Backward Ray Tracing Technique Research Articles

Shadows of black holes with dark matter halo

We investigate the shadow of an exact black hole solution of Einstein's equations recently proposed by Cardoso et al., to describe a supermassive black hole immersed in a dark matter halo. We analyze and discuss the light rings and the gravitational lensing of this spacetime comparing them with an isolated Schwarzschild black hole. Using backward ray-tracing techniques, we study the shadows cast by such black hole when illuminated by a celestial sphere that emits radiation isotropically. We find that when the dark matter distribution concentrates near the event horizon of the black hole, multiple light rings emerge. In this high compactness regime, the shadows and gravitational lensing are significantly different from the Schwarzschild one. We also use the M87* and SgrA* shadow data, obtained by the Event Horizon Telescope collaboration, to constrain the parameters of the dark matter halo.

Curved Computer-Generated Integral Imaging Based on Backward Ray-Tracing Technique

In traditional computer-generated integral imaging (CGII) methods, the generated elemental image array (EIA) is flat, and it doesn't fit for curved integral imaging (II) systems. Here, a curved CGII method was proposed for curved II system. In the proposed method, multiple virtual camera arrays (VCAs) were built up to determine the origins and directions of the traced rays. Combined with the backward ray-tracing (BRT) technique, a curved EIA was generated, and the rendering time was the same as the BRT-CGII of flat II system. A curved II system consisting of a curved organic light emitting diode display screen, a curved lens array and a curved optical diffuser screen was built up in the experiment. The proposed curved CGII method generated correct curved EIA for the curved II system, and the system presented vivid 3D images with the viewing angle as wide as 80° × 50°.

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes* *Supported by the National Key R&D Program of China (2020YFC2201400)

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.

Diffraction- and Reflection-Aware Multiple Sound Source Localization

In this article, we present a novel localization method for multiple sources in indoor environments. Our approach can estimate different propagation paths, including the reflection and diffraction paths of sound waves based on a backward ray tracing technique. To estimate diffraction propagation paths, we combine a ray tracing algorithm with a uniform theory of diffraction model by exploiting the diffraction properties as propagation paths bend around the wedges of obstacles. We reconstruct the 3-D environments and wedges of obstacles in the precomputation phase and utilize these outcomes to generate primary, reflection, and diffraction acoustic rays in the runtime phase. We localize multiple sources when identifying the convergence regions of these acoustic rays based on Monte Carlo localization (MCL). Our approach supports not only stationary but also moving sources of human speech and clapping sounds. Our approach can also handle nonline-of-sight (NLOS) sources and distinguish between active and inactive source states. We evaluated and analyzed our algorithm in multiple scenarios containing obstacles and NLOS sources. Our approach can localize moving sources with the average of distance errors of 0.65 and 0.74 m in single and multiple source cases, respectively, in rooms, 7 m by 7 m in size with a height of 3 m; errors are measured according to the L2 distance between the estimated and actual source positions. We observed a 130% improvement of the localization accuracy over the prior work (J.-M. Valin <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> ).

An Improved Ray-Tracing Algorithm for SBR-Based EM Scattering Computation of Electrically Large Targets

We put forward an improved ray-tracing algorithm to obtain a fast prediction of the radar cross section (RCS) for electrically large complex targets using the shooting and bouncing ray (SBR) method. Our algorithm employs a rope-based kd-tree data structure together with the neighbor-facet-tree based backward ray-tracing technique. The proposed algorithm shows excellent performance in the evaluation of scattering properties of the electrically large targets at high frequency. To assess and validate the proposed method, we compute the RCS of electrically small targets and of a realistic aircraft model and compare results with those of the traditional SBR method and multilevel fast multipole method. The agreement of the results together with the runtime performance demonstrate the accuracy and efficiency of our method.

Tomographic reconstruction of light field PIV based on a backward ray-tracing technique

The calculation of the weight matrix is one of the key steps of the tomographic reconstruction in the light field particle image velocimetry (light field PIV) system. At present, the existing calculation method of the weight matrix in light field PIV based on the forward ray-tracing technique (named Fahringer’s method) is very time-consuming. To improve the computational efficiency of the weight matrix, this paper presents a computational method for the weight matrix based on the backward ray-tracing technique in combination with a Gaussian function (named the Gaussian function method). An expectation–maximization algorithm is employed for the reconstruction of the 3D particle field, and a summed line-of-sight (SLOS) estimation is further used to accelerate the reconstruction process. The computational accuracy and efficiency of the weight matrix, the reconstruction quality of the 3D particle field, and the velocity field accuracy by the Gaussian function method are numerically investigated. Finally, experiments are carried out to verify the feasibility of the weight matrix by the Gaussian function method. The numerical results illustrated that the Gaussian function method can improve the computational efficiency of the weight matrix more than ten times. The SLOS is capable of further accelerating the computational efficiency of the overall reconstruction process, including the pre-determination, the calculation of the weight matrix and the reconstruction. The velocity field accuracy by the Gaussian function method is almost the same as that by Fahringer’s method. The experimental results of the three-dimensional and three-component velocity field of a laminar flow further verify the feasibility of the computational method for the weight matrix based on the Gaussian function method.

