comparing the simulated wave amplitudes in a slowly changing, magnetized plasma to the predicted amplitudes using the WKB approximation. This test shows good agreement between FARR and the cold plasma dispersion relations for O, X, R, and L modes, while also highlighting key differences from working in the time-domain. Finally, we conclude by comparing the propagation path of an HF pulse reflecting from the bottomside ionosphere. This path compares well to ray tracing simulations, and demonstrates the code’s ability to address realistic ionospheric propagation problems.

Particle-in-cell simulations of expanding high energy density plasmas with laser ray tracing

The design and analysis of high energy density (HED) laser experiments typically rely on radiation hydrodynamics simulations. However, some laser–plasma interaction regimes are not collisional and cannot be adequately modeled with hydrodynamics. For example, strongly driven magnetic reconnection and magnetized collisionless shock experiments possess extended hydrodynamic or even kinetic properties, necessitating first-principles kinetic simulations. In this paper, we present the benchmarking and first results obtained with a laser-ray-tracing and inverse bremsstrahlung absorption module implemented in the particle-in-cell code PSC. The simulation results are compared to radiation hydrodynamic simulations using the FLASH code as well as analytical estimates. We successfully benchmark the energy deposition model and overall hydrodynamic evolution of the systems. We also consider possible kinetic effects that may be expected from laser-target ablation in the HED regime, including non-local transport and two-temperature effects.

Outcomes of Zero Power Intraocular Lenses: Insights into the Keratometric Index and Axial Length.

We analyzed intraocular lens (IOL) power calculation in a series of patients with a zero diopter power implant. The idea was to bypass the Estimated Lens Plane (ELP), an important variable in normal IOL calculation. Large multi-center group practice. Retrospective, observational study. A consecutive series of patients undergoing cataract surgery after optical biometry and implantation of a zero (0.0 D) power IOL were studied. Complete biometry was performed with an optical low coherence optical biometer. The predicted refraction was calculated with and without recalibrating the axial length (AL) using a Sum-Of-Segments (SOS) approach with the Hoffer Q, Holladay 1, SRK/T, Haigis, Barrett Universal II, and Olsen formulas. A ray tracing model to back-calculate the corneal power from the observed postoperative refraction and AL was also included. In 52 eyes of 52 patients, mean prediction errors for the Hoffer Q, Holladay 1, SRK/T, Haigis, Barrett Universal II, and the Olsen formulas were +1.48, +1.15, +0.91, +0.65, +0.15 and +0.11 D respectively using standard AL and after SOS correction of the AL the mean errors changed to +1.08, +0.75, +0.52, +0.26, -0.25, and -0.27 D respectively. The mean back-calculated corneal power was 1.25 D lower than the mean keratometer reading using the standard keratometric index of 1.3375 and corresponded to an effective index of 1.328. The hyperopic error commonly seen in highly myopic eyes with classical thin-lens formulas is only partly corrected by SOS recalibration of the AL. We suggest the source of the residual error is an incorrect keratometric index.

Latitude- and temperature-based optimization of beam-down solar central receiver systems

Optical and energetic characteristics are studied for beam-down solar central receiver (SCR) systems. The geometrical configuration of the beam-down SCR system is optimized for maximum solar-to-thermal conversion efficiency, taking into account the effects of latitude and receiver temperature. System characterization and optimization are undertaken with a numerical model combining an in-house developed Monte-Carlo ray tracing optical model and a simplified receiver heat transfer model. A differential evolution (DE) algorithm is applied to automate the optimization process. Parallel computing using OpenMP is employed to reduce the computational time. From the simulations, the optimized optical configurations of the beam-down SCR systems under the specified conditions of receiver temperature and latitude are discovered. Under the assumptions made in this study, it is found that the acquired radiative power at the receiver aperture from the optimized systems ranges from about 35 MW to 45 MW, and the eccentricity of the hyperboloidal tower reflector is between 1.6 and 1.7. The maximum achievable solar-to-thermal conversion efficiency decreases from 0.43 to 0.36 when an SCR system operated at 1,800 K is moved from latitude 0° to 50°, mainly due to the increased cosine and shading losses with higher latitudes. In addition to reduced efficiencies, the heliostat field gets larger for higher latitudes, worsening its techno-economic performance when considering the cost per unit of useful energy output. A clear trend of efficiency decrease with the higher receiver temperature is demonstrated, resulting from the significant increase of receiver radiative emission losses with the temperature.

Numerical investigation of infrared imaging of multi-UAV formation under cloud and rain weather conditions

Infrared imaging is essential for detecting multiple unmanned aerial vehicle (UAV) targets detection to capture flight altitude and behavior. This study focused on a typical stealth UAV formation with a flying-wing configuration. Considering the attenuation effects of clouds and rain on the infrared spectrum, a ground-based infrared imaging algorithm was developed. Infrared radiation imaging was conducted using the apparent ray tracing method and mesh clipping technology. The infrared radiation intensity distribution of the UAV formation target within the 8.0–12.0 μm band was calculated, and infrared thermal images incorporating the occlusion effect were obtained. The results showed that the radiance of the multi-UAV formation was approximately 8.0 × 10−5 W/Sr, which was 103–104 orders of magnitude lower than that under standard atmospheric conditions under cloudy weather conditions. The infrared radiance was approximately 1.7 × 10−5 W/Sr, which was 104–105 lower than that under standard atmospheric conditions under rainy weather conditions.

Ultra-small spectral confocal displacement sensors based on GRIN lenses

Spectral confocal displacement sensors have been widely used in various precision measurement fields such as aerospace, biology, and medicine due to their advantages of high accuracy, non-contact, fast response, and high resolution. In this paper, a new method of spectral confocal measurement of a ultra-compact probe based on a GRIN lens, to our knowledge, is proposed. Through ray tracing analysis, it is found that the axial dispersion is close to linear in a specific wavelength range, and a theoretical model of spectral confocal measurement with the GRIN lens is deduced. A GRIN lens with a diameter of 1 mm and a length of 6.59 mm was prepared by the ion-exchange method and used as a dispersive objective lens in a homemade spectral confocal measurement system. The system was calibrated to have an axial measurement range of 440 µm, an axial resolution better than 0.5 µm, a maximum standard deviation of 0.749 µm, and a relative error of less than 2%. In addition, the system was successfully applied to 3D surface contour scanning, demonstrating its potential for 3D scanning. The results show that the system has the advantages of simple structure, low cost, easy integration, and excellent performance.

Simulation of ultra-fast structured illumination in single-photon sensitive single-pixel lidar

This study presents a novel single-pixel imaging lidar system utilizing individually addressable VCSEL arrays and single-photon detection for high-speed structured illumination and accurate reflectance estimation. VCSEL arrays as spatial light modulators offer modulation rates several orders of magnitude higher than conventional DMD-based systems. This capability allows for more measurements, reducing the effect of noise and enabling accurate angle of incidence estimation at the level of individual points, without the need for separate surface normal estimation from dense point clouds. The research developed a detailed measurement model and inverse rendering workflow, which were evaluated using ray tracing simulations that generated full-waveform intensity data. The proposed method achieved millimeter-level precision in range measurements and accurate reflectance estimates by leveraging local angle of incidence information. Future research may explore additional applications of the local angle of incidence information and further validate the model in real-world scenarios.

Ion momentum mapping in photodissociation and Coulomb explosion events using ion time-of-flight analyzers

Abstract Modern light sources such as free electron lasers allow for tracking photoinduced events with an unprecedented accuracy. Ion spectroscopy is a particularly useful tool, revealing, e.g., momentum correlations in dissociation and Coulomb explosion patterns. Determining ion momentae and their relationship with the highest achievable accuracy is therefore very valuable. Here, we develop a systematic approach of accurate ion momentum determination in Wiley-McLaren type ion time-of-flight spectrometers taking into account also field penetration effects. The developed analytical formulae at various level of approximation are compared with ray tracing simulations and the effects are also illustrated on an experimental example.

Spectral shifts in partially coherent light beams passing through a crystalline human eye lens

Our objective is to quantify the spectral changes occurring in partially coherent light beams as they interact with the crystalline lens of the human eye. The study reveals a significant alteration in the wavelength of random light beams as they traverse through the human eye. The methodology comprises three key components: the ABCD matrix elements of the lens, the cross-spectral density matrix of the light beam, and the spectral shifts in the beam during propagation. Following an initial examination of how the crystalline human eye lens responds to stochastic light, we can now analyze the interaction of various types of light with the eye lens. The entering light is broadband, exhibiting a range of coherence values from incoherent to fully coherent. By employing the diffraction theory of optics alongside ray tracing methods, we observe wavelength shifts in partially coherent light passing through the human eye lens. The study involves directing unpolarized random light with a cross-sectional radius of approximately 0.3 mm numerically to the lens surface, situated at the minimum pupil radius of around 0.5 mm. The propagation is then analyzed over a distance of 17 mm after the lens, representing the typical length of the vitreous humor. Numerical plots demonstrate a wavelength shift in the incident light (with a Gaussian profile). In summary, our findings indicate that the correlation effects of nearly natural light on the gradient index of the human eye lens lead to a notable spectral shift.

Ray tracing simulation and experimental validation for millimeter-wave massive MIMO systems

Abstract Accurate channel characterization is extremely helpful in channel estimation, channel coding, and many other parts of communication system design and can effectively reduce overhead. Ray tracing (RT) shows accurate channel reconstruction for specific maps, but the multipath propagation in indoor scenes is far more complex than in outdoor scenes leading to a challenge for RT. This work presents and validates an RT tool for a massive multiple-input multiple-output (MIMO) system in the millimeter-wave frequency bands with the associated channel beamforming algorithm and provides ideas for channel estimation algorithm in subsequent MIMO systems. The impact of the order of interactions, e.g. reflections and diffractions on the channel impulse response reconstruction are analyzed in the RT simulation. The comparison between RT simulated and measured results shows a reasonable level of agreement. The presented RT tool that can provide complete and accurate channel information is of high value for the design of reliable communication systems.

Correction of Wavefront Distortion in Common Aperture Optical Systems Based on Freeform Lens

The common aperture optical system enhances light utilization efficiency during the imaging process by utilizing a single shared aperture. This approach not only facilitates independent synchronous multi-band imaging across various applications but also reduces the complexity, size, and cost of optical systems. However, conventional common aperture optical systems typically employ inclined plates or prisms for spectral splitting, which can introduce wavefront distortion in the transmission light path, an issue that is particularly problematic in imaging systems with a large field of view. In this work, we propose employing a freeform lens to correct wavefront distortion arising from imperfections within an optical system. We present a design methodology for the freeform lens based on ray tracing techniques. The application of this freeform lens effectively mitigates wavefront distortion in an infrared dual-band composite detection system, resulting in commendable optical performance across both mid-infrared and far-infrared bands.

Correction: Grid-induced bounding volume hierarchy for ray tracing dynamic scenes

Correction: Grid-induced bounding volume hierarchy for ray tracing dynamic scenes

Design and Evaluation of Noise Simulation Algorithm Using MATLAB Ray Tracing Engine for Noise Assessment and Prediction

The Malaysian Department of Occupational Safety and Health (DOSH) reported that noise-induced hearing loss (NIHL) accounted for 92% of occupational diseases in 2019. To address this, accurate risk assessment is crucial. The current noise evaluation methods are complex and time-consuming, relying on manual calculations and field measurements. An easy-to-use, open-source noise simulator that directly compares the output with national standards would help mitigate this issue. This research aims to develop an advanced noise evaluation tool to assess and predict unregulated workplace noise, providing tailored safety recommendations. Using a representative plant layout, the Sound Pressure Level (SPL) is calculated using MATLAB’s ray tracing propagation model. The model simulates all possible transmission paths from the source to the receiver to derive the resultant SPL. A noise simulation application featuring a graphical user interface (GUI) built with MATLAB’s App Designer (version: R2024a) automates these computations. The simulation results are validated against the DOSH’s safety standards in Malaysia. Additional safety metrics, such as the recommended maximum exposure time and the required Noise Reduction Rating (NRR) for hearing protection, are calculated based on the SPLs for hazardous locations. The simulation algorithm’s functionality is validated against manual calculations, with an average deviation of just 3.06 dB, demonstrating the model’s precision. This tool can assess and predict indoor noise levels, provide information on optimal exposure limits, and recommend necessary protective measures, ultimately reducing the risk of NIHL in factory environments. It can potentially optimise plant floor operations for existing and new facilities, ensuring safer shift operations and reducing worker noise hazard exposure.

Depth of focus as a function of spherical aberration using adaptive optics in pseudophakic subjects.

To measure visual acuity at three different defocus planes in pseudophakic subjects with varying levels of spherical aberration induced by an adaptive optics visual simulator. The study aimed to simulate Extended Depth of Focus (EDOF) intraocular lenses (IOLs). Private hospital (IMO, Barcelona, Spain). Observational case series; modelling theory. Through-focus visual acuity was measured in 26 pseudophakic subjects (age 63 ± 10 years old) with an adaptive optics visual simulator optimized for clinical use (VAO, Voptica SL, Murcia, Spain). Measurements were made under five different conditions of induced negative spherical aberration: 0, -0.07, -0.15, -0.23 and -0.30 μm (pupil diameter: 4.5 mm). Results were also modelled using ray tracing simulations. On average, depth of focus was extended when spherical aberration increased from -0.07 to -0.15 μm (4.5 mm pupil diameter). Some indivisuals (27%) experienced improved depth of focus with higher magnitudes of spherical aberration, while others (23%) exhibited no benefit from increased (negative) SA, as visual acuity dropped below acceptable levels. Depth of focus calculations based on ray tracing showed general agreement with the measurements. The visual conditions of EDOF IOLs were artificially recreated in a population of pseudophakic patients implanted with a monofocal IOL. The variability seen across subjects in visual acuity at different defocus planes suggests that visual simulators might be capable of screening subjects for suitability and tolerability of these advanced technology lenses.

Efficient evaluation of the Jacobian in the damped least-squares method for optical design problems using algorithmic differentiation.

The fast evaluation of the Jacobian is an essential part of the optimization of optical systems using the damped least-squares algorithm. While finite differences provide an intuitive way to approximate derivatives, algorithmic differentiation is a technique to evaluate them exactly. However, applying algorithmic differentiation to a ray tracing routine for optical systems with many parameters is computationally expensive, where the main costs are caused by the determination of the ray-surface intersection. To overcome this disadvantage, we present a mathematical analysis of the ray-surface intersection and its efficient differentiation in both forward and reverse mode algorithmic differentiation. Futhermore the structure of the optimization variables and operands is exploited to derive a method that allows computation of the Jacobian in the same order of computational complexity as the primal ray trace. The method is successfully tested for a rotationally symmetric lens system and a freeform design task.

Evaluation of the incidence of optical and physical characteristics on the performance of a Fresnel Linear Collector prototype

This article aims to evaluate the optical and thermal behavior of a small Fresnel linear concentrator prototype developed under the appropriate technology paradigm. The system was developed by the Energy, Automation and Control Systems Research Group of the Technological Units of Santander, Colombia for water heating. The study of the device was developed from a series of simulations that took into account the optical and thermal factors of the real system, and a series of alternative scenarios that seek to improve the performance of the device were evaluated. The simulation process was carried out by applying the "TRNSYS" Software in order to study the dynamic behavior of the concentrator and the "Soltrace" Software applying the Monte Carlo Ray Tracing method. The results obtained showed that the improvement scenarios proposed to evaluate the optical characteristics of the primary reflection system do not significantly increase the performance of the device, while the optical characteristics applied to the secondary reflection system do reflect a significant in-crease. Finally, the variation of flow and the area of the preheater show a direct relationship in performance, reaching values that predict the ideal value of the operating variable.

Curvature Determination Method for Diverging Acoustic Lens of Underwater Acoustic Transducer.

Underwater acoustic transducers need to expand the coverage of acoustic signals as much as possible in most ocean explorations, and the directivity indicators of transducers are difficult to change after the device is packaged, which makes the emergence angle of the underwater acoustic transducer limited in special operating environments, such as polar regions, submarine volcanoes, and cold springs. Taking advantage of the refractive characteristics of sound waves propagating in different media, the directivity indicators can be controlled by installing an acoustic lens outside the underwater acoustic transducer. To increase the detection range of an underwater acoustic transducer in a specific marine environment, a curvature-determining method for the diverging acoustic lens of an underwater acoustic transducer is proposed based on the acoustic ray tracing theory. The relationship equation between the original directivity indicators of the underwater acoustic transducer and the emergence angle in the specific environment is constructed, and the slope of the acoustic lens at different positions of the underwater acoustic transducer is obtained by a progressive solution. Then, the least squares polynomial fitting of the acoustic lens slope at all the refractive positions is carried out to obtain the optimal curvature of the acoustic lens. Experiments are designed to verify the effectiveness of the curvature determination method for the diverging acoustic lens of an underwater acoustic transducer, and the directivity indicators of acoustic lenses under different materials and different marine environments are analyzed. The experimental results show that the acoustic lens can change the directivity of the underwater acoustic transducer without changing the acoustic unit array, and the curvature of the acoustic lens directly affects the directivity indicators after refraction, so the method proposed in this paper has important reference value for determining the optimal shape of the diverging acoustic lens.

Design and Fabrication of Orthokeratology Lens with Multi-Linear and Spherical Aberration Corrected for Myopia Control

Myopia, an increasingly grave public health concern, necessitates the implementation of various techniques for its management. These techniques predominantly comprise the employment of spectacles correction, orthokeratology (ortho-k), and soft bifocal and multifocal lenses. In the present study, a pioneering polish-free ortho-k lens was devised, featuring two reverse lines and three alignment lines, which, respectively, expedite the shaping process and enhance centration. The structural blueprint of the ortho-k lens, along with the simulation of fluorescence staining, was executed employing the FocalPoints software V7.0 (Advance Medical, Milan, Italy). Subsequently, lens aberration elimination was accomplished through ray tracing utilizing ZEMAX software V13.0 (Focus Software, Wixom, MI, USA). The fabrication of the lens was carried out via high-precision lathe turning using the UPC 100 Vision instrument (SCHNEIDER, Ratingen, Germany). The power profile of the ortho-k lens was measured using the CONTEST 2 apparatus (ROTLEX, Omer, Israel). The surface quality was observed under a 200× microscope (ZEISS, Oberkochen, Germany). The fitting of the lens was assessed through the utilization of both Slit-lamp microscopy (MediWorks, Shanghai, China) and Corneal topographer (Medmont E300, Melbourne, VIC, Australia)

Simulation of the optical caustics associated with the secondary rainbow for tilted oblate droplets illuminated by a Gaussian beam

In this study, vector ray tracing is used to compute optical caustic associated with the secondary rainbow for an oblate spheroidal droplet illuminated by a Gaussian beam. The optical caustics are classified as rainbow fringes and hyperbolic umbilical fringes. By comparing with the optical caustics for droplet with parallel beam illumination, the influence of the Gaussian beam on the optical caustics is studied. The curvature of the rainbow fringes and the horizontal and vertical location of the cusp caustics are discussed for droplets with different droplet-to-beam ratios (i.e. the ratio of the equatorial radius of the droplet to the waist radius of the Gaussian beam). Furthermore, the optical caustics of tilted droplets were investigated and compared with those of the aligned droplets, based on the boundary of outgoing rays. The long-term aim is to develop a novel method for measuring the aspect ratio of oblate droplets with arbitrary orientation.