Ray Tracing Approach Research Articles

Particle imaging through planar shock waves and associated velocimetry errors

When imaging particles through a shock wave, the resulting particle image appears blurred and at the wrong location, which is referred to as a position error. Particle image doublets are observed if only part of the light scattered by a particle is deflected or reflected by the shock. These optical distortions are due to the jump in the refractive index that occurs over the shock. Within the context of popular particle-based velocimetry techniques, such as particle image velocimetry and particle tracking velocimetry, the position error propagates into an error in the measured velocity. These particle image distortions and associated errors are assessed and quantified in this paper for the case of planar shocks by means of a light ray tracing approach and by experiments. The errors are shown to be most sensitive to the angle between the viewing direction and the plane of the shock. Increasing this angle to modest values (~5°) is a particularly effective way to decrease the relative velocity error. Looking at the shock from the high-density side is recommended when the accurate determination of the particle response to the shock wave is desired.

Spectral and total effective emissivity of a nonisothermal blackbody cavity formed by two coaxial tubes

A blackbody cavity is developed for continuously measuring the temperature of molten steel, which consists of a cylindrical outer tube with a flat bottom, a coaxial inner tube, and an aperture diaphragm. The ray-tracing approach based on the Monte Carlo method was applied to calculate the effective emissivity for the nonisothermal cavity with a diffuse wall. The influence of the wall temperature distribution on the spectral and total effective emissivity was studied for various cavity geometrical parameters. For a practical blackbody cavity of the temperature sensor used in the tundish, the average spectral effective emissivity was calculated and verified. Our results will help optimize the novel sensor design and use it better for measuring the temperature of molten steel.

Signature simulation of infrared target by tracing multiple areal sources

The traditional ray tracing approach for infrared (IR) target simulation takes into account the radiance emitted from the target in the scene, resulting in an incomplete IR signature of a target. We present a practical method to enable the identification of the signature by considering radiation exchanges among all sources in the scene. Any source would contribute radiance to a target of interest. Therefore, the radiance of a target received by an IR imager includes self-emission and reflectance, where the reflectance is contributed due to radiation exchanges from other sources. Field experiments were performed to demonstrate our proposed method by comparisons of radiance profiles between our simulated images and the real scene images. It shows that our simulated images achieve a better match with the data than those generated by the traditional approach.

Design and management of a powder diffraction beamline for Line Profile Analysis: a realistic ray-tracing approach

Most synchrotron radiation X-ray diffraction (XRD) beamlines have been primarily designed for studying conventional materials, whereas a modern approach to nanomaterials requires a complete control of the diffracted signal, and therefore of the optics and general setup of the beamline. This requirement is especially relevant when Line Profile Analysis is pushed to the limits of large domain sizes, small deformations, or low defects concentration, which is a driving force to use synchrotron radiation XRD. We combine the SHADOW ray-tracing optical simulation with the calculation of powder diffraction profile from standard materials, into a high-level workflow environment based on the ORANGE software. Algorithms are developed to reproduce optical elements in a realistic form, so to evaluate the effects of aberrations, with the final purpose of reconstructing the Instrumental Profile Function of the beamline, with the possibility of investigating the role of each separate element. The results of this work can be of interest to most beamlines as a powerful tool for the design of setups of existing as well as new beamlines.

Variability in shortwave irradiance caused by forest gaps: Measurements, modelling, and implications for snow energetics

Solar irradiance in and around forest gaps plays a key role in determining the snowmelt patterns that shape how forest gaps influence spring snow cover retention relative to open or continuously forested landscapes. To reduce uncertainty in forest gap snowmelt estimation, a new canopy solar transmittance model was developed to include the effects of shading and enhanced transmittance. The model couples a new a ray tracing approach with an existing canopy solar radiation extinction and transmission model. The new model analytically solves for the path length of a solar ray (beam) through a forest canopy and potential intersection(s) with a forest gap conceptualized as an upright circular cylinder surrounded by homogeneous forest. The model was tested alongside simpler transmittance models that ignored shading and treated the canopy as either a binary (open or forested) classification or that used proximal canopy descriptors. The models were evaluated using measurements of shortwave radiation from 20 pyranometers in and around a 56 m diameter gap in a coniferous forest. Errors from ignoring shading were greatest in the gap near the forest edge and in the forest nearest the northern gap edge. The new model reduced these errors; at the 20 pyranometer locations, individual biases up to +356Wm−2 and average biases up to +101Wm−2 were reduced to better than ±5Wm−2. Results suggest that an accurate description of spatial variability of solar irradiance in and around a forest gap requires explicit treatment of the effects of shading into a gap and enhanced transmittance beyond the gap extent; this is dependent upon solar position, gap and forest geometry, and location relative to the gap. A sensitivity experiment with the forest gap – ray trace model in which gap size, latitude, and day of year were varied under clear-sky conditions showed that cumulative daily solar irradiance has high spatiotemporal variability. The maximum of the spatial coefficient of variation (CV) of cumulative daily irradiance was a function of gap size and solar angles; smaller (larger) gaps and lower (higher) solar elevation angle ranges were more diffuse- (direct beam-) dominated with reduced (increased) spatial variability relative to the mean. It is found that there is no standard impact of a forest gap on shortwave irradiance – the impact of gap size on clear sky solar irradiance depends on forest structure, date, and latitude.

Omnidirectional underwater camera design and calibration.

This paper presents the development of an underwater omnidirectional multi-camera system (OMS) based on a commercially available six-camera system, originally designed for land applications. A full calibration method is presented for the estimation of both the intrinsic and extrinsic parameters, which is able to cope with wide-angle lenses and non-overlapping cameras simultaneously. This method is valid for any OMS in both land or water applications. For underwater use, a customized housing is required, which often leads to strong image distortion due to refraction among the different media. This phenomena makes the basic pinhole camera model invalid for underwater cameras, especially when using wide-angle lenses, and requires the explicit modeling of the individual optical rays. To address this problem, a ray tracing approach has been adopted to create a field-of-view (FOV) simulator for underwater cameras. The simulator allows for the testing of different housing geometries and optics for the cameras to ensure a complete hemisphere coverage in underwater operation. This paper describes the design and testing of a compact custom housing for a commercial off-the-shelf OMS camera (Ladybug 3) and presents the first results of its use. A proposed three-stage calibration process allows for the estimation of all of the relevant camera parameters. Experimental results are presented, which illustrate the performance of the calibration method and validate the approach.

Assessment of a fully 3D Monte Carlo reconstruction method for preclinical PET with iodine-124

Iodine-124 is a radionuclide well suited to the labeling of intact monoclonal antibodies. Yet, accurate quantification in preclinical imaging with I-124 is challenging due to the large positron range and a complex decay scheme including high-energy gammas. The aim of this work was to assess the quantitative performance of a fully 3D Monte Carlo (MC) reconstruction for preclinical I-124 PET. The high-resolution small animal PET Inveon (Siemens) was simulated using GATE 6.1. Three system matrices (SM) of different complexity were calculated in addition to a Siddon-based ray tracing approach for comparison purpose. Each system matrix accounted for a more or less complete description of the physics processes both in the scanned object and in the PET scanner. One homogeneous water phantom and three heterogeneous phantoms including water, lungs and bones were simulated, where hot and cold regions were used to assess activity recovery as well as the trade-off between contrast recovery and noise in different regions. The benefit of accounting for scatter, attenuation, positron range and spurious coincidences occurring in the object when calculating the system matrix used to reconstruct I-124 PET images was highlighted. We found that the use of an MC SM including a thorough modelling of the detector response and physical effects in a uniform water-equivalent phantom was efficient to get reasonable quantitative accuracy in homogeneous and heterogeneous phantoms. Modelling the phantom heterogeneities in the SM did not necessarily yield the most accurate estimate of the activity distribution, due to the high variance affecting many SM elements in the most sophisticated SM.

Satellite observations of cirrus clouds in the Northern Hemisphere lowermost stratosphere

Abstract. Here we present observations of the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) of cirrus cloud and water vapour in August 1997 in the upper troposphere and lower stratosphere (UTLS). The observations indicate a considerable flux of moisture from the upper tropical troposphere into the extratropical lowermost stratosphere (LMS), resulting in the occurrence of high-altitude optically thin cirrus clouds in the LMS. The locations of the LMS cloud events observed by CRISTA are consistent with the tropopause height determined from coinciding radiosonde data. For a hemispheric analysis in tropopause relative coordinates an improved tropopause determination has been applied to the European Centre for Medium-Range Weather Forecasts (ECMWF) temperature profiles. We found that a significant fraction of the cloud occurrences in the tropopause region are located in the LMS, even if a conservative overestimate of the cloud top height (CTH) determination by CRISTA of 500 m is assumed. The results show rather high occurrence frequencies (~ 5%) up to high northern latitudes (70° N) and altitudes well above the tropopause (> 500 m at ~350 K and above) in large areas at mid- and high latitudes. Comparisons with model runs of the Chemical Lagrangian Model of the Stratosphere (CLaMS) over the CRISTA period show a reasonable consistency in the retrieved cloud pattern. For this purpose a limb ray tracing approach was applied through the 3-D model fields to obtain integrated measurement information through the atmosphere along the limb path of the instrument. The simplified cirrus scheme implemented in CLaMS seems to cause a systematic underestimation in the CTH occurrence frequencies in the LMS with respect to the observations. The observations together with the model results demonstrate the importance of isentropic, quasi-horizontal transport of water vapour from the subtropics and the potential for the occurrence of cirrus clouds in the lowermost stratosphere and tropopause region.

Scattering of ECRF waves by edge density fluctuations and blobs

The scattering of electron cyclotron waves by density blobs embedded in the edge region of a fusion plasma is studied using a full-wave model. The full-wave theory is a generalization of the usual approach of geometric optics ray scattering by blobs. While the latter allows for only refraction of waves, the former, more general formulation, includes refraction, reflection, and diffraction of waves. Furthermore, the geometric optics, ray tracing, model is limited to blob densities that are slightly different from the background plasma density. Observations in tokamak experiments show that the fluctuating density differs from the background plasma density by 20% or more. Thus, the geometric optics model is not a physically realistic model of scattering of electron cyclotron waves by plasma blobs. The differences between the ray tracing approach and the full-wave approach to scattering are illustrated in this paper.

A skew ray tracing approach for error analysis of a light ray path for optical systems with asymmetrical optical axes

A skew ray tracing approach for error analysis of a light ray path for optical systems with asymmetrical optical axes

Analytical Model for Optical Scattering of Infrared Laser by Nonspherical Raindrops

Analytic model was developed to investigate the interaction of infrared laser with nonspherical raindrops. The method based on Fraunhofer diffraction and geometrical optics was presented to obtain the analytic solution for single-scattering properties by approximate ellipsoid raindrops. Light scattering patterns were obtained for different drop sizes and shapes. Computational results demonstrate that the scattering of raindrops was contributed by both Fraunhofer diffraction and geometric scattering, and the results obtained from analytic formulas were consistent with the conclusions of using Monte Carlo ray tracing approach.

Features of Afterbody Radiative Heating for Earth Entry

Radiative heating is identified as a major contributor to afterbody heating for Earth entry capsules at velocities above . Because of rate-limited electron–ion recombination processes, many of the electronically excited N and O atoms produced in the high-temperature/pressure forebody remain as they expand into the afterbody region, which results in significant afterbody radiation. Large radiative heating sensitivities to electron-impact ionization rates and escape factors are identified. Ablation products from a forebody ablator are shown to increase the afterbody radiation by nearly 40%, due to the influence of CO on the vibrational-electronic temperature. The tangent-slab radiation transport approach is shown to overpredict the radiative flux by as much as 50% in the afterbody, therefore making the more computationally expensive ray-tracing approach necessary for accurate radiative flux predictions. For the Stardust entry, the afterbody radiation is predicted to be nearly twice as large as the convective heating during the peak heating phase of the trajectory. Comparisons between simulations and the Stardust Echelle observation measurements, which are shown to be dominated by afterbody emission, indicate agreement within 20% for various N and O lines. Similarly, calorimeter measurements from the Fire II experiment are identified as a source of validation data for afterbody radiation. For the afterbody calorimeter measurement closest to the forebody, which experiences the largest afterbody radiative heating component, the fully catalytic convective heating prediction alone is shown to underpredict the measurement by up to 60%. Agreement with the measurements is improved to within 20% with the addition of afterbody radiation. These comparisons with Stardust and Fire II measurements confirm that afterbody radiation is a valid heating mechanism that requires consideration in future vehicle designs.

Combining structures on different length scales in ray tracing: analysis of optical losses in solar cell modules

Solar cell modules consist of optically relevant geometric structures on very different length scales. While the whole module and the solar cells are on a scale of meters and centimeters, the pyramids etched on mono-crystalline Si cells (for enhancing light-trapping) have sizes in the micrometer range. The simulation domain cannot be reduced substantially to still capture module specific effects. Hence, these large differences in length scale have so far prohibited a detailed ray tracing analysis of entire modules. In this work, we developed a ray tracing approach that separates large and small scale geometries into different simulation domains; the simulated photon automatically switches between the different domains as needed. With this approach, it is possible to simulate whole modules on current desktop computers within reasonable time. We demonstrate the capabilities of this method by analyzing the optical losses in solar cell modules from mass production, as well as in modules under development that have no encapsulant. Our ray tracing method can be applied to any geometric structures containing different length scales.

Geometry-invariant GRIN lens: finite ray tracing.

The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.

On the Use of FDTD and Ray-Tracing Schemes in the Nanonetwork Environment

In this letter, the finite difference time-domain (FDTD) method and the ray-tracing (RT) technique are systematically revisited and compared as potential tools that can reliably characterize new protocols for emerging nanonetwork applications. To this aim, a set of efficient simulation schemes for the precise prediction of the reception quality in various communication scenarios is presented. In particular, each algorithm involves a similar configuration with a realistic transmitter/receiver model and multiple obstacles sized up to some micrometers. The proposed analysis reveals that, unlike conventional assessments, the RT approach can be successfully employed at nanoscale dimensions, with increasing accuracy at higher frequencies, as a tool for fast received-energy estimations, since its results are in acceptable agreement with the respective FDTD data. These significant deductions are, finally, substantiated by a theoretical formulation equivalent to that of frequency selective surfaces.

Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies

AbstractMany theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.

Simulation of radar echoes from Mars' surface/subsurface and inversion of surface media parameters

A two-layer model of Mars' regolith/bedrock media with a cratered rough surface/subsurface is presented for radar echo simulation of planetary exploration research. The numerical approach of geometric ray tracing for the scattering of rough surfaces, which is digitized by the triangulated network, is applied to the calculation of the scattering and imaging simulation of radar range echoes. Numerical simulations of a cratered rough surface generated by the Monte Carlo method are used to analyze the functional dependence of radar range echoes at 1–50 MHz center frequencies upon the surface/subsurface feature and the parameters of the layering media, that is, layer depth and dielectric properties. The radar range echoes from two areas of the real Mars surface, which is described by digital elevation model data with a resolution of 1 m × 1 m and a vertical error of less than 1 m, are also simulated and analyzed. Based on these simulations, this study presents a numerical imaging test of radar sounder at center frequencies 1–50 MHz for exploration of different dielectric regolith and bedrock media. The channel 50 MHz with high resolution might be an optimal frequency. Finally, inversion of the dielectric constants of the two-layer media and the regolith layer thickness are developed.

Low temperature high current ion beams and laminar flows

Self-consistent Vlasov-Poisson equilibria for the extraction of ions with low temperature T i are discussed, with comparison to the laminar flow case T i = 0, in two dimensional diodes. Curvilinear coordinates aligned with laminar beam flow lines are extended to the low ion temperature case, with a reduced current density j d , expressed with cathode integrals. This generalizes one-dimensional interpolation between rays along the cathode coordinate to multidimensional integrations, including also the momentum components, so that j d is free from the granularity defect and noise, typical of standard ray tracing approach. A robust numerical solution procedure is developed, which allows studying current saturated extraction and drift tube effects. A discussion of particle initial conditions determines the emission angles and shows that temperature effect at beam edge is partly balanced by the focus electrode inclination. Results for a typical diode are described, with detail about normalized emittance, here taken strictly proportional to the x − p x phase space area, for a beam with non uniform velocities.

Axial ultrasound B-scans of the entire eye with a 20-MHz linear array: correction of crystalline lens phase aberration by applying Fermat's principle.

In ophthalmic ultrasonography the crystalline lens is known to be the main source of phase aberration, causing a significant decrease in resolution and distortion effects on axial B-scans. This paper proposes a computationally efficient method to correct the phase aberration arising from the crystalline lens, including refraction effects using a bending ray tracing approach based on Fermat's principle. This method is used as a basis to perform eye-adapted beamforming (BF), with appropriate focusing delays for a 128-element 20-MHz linear array in both emission and reception. Implementation was achieved on an in-house developed experimental ultrasound scanning device, the ECODERM. The proposed BF was tested in vitro by imaging a wire phantom through an eye phantom consisting of a synthetic gelatin lens anatomically set up in an appropriate liquid (turpentine) to approach the in vivo velocity ratio. Both extremes of accommodation shapes of the human crystalline lens were investigated. The performance of the developed BF was evaluated in relation to that in homogeneous medium and compared to a conventional delay-and-sum (DAS) BF and a second adapted BF which was simplified to ignore the lens refraction. Global expectations provided by our method with the transducer array are reviewed by an analysis quantifying both image quality and spatial fidelity, as well as the detrimental effects of a crystalline lens in conventional reconstruction. Compared to conventional array imaging, the results indicated a two-fold improvement in the lateral resolution, greater sensitivity and a considerable reduction of spatial distortions that were sufficient to envisage reliable biometry directly in B-mode, especially phakometry.

Multiple interfacing between classical ray-tracing and wave-optical simulation approaches: a study on applicability and accuracy.

In this study the applicability of an interface procedure for combined ray-tracing and finite difference time domain (FDTD) simulations of optical systems which contain two diffractive gratings is discussed. The simulation of suchlike systems requires multiple FDTD↔RT steps. In order to minimize the error due to the loss of the phase information in an FDTD→RT step, we derive an equation for a maximal coherence correlation function (MCCF) which describes the maximum degree of impact of phase effects between these two different diffraction gratings and which depends on: the spatial distance between the gratings, the degree of spatial coherence of the light source and the diffraction angle of the first grating for the wavelength of light used. This MCCF builds an envelope of the oscillations caused by the distance dependent coupling effects between the two diffractive optical elements. Furthermore, by comparing the far field projections of pure FDTD simulations with the results of an RT→FDTD→RT→FDTD→RT interface procedure simulation we show that this function strongly correlates with the error caused by the interface procedure.