Backward ray tracing based rectification for real-time integral imaging display system

In an integral imaging (InI) display system, the deviation of the lens position results in blur and distortion of the reconstructed three-dimensional (3D) image. To achieve undistorted and real-time 3D images, an image correction method based on the backward ray tracing (BRT) technology is presented. By finding the correct pixel-to-ray correspondence, the origin and the direction of the light ray for every pixel in elemental image array (EIA) are reset, and the corrected 3D image is obtained based on the BRT technique. Experimental results demonstrate the feasibility and effectiveness of the proposed method, and the structural similarity (SSIM) index of the reconstructed 3D image increased by 20∼30% compared with that without calibrating. The frame rate of EIA generation is over 40 fps, which can realize real-time generation.

Backward ray tracing based high-speed visual simulation for light field display and experimental verification.

The exiting simulation method is not capable of achieving three-dimensional (3D) display result of the light field display (LFD) directly, which is important for design and optimization. Here, a high-speed visual simulation method to calculate the 3D image light field distribution is presented. Based on the backward ray tracing technique (BRT), the geometric and optical models of the LFD are constructed. The display result images are obtained, and the field of view angle (FOV) and depth of field (DOF) can be estimated, which are consistent with theoretical results and experimental results. The simulation time is 1s when the number of sampling rays is 3840×2160×100, and the computational speed of the method is at least 1000 times faster than that of the traditional physics-based renderer. A prototype was fabricated to evaluate the feasibility of the proposed method. From the results, our simulation method shows good potential for predicting the displayed image of the LFD for various positions of the observer's eye with sufficient calculation speed.

Optical-irradiance ray-tracing model for the performance analysis and optimization of a single slope solar still

This paper describes an optical-irradiance model devised to analyze the performance and geometrical optimization of a single slope solar still. The three-dimensional backward ray-tracing technique, along with Latin Hypercube Sampling (LHS) was used to statistically generate the sampled incoming rays. Validation was conducted in four geometrical scenarios using ray-tracing with a single ray. Results were then compared to the output of the 3D modeling program. The sampled rays were then simulated to obtain complete collection of irradiance in these scenarios and the optical efficiency was evaluated. The model was then used to investigate the effects of changing the aspect ratio and the cover angles on the optical and irradiance performance of six different still designs. Later, the model was used to develop powerful tools with the following applications: (i) selecting the optimum aspect ratio and cover angle so the desired optical performance can be obtained at a given time of day and (ii) evaluating the day-round performance of a still design based on the combination of the ranges of aspect ratio and cover angle. They are explained via a case study conducted in Auckland (New Zealand).

High-efficiency photorealistic computer-generated holograms based on the backward ray-tracing technique

Holographic displays can provide the complete optical wave field of a three-dimensional (3D) scene, including the depth perception. However, it often takes a long computation time to produce traditional computer-generated holograms (CGHs) without more complex and photorealistic rendering. The backward ray-tracing technique is able to render photorealistic high-quality images, which noticeably reduce the computation time achieved from the high-degree parallelism. Here, a high-efficiency photorealistic computer-generated hologram method is presented based on the ray-tracing technique. Rays are parallelly launched and traced under different illuminations and circumstances. Experimental results demonstrate the effectiveness of the proposed method. Compared with the traditional point cloud CGH, the computation time is decreased to 24 s to reconstruct a 3D object of 100×100 rays with continuous depth change.

High-efficient rendering of the multi-view image for the three-dimensional display based on the backward ray-tracing technique

Computer-generated multi-view (MV) image for the three-dimensional (3D) display with lenticular lens arrays based on the backward ray-tracing technique is presented. To overcome the limitations of the traditional ray-tracing technique, whose minimum operating unit is the pixel, the proposed method can be applied at the sub-pixel level. The quality of the generated 3D image is not reduced, in contrast to existing methods for converting 2D images to 3D. Compared to the previous each camera viewpoint independent rendering method, the backward ray-tracing technique directly renders the final MV image rather than all the single-viewpoint images. Accordingly, the total render time is substantially reduced. Experimental results show that our proposed method significantly increases the simplicity and efficiency of the rendering process, especially ensuring the resolution of the final MV 3D image. Experimental results for 3D display with the generated 32-viewpoint 3D images are presented.

Hurricane Imaging Radiometer (HIRAD) Wind Speed Retrievals and Validation Using Dropsondes.

Surface wind speed retrievals have been generated and evaluated using Hurricane Imaging Radiometer (HIRAD) measurements from flights over Hurricane Joaquin, Hurricane Patricia, Hurricane Marty, and the remnants of Tropical Storm Erika, all in 2015. Procedures are described here for producing maps of brightness temperature, which are subsequently used for retrievals of surface wind speed and rain rate across a ~50 km wide swath for each flight leg. An iterative retrieval approach has been developed to take advantage of HIRAD's measurement characteristics. Validation of the wind speed retrievals has been conducted, using 636 dropsondes released from the same WB-57 high altitude aircraft carrying HIRAD during the Tropical Cyclone Intensity (TCI) experiment. The HIRAD wind speed retrievals exhibit very small bias relative to the dropsondes, for winds tropical storm strength (17.5 m s-1) or greater. HIRAD has reduced sensitivity to winds weaker than tropical storm strength, and a small positive bias (~2 m s-1) there. Two flights with predominantly weak winds according to the dropsondes have abnormally large errors from HIRAD, and large positive biases. From the other flights, root mean square differences between HIRAD and the dropsonde winds are 4.1 m s-1 (33%) for winds below tropical storm strength, 5.6 m s-1 (25%) for tropical storm strength winds, and 6.3 m s-1 (16%) for hurricane strength winds. Mean absolute differences for those categories are 3.2 m s-1 (25%), 4.3 m s-1 (19%), and 4.8 m s-1 (12%), with bias near zero for tropical storm and hurricane strength winds.

High-efficient computer-generated integral imaging based on the backward ray-tracing technique and optical reconstruction.

A high-efficient computer-generated integral imaging (CGII) method is presented based on the backward ray-tracing technique. In traditional CGII methods, the total rendering time is long, because a large number of cameras are established in the virtual world. The ray origin and the ray direction for every pixel in elemental image array are calculated with the backward ray-tracing technique, and the total rendering time can be noticeably reduced. The method is suitable to create high quality integral image without the pseudoscopic problem. Real time and non-real time CGII rendering images and optical reconstruction are demonstrated, and the effectiveness is verified with different types of 3D object models. Real time optical reconstruction with 90 × 90 viewpoints and the frame rate above 40 fps for the CGII 3D display are realized without the pseudoscopic problem.

A New Method for Reconstruction of Corneal Topography with Placido Disk System

Many methods to reconstruct the corneal topography are based on the Placido disk system. The skew rays can contribute errors to the system when using the reflection image with these methods. To overcome this limitation, a backward ray tracing technique is developed. By performing this technique, a continuous surface representation of the cornea is obtained. The error analysis shows an enhanced accuracy in reconstructing the corneal topography. The colormaps of corneal surface powers are also drawn for graphic representations of corneal topography.

Analysing the impact of reflectance distributions and well geometries on vertical surface daylight levels in atria for overcast skies

This study investigated the impacts of different diffuse reflectance distributions and well geometries on vertical daylight factors and vertical internally reflected components in atria. Two forms of reflectance distribution patterns of wall surface were examined: horizontal and vertical reflectance band variation. The square atrium models studied have a broader WI range of 0.25–2.0, which represent shallow, medium and high atria. Radiance, a powerful package based on backward ray tracing technique, was used for the simulations of vertical daylight levels. The results show that different reflectance distributions of square atrium walls do have an impact on the vertical daylight factors and vertical internally reflected components under overcast sky condition. The impact relates to the orientation of the band with different reflectance distributions on the wall. Compared with the vertical band surface, the horizontal band surface has a much more complicated effect. The horizontal distributions of the reflectances significantly affects the vertical daylight levels at the locations more than 30% atrium height on the wall. For an atrium with a height more than 1/2 the width, the effect tends to increase with the increasing well index. The vertical distributions of the reflectance, nevertheless, do not substantially take effect on the vertical daylight levels in atria except for some special reflectance distribution patterns.

Comment on “On the cause of the 1908 Messina tsunami, southern Italy” by Andrea Billi et al.

[1] The December 28th 1908 Messina Earthquake has been ranked as one of the most destructive events of the last centuries [Davison, 1936] The damages produced by ground shaking were aggravated by the effects of a remarkable tsunami, with up to 11 m of run-up height, that followed the earthquake [Omori, 1909; Baratta, 1910; Tinti et al., 2004]. The location of the causative fault is still a matter of debate [e.g., Argnani et al., 2009], the modelling of the associated tsunami [Tinti and Armigliato, 2003] allowing uncertainty. [2] Billi et al. [2008] have recently proposed that the tsunami that stroke the coast of the Strait in December 1908 originated from a large submarine landslide (20 km) located offshoