Standard Ray Tracing Research Articles

Deriving spectra from colors and rendering light interference

A new method for transforming colors into spectra, which we applied to rendering light interference using a standard ray tracer, significantly enhances color-based rendering software and graphics platforms.

Analysis of the fringe field region of magnetic quadrupole lenses: field measurements and ion optical calculations

An investigation into the minimisation of the duodecapole fringe field components of magnetic quadrupole lenses has been conducted at Melbourne. As part of this program, a detailed field mapping of the fringe field region of the Melbourne magnetic quadrupole lenses has been conducted (G.R. Moloney, D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B 54 (1991) 24). The field mapping technique measures the radial magnetic field component, B r over the three cylindrical coordinates, r, α and z. We have also conducted a program of modifying the pole tip termination of the lenses to reduce the duodecapole field components. Complete magnetic field measurements for the modified lens pole tips have been presented previously (G.R. Moloney, D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B 77 (1993) 35–38). This paper presents an Ion Optical analysis of the effects of the fringe field components on the beam optics of the Melbourne Microprobe systems. The optical effects are calculated with a new computer code developed at Melbourne. Standard numerical ray tracing is performed utilising Runge-Kutta techniques.

Self-diffraction effects of electron cyclotron Gaussian beams on noninductively driven current in the International Thermonuclear Experimental Reactor tokamak

The role of diffractive effects not included in standard ray tracing calculations on electron cyclotron current drive (ECCD) is analyzed for an International Thermonuclear Experimental Reactor (ITER) [P. H. Rebut, Fusion Eng. Design 30, 85 (1995)] tokamak configuration, using a quasioptical approach. The power absorbed and the current generated by highly collimated Gaussian beams of electron cyclotron waves (ECW) is calculated using realistic ITER equilibria, relativistic treatment of the wave propagation, and of the driven current, expressed in the formalism of 13 moments transport equations. Effects of beam diffraction on the generated current profile are found to be non-negligible, particularly for off-axis power deposition.

General near‐zone light source model and its application to computer‐automated reflector design

The goal of this work is to develop a general light source model that is physically accurate, intuitively descriptive, computationally convenient, and applicable to real sources. It solves two major problems in illumination optics: near zone general extended light source charac- terization for accurate image rendering and ray tracing, and computer- automated reflector design using the resulting near-zone model. The main approach is to combine measurements with Fourier analysis, using judiciously chosen coordinate systems and orthogonal fitting functions. This has several advantages over standard ray tracing: it provides for natural data compression and interpolation; it bypasses the problem of computing the radiance distribution of a real source by using actual pin- hole CCD camera measurements; and it eliminates the computationally intensive ray-filament intersection problem by transforming the source into an equivalent nonuniform spherical radiator. A method for treating the occlusion of rays by the extended filament, with only spherical inter- section calculations, is also discussed. The application of the method is illustrated by the problem of designing a smooth specular reflector to cast a desired intensity distribution on a distant screen for a given source. The problem becomes a straightforward numerical optimization of the perturbations to a base reflector shape. An algorithm to provide a first guess for the perturbations based on the shape of the image perim- eter is also described. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: near-zone light source model; computer-automated reflector de- sign.

An automated ray method for diffraction modelling in complex media

SUMMARY We present the computational concept and first results of an automated 2-D ray-tracing algorithm which combines the standard ray method with the method of edge waves and paraxial ray tracing. Reliable ray synthetic seismograms are obtained for subsurface structures of high complexity. Both diffracted and multiple diffracted arrivals are automatically computed, complementing all types of primary arrivals (reflected, multiple reflected, converted waves, etc~} where geometric shadow zones are caused by edges (inhomogeneities) in the subsurface model. The method of computation can be summarized as follows: (1) during standard ray tracing, properties of central and paraxial rays are computed for a set of neighbouring rays. (2) Diffraction points (edges) are identified by comparing the amplitude and traveltime differences of neighbouring rays with the corresponding values of their paraxial approximation. ~3) Detected edges are used as source points for diffracted rays. ( 4) Repetition of (1)-(3) for diffracted rays allows computation of multiple diffractions ('diffracted diffractions'). (5) The amplitude decay of diffracted arrivals is computed according to the theory of edge waves. Its critical variables are expressed in terms of second-order paraxial traveltimes. The method is demonstrated for a simple and complex synthetic model and a real data complex

Stereoscopic ray-tracing

In this paper, we describe a method to create an approximate ray-traced stereoscopic pair by transforming a fully raytraced left-eye view into an inferred right-eye view. Performance results from evaluating several random scenes, which indicate that the second view in a stereoscopic image can be computed with as little as 5% of the effort required to fully ray-trace the first view, are presented. We also discuss worst-case performance of our algorithm and demonstrate that our technique is always at least as efficient as two passes of a standard ray-tracer.

The propagation of low‐frequency whistler waves driven by ion beams in the magnetotail

The existence in the Earth's magnetotail of magnetic field and plasma density inhomogeneities can influence the propagation of electromagnetic waves in the lobe and plasma sheet. This is important in understanding the origin of magnetic noise bursts that are observed near the neutral sheet since the waves may not necessarily be generated locally but can be excited in other regions of the tail and propagate towards the central plasma sheet due to the presence of the global inhomogeneities. In this paper the generation and propagation of low‐frequency whistler waves excited by ion beams in the plasma sheet boundary layer is examined. The trajectories of waves that are generated inside the plasma sheet boundary layer are followed using standard ray tracing techniques assuming a Harris‐type neutral sheet magnetic field profile and with the density chosen such that the total pressure remains constant. The wave energy is calculated along the wave path taking into account growth due to the ion beam while the wave is in the plasma sheet boundary layer, and damping due to resonant interactions with the background plasma. Results show that the electromagnetic waves are guided towards the central plasma sheet by the plasma gradients but are damped out before reaching the neutral plane itself due to Cerenkov resonance with the hot central plasma sheet background ions. The amplitudes and final positions of the waves depend on the temperature of the background plasma, the ion beam drift speed, and the ion beam thermal speed.

Fresnel volume ray tracing

The concept of “Fresnel volume ray tracing” consists of standard ray tracing, supplemented by a computation of parameters defining the first Fresnel zones at each point of the ray. The Fresnel volume represents a 3-D spatial equivalent of the Fresnel zone that can also be called a physical ray. The shape of the Fresnel volume depends on the position of the source and the receiver, the structure between them, and the type of body wave under consideration. In addition, the shape also depends on frequency: it is narrow for a high frequency and thick for a low frequency. An efficient algorithm for Fresnel volume ray tracing, based on the paraxial ray method, is proposed. The evaluation of the parameters defining the first Fresnel zone merely consists of a simple algebraic manipulation of the elements of the ray propagator matrix. The proposed algorithm may be applied to any high‐frequency seismic body wave propagating in a laterally varying 2-D or 3-D layered structure (P, S, converted, multiply reflected, etc.). Numerical examples of Fresnel volume ray tracing in 2-D inhomogeneous layered structures are presented. Certain interesting properties of Fresnel volumes are discussed (e.g., the double caustic effect). Fresnel volume ray tracing offers numerous applications in seismology and seismic prospecting. Among others, it can be used to study the resolution of the seismic method and the validity conditions of the ray method.

Pixel-selected ray tracing

An acceleration method based on an idea that T. Whitted (Commun. ACM, vol.23, no.6 pp.343-349, June 1980) presented on ray tracing is discussed. He proposed making antialiased images by hierarchical adaptive oversampling. The present authors use hierarchical adaptive undersampling to reduce the number of pixels whose intensity must be calculated by ray tracing. To implement pixel-selected ray tracing (PSRT), homogeneous regions in images must first be found. Generally, adaptive undersampling can result in some image-quality defects, because small objects and parts of thin or wedge-shaped objects may disappear when they are located between the initially sampled pixels. PSRT has an improved algorithm that uses pixels with the correct object information from among the sampled pixels to find pixels with erroneous color and correct them. Moreover, PRST uses ray-object intersection trees for precise classification of the homogeneity of regions and for fast intensity calculation in homogeneous regions. Experimental results are presented. They show that PSRT is two to nine times faster than standard ray tracing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vicinity ray tracing: an alternative to dynamic ray tracing

SUMMARY A method for computing seismic wavefields in a high-frequency approximation is proposed based on the integration of the kinematic ray tracing equations and a new set of differential equations for the dynamic properties of the wavefront, which we call the vicinity ray tracing (VRT) equations. These equations are directly obtained from the Hamiltonian in ray centred coordinates, using no paraxial approximations. This system is comparable to the standard dynamic ray tracing (DRT) system, but it is specified by fewer equations (four versus eight in 3-D) and only requires the specification of velocity and its first spatial derivative along a ray. The VRT equations describe the trajectory of a ray in the ray centred coordinates of a reference ray. Quantities obtained from vicinity ray tracing can be used to determine wavefront curvature, geometric spreading, traveltime to a receiver near the reference ray, and the KMAH index of the reference ray with greater numerical precision than is possible by differencing kinematically traced rays. Since second spatial derivatives of velocity are not required by the new technique, parametrization of the medium is simplified, and reflection and transmission of beams can be calculated by applying Snell's law to both vicinity rays and central rays. Conversion relations between VRT and DRT can be used to determine the paraxial vicinity of DRT, in which the errors of the paraxial approximations of DRT remain small. In either DRT or VRT, the width of Gaussian beams can be physically defined from the width of the Fresnel volume surrounding the central ray. Because no paraxial approximations are made, the superposition of the Gaussian beams defined from vicinity rays should exhibit a much slower breakdown in accuracy as the scale length of the medium given by ν/Δν/ approaches the beamwidth.

Gaussian beam tracing for computing ocean acoustic fields

The method of Gaussian beam tracing has recently received a great deal of attention in the seismological community. In comparison to standard ray tracing, the method has the advantage of being free of certain ray-tracing artifacts such as perfect shadows and infinitely high energy at caustics. It also obviates the need for eigenray computations. The technique is especially attractive for high-frequency, range-dependent problems where normal mode, FFP, or parabolic models are not practical alternatives. The Gaussian beam method associates with each ray a beam with a Gaussian intensity profile normal to the ray. The beamwidth and curvature are governed by an additional pair of differential equations, which are integrated along with the usual ray equations to compute the beam field in the vicinity of the central ray of the beam. We have adapted the beam-tracing method to the typical ocean acoustic problem of a point source in a cylindrically symmetric waveguide with depth-dependent sound speed. We present an overview of the method and a comparison of results obtained by conventional ray-tracing, beam-tracing, and full-wave theories. These results suggest that beam tracing is markedly superior to conventional ray tracing.

Caustics and specular reflection models for spherical objects and lenses

Ray tracing is a most powerful and elegant rendering technique and is able to render shadows, reflections, and refractions very nicely. However, reflections and refractions in ray tracing simulate the reflected and refracted “eye” ray and not the “light” ray. Standard ray tracing techniques therefore suffer from a lack of specular interreflection and caustics. This paper proposes an algorithm to render reflected and refracted “light” rays for spherical objects and lenses. Indirect illumination is a result of the reflection of light rays. Reflected light may be considered an additional light source; if it is included in the intensity calculation, indirect illumination can be rendered. The refracted light is noticeable as a focal point for a convex lens, and as dispersed light in a concave lens. The dispersed light has low intensity which may be insignificant for the illumination calculations. In the case of a convex lens, light rays become extremely directional and light energy increases. The result appears as caustics. The proposed algorithm is limited to a collimated light ray and does not account for the case of dispersed light.

Calculation of underwater acoustic fields by Gaussian beam tracing

The method of Gaussian beam tracing has recently received a lot of attention in the seismological community. In comparison to standard ray tracing, the method has the advantage of being free of certain ray tracing artifacts such as perfect shadows and infinitely high energy at caustics. The technique is especially attractive for high-frequency problems or problems with complex bathymetry where normal mode, FFP, or parabolic models are not practical alternatives. The Gaussian beam method associates with each ray a beam with a Gaussian intensity profile normal to the ray. The beam curvature and width are governed by an additional pair of differential equations that are integrated along with the usual ray equations to compute the beam field along the ray. Analytic solutions to the beam equations are available for certain canonical problems, including the cases where the sound speed or square of the index of refraction is a linear function of the space variables. Thus ray tracing codes that employ patches of such domains are easily adapted to the beam tracing method. We present an overview of the method and results for certain ocean acoustic scenarios, which illustrate the performance of the method.

Ray Tracing Using the IBM Card Programmed Electronic Calculator*

The IBM Card Programmed Electronic Calculator has been applied to the problem of lens design. Optical design is an inverse process consisting of a provisional choice of optical parameters, an exhaustive mathematical study of such a tentative prescription, and subsequent refinement of the lens system.The standard ray tracing equations can be adapted easily for machine use. The mathematical treatment is algebraic rather than trigonometric. Examples of meridional and skew ray tracing are given. A satisfactory lens has been calculated and tested entirely by machine methods.The machine is expected to be of value in the refining of optical systems, in the determination of optical shop tolerances, and in the investigation of existing prescriptions.