Geometrical Optics Ray Tracing Research Articles

Optimization Design of Heliostat Field Based on Biomathematical Models

The optimal design of heliostat field in solar power generation device is studied Heliostat field generates high temperature by focusing the sunlight reflected from the mirror surface, thus pushing the turbine to generate electricity. In order to improve the efficiency of power generation, this paper optimizes the parameters of heliostat field, establishes a single-objective optimization model, and uses mixed strategy whale optimization algorithm to solve it. Through geometric optical analysis and ray tracing model, the optical efficiency of heliostat field and the annual average output thermal power per mirror area are calculated. Finally, through the discussion and analysis of the model, the optimization design method is evaluated

One-Sixteenth Spherical Homogeneous Dielectric Lens Antenna Using Partially Reflective Surface for Size Reduction and High-Gain Radiation

Size reduction of a 1/16 spherically sectoral homogeneous dielectric lens antenna is developed in this letter by integrating a planar partially reflective surface (PRS) to produce high-gain radiation. Such a PRS, optimized by a full-wave simulator and the geometrical optics (GO) ray tracing method, has replaced the external longitude portions of ground planes in the original sectoral lens antenna to make an aperture size of 11 × 15 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which reduces the radius of the spherical dielectric lens by more than 33.3% (from 6 to 4 cm). The overall antenna length is reduced by 56% (from 15 to 6.59 cm). The PRS plate with a ground plane is designed by ray tracing to reach a relatively uniform field distribution on the PRS aperture for high-gain radiation. An antenna gain of 18.94 dBi has been achieved at 9 GHz from a sectoral lens fabricated by a 3-D printer using ABS (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> = 2.429) material. The design was well validated by both numerical simulations and measurements with good agreement.

Identify the limits of geometric optics ray tracing by numerically solving the vector Kirchhoff integral.

The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p2 times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.

ECRad: An electron cyclotron radiation transport solver for advanced data analysis in thermal and non-thermal fusion plasmas

We present a code for the large-scale data analysis of electron cyclotron emission (ECE) measurements from magnetized plasmas called ECRad – the Electron Cyclotron Radiation transport model for Advanced Data analysis. Its key features are low computational cost, high robustness and the capability to predict ECE spectra of plasmas with non-thermal electron populations. This is accomplished by combining the absorption coefficient given by Albajar et al. (2007) and a corresponding emissivity for the radiation transport with geometrical optics ray tracing for the computation of the diagnostic line of sight. Another important aspect of ECRad is that it has passed a large amount of verification tests against real measurements by conventional, oblique and ECE imaging diagnostics.This paper explains the physical model of ECRad and its implementation. Furthermore, it is discussed how the code can be used for the inference of the electron temperature from ECE measurements and how an oblique ECE diagnostic can be cross-calibrated with ECRad.

Scattering of light by dense particulate media in the geometric optics regime

We present a hybrid radiative transfer geometric optics approximation to model multiple light scattering in arbitrary finite discrete random media in the geometric optics regime. In the hybrid model, the medium is divided into a mantle composed of discrete particles and into a diffusely scattering core. In the mantle, multiple scattering is handled by using a ray-tracing algorithm with the generalized Snel’s law for inhomogeneous waves, whereas, in the core, ray tracing with diffuse scatterers is incorporated to approximate multiple scattering and absorption. The extinction distances required to compute the scattering in the core are derived numerically by tracing the distances of the scattering and absorption events instead of using the classical extinction mean free path length. We have written a new framework that can treat arbitrary meshes consisting of watertight surface meshes with multiple diffuse scatterers and refractive indices. Comparison between the “ground truth” obtained from pure geometric optics ray tracing, the solutions obtained by using radiative transfer, and the hybrid model show that the hybrid model can produce better results, particularly, if a densely-packed medium is studied. In the future, the new approximation could be used to solve light scattering from larger media, such as asteroid surfaces, that are out of reach for the pure geometric optics methods due to their computational complexity.

Simulating schlieren and shadowgraph images from LES data

Geometrical optics ray-tracing is used to derive schlieren and shadowgraph images from large-eddy simulation (LES) data of a jet in supersonic crossflow and to compare with experimental data. Including the components of the optical system that forms the image in the simulation is found to be important. The technique produces images that replicate flow physics more faithfully than straight-line path integration and other techniques, and more efficiently than physical-optics techniques. Applications of these simulated images are demonstrated in supersonic flows. Time-correlated pairs of shadowgraph images taken from the LES using this technique are used in conjunction with an image-correlation velocimetry technique to compare the estimated convection velocity field in the LES to that of experiments of the same flow. Agreement between the two is good with a maximum variance of 5% by some metrics. This technique can aid in the validation of LES results, allowing quantitative comparison between experiment and simulation, and to extract information unattainable by experiment alone. Comparisons of simulated and experimental jet penetration into the supersonic freestream are also made.Graphic abstract

Geometrical-optics computer model of metal-knitted mesh for calculations of solar pressure on space deployable antenna reflectors.

A novel computer 3D model is presented for calculations of optical parameters (transmittance, reflectance, and absorbance) of a metal-knitted mesh textile as a structural element of deployable antenna reflectors for space satellites. The model is based on geometrical-optics ray tracing upon diffuse scattering of a broadband light source (Sun) at a complex knitted mesh structure with different inclinations to the radiative source. The proposed computer model is built for the special type of metal-wire textile (two-bar large void tricot) possessing extremely high transmittance and is verified by comparison with the experimental measurements of light scattering parameters of real antenna mesh samples of data-relaying satellites (Russian series "Loutch"). The model is used for calculations of solar radiation pressure exerted on a knitted mesh antenna reflector and gives the maximal pressure value of about 0.28 μN/m2.

Numerical description of mode coupled waves in inhomogeneous magnetized plasmas

Geometrical optics (GO) ray tracing has been widely used for a description of electron cyclotron resonance waves in inhomogeneous magnetized fusion plasmas. However, this reduced approach is not correct in sufficient low density plasmas with a sheared magnetic field, where mode coupling between two electromagnetic-like cold plasma modes can occur. Here, we extend a ray tracing method based on the first-order theory of extended geometrical optics (XGO), which captures mode coupled complex amplitude between O and X mode along the ray trajectory. In our approach, reference ray is calculated with ray equation to satisfy the lowest-order part of XGO theory and an evolution of complex amplitude profile along the reference ray is calculated with partial differential equation derived from first-order terms. Calculation results performed by extended ray tracing are in good agreement with 1D full wave analysis. By introducing second-order terms into our numerical approach, diffraction will be treated.

Phase-Gradient Meta-Dome for Increasing Grating-Lobe-Free Scan Range in Phased Arrays

This paper presents a simple and effective way to increase the scan range of phased array antennas by using a metasurface (MTS) curved dome. The technique is based on a phase-gradient passive MTS that deflects the incident rays coming from the array aperture, and on a predistortion of amplitude and phase applied to the original phased array. We assume, therefore, to have at disposal an array capable of electronic beam scanning over a limited angular range with control of amplitude and phase. Geometrical optics ray tracing is used for the design of the metadome and physical optics for the analysis. For the sake of simplicity, the idea is illustrated here for a 2-D scan case; however, the extension to full 3-D scanning appears to be straightforward.

Computational Tools and Approaches for Design and Control of Coating and Composite Color, Appearance, and Electromagnetic Signature

The transport behavior of electromagnetic radiation through a polymeric coating or composite is the basis for the material color, appearance, and overall electromagnetic signature. As multifunctional materials become more advanced and next generation in-service applications become more demanding, a need for predictive design of electromagnetic signature is desired. This paper presents various components developed and used in a computational suite for the study and design of electromagnetic radiation transport properties in polymeric coatings and composites. Focus is given to the treatment of the forward or direct scattering problem on surfaces and in bulk matrices of polymeric materials. The suite consists of surface and bulk light scattering simulation modules that may be coupled together to produce a multiscale model for predicting the electromagnetic signature of various material systems. Geometric optics ray tracing is used to predict surface scattering behavior of realistically rough surfaces, while a coupled ray tracing-finite element approach is used to predict bulk scattering behavior of material matrices consisting of microscale and nanoscale fillers, pigments, fibers, air voids, and other inclusions. Extension of the suite to color change and appearance metamerism is addressed, as well as the differences between discrete versus statistical material modeling.

Physically-based simulation of rainbows

In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops.

New regime map of the geometric optics approximation for scattering from random rough surfaces

The electromagnetic wave scattering from random roughness surfaces is a technologically important but challenging problem. There is a significant amount of interest in understanding the radiative properties of the rough surfaces for diverse applications. On one end, the rigorous models require the solutions of complex formulations of the Maxwell's equations or rely on various numerical schemes, which typically are computationally intensive. On the other hand, it has been found that the geometric optics (GO) ray tracing approximation method produces reasonably accurate radiative property predictions in some cases and with little computational effort. However, the latter ignores the wave interference and polarization effects, which are important when the wavelength is on the same order or larger than the geometrical length scale. It is therefore important to quantify the accuracy of the GO approximation. This study reports a new regime map based on the comparisons of the GO and finite-difference time-domain solutions.

Implementation of physical optics analysis of spiral antenna radiations in the presence of Bor radome structure for the application of direction finding

A practical physical optics (PO) implementation procedure is employed to study the radiations of multi‐arm spiral antennas in the presence of a body of revolution (BOR) radome structure in direction finding applications. This procedure potentially simplifies the geometrical optics ray tracing procedure based on characteristics of spiral antennas, which is required to define the equivalent currents of PO, and provides efficient formulations to compute the radiation fields due to PO currents that are equivalent to the radiation of spiral antennas in the presence of the same type radome structure.

Geometric optics-based design of laser beam shapers

When diffraction effects are not important, geometrical optics (ray tracing, conservation of energy within a bundle of rays, and the constant optical path length condition) can be used to design laser beam shapers by solving beam shaping equations or by optimizing a beam shaping merit function for the configurations, including aspheric ele- ments or spherical-surface gradient-index lenses, which are required to change the input irradiance and phase profile into a more useful form. Geometrical optics-based methods are presented for shaping both rota- tionally and rectangular symmetric laser beam profiles. Solutions of the beam shaping equations are presented for a two-plano-aspheric lens system for shaping a circular symmetric Gaussian beam into a top-hat output beam profile and a two-mirror system with no central obscuration for shaping an elliptical Gaussian input beam into a Fermi-Dirac output beam profile. © 2003 Society of Photo-Optical Instrumentation Engineers.

Beam tracing in inhomogeneous anisotropic plasmas

An asymptotic method for solving the wave equation in the short-wavelength limit is presented. This method, called beam tracing, takes into account the wave properties, i.e., diffraction and interference. It reduces the full wave equation to a set of ordinary differential equations. In this respect, it differs from all other asymptotic techniques describing diffraction which end up with much more complicated partial differential equations. The resulting system of beam tracing equations is expressed in terms of the same Hamiltonian function as in geometric optics (ray tracing) and, similar to the ray tracing, allows powerful numerical solving algorithms. Thus the beam tracing combines the simplicity of ray tracing with a description of the wave phenomena, which are not included in the ray tracing. The beam tracing technique provides an efficient tool for calculation of wave fields in all problems where the short-wave approximation is applicable such as rf heating, current drive and plasma diagnostics with microwave beams.

SABOR: description of the methods applied for a fast analysis of horn and reflector antennas

The program presented in this paper is intended to provide a valuable aid for teaching antennas to electrical engineers, and to provide fast and accurate pre-designs for professionals. This paper covers the theory and numerical techniques used in SABOR. In summary, this program computes the radiated field of an aperture antenna (horn or reflector), using a common engine based on the Gauss-Legendre quadrature method for evaluating the radiation integrals. For horn, the aperture fields are the usual dominant modes of the feed waveguide, with a quadratic phase correction. For reflectors, the aperture fields are computed using geometrical optics ray tracing from the feed horn. Also, equivalent-reflector concepts are applied for dual-reflector antennas. The paper includes some examples to demonstrate the most important features of the program.

Predicting outdoor noise propagation

The propagation of sound outdoors involves spreading, absorption, interaction with the surface, refraction, diffraction, and scattering. Although there is still no widely accepted prediction scheme that includes all of these effects, the understanding of individual phenomena and contribution to transmission loss along the propagation path has steadily advanced. Transmission loss due to atmospheric absorption is standardized. The effects of real ground surfaces are predictable for a wide range of surfaces. Modern numerical techniques described in a different special session allow one to predict refraction and diffraction in an inhomogeneous atmosphere. These predictions are far superior to simple geometrical optics ray tracing at moderate and low frequencies. Diffraction by barriers of regular geometry can be predicted analytically but irregular shapes require further developments. Scattering by atmospheric turbulence as well as foliage requires additional work prior to providing engineering estimates well based upon experiment.

Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics

Mie theory and geometrical-optics ray tracing are used to obtain the distribution of electric energy density inside a nonabsorbing micrometer-sized sphere illuminated by a polarized plane wave. The Mie solution shows the multiply reflected geometrical-optics rays inside a sphere having a diameter of ~ 150 free-space wavelengths (size parameter = circumference/wavelength = 500). The geometrical-optics result shows the major features of the Mie solution and provides a physical interpretation of the electromagnetic interactions that result in the observed energy-density distributions. Both solutions show internal on-axis energy-density maxima inside the shadow surface of the sphere. The region of greatest enhanced energy density is approximately one internal wavelength in diameter and approximately twenty internal wavelengths in length.

Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer

High-frequency propagation of electromagnetic wavefields from an extended planar aperture distribution through a complicated environment is addressed. Geometric optical ray tracing provides a versatile approximate approach to the class of problems, but it fails in transition regions surrounding shadow boundaries and caustics. The uniformity required there can be established by field tracking with Gaussian beams. The basic theory is summarized and applied to the two-dimensional test problem of transmission of radiation from a finite one-dimensional plane aperture through a planar dielectric layer. For a truncated uniform or focused aperture illumination, tracking the edge or caustic transition regions through the layer when it is located within the Fresnel zone of the aperture poses a problem of substantial complexity. It is shown that narrow-waisted beams, which can be propagated in their far zone as complex ray fields, reconstruct the correct transmitted field in these cases, as established independently by numerical evaluation of an exact spectral integral.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ray analysis of two-dimensional radomes

The fields transmitted from a line source through a two-dimensional curved dielectric layer of variable thickness are constructed by geometric-optical ray tracing that accounts for multiple reflections on the concave side, where the source is located, as well as for reflections between the layer boundaries. Moreover, internally trapped rays, excited by evanescent tunneling, are included when source and observer are near the layer boundaries but laterally displaced along it. By applying Poisson summation to the ray series, the multiple reflected contributions, for weakly tapered configurations, can be summed to yield trapped and leaky local modes guided along the layer, as well as a ray field that incorporates a plane layer transmission coefficient, with curvature and slope corrections, instead of the conventional coefficients for individual boundaries. Detailed calculations are performed for the special cases of a circularly curved layer of constant thickness and a tapered layer with nonparallel plane boundaries. For the former, the various ray-optically derived solutions agree completely with those obtained from a rigorous analysis. For the latter nonseparable configuration, no rigorous solution is available. With direct summation of conventional ray fields taken as a reference, extensive numerical results demonstrate the economies effected by the collective ray formulation and the importance of including the curvature or slope corrections in the equivalent slab transmission coefficients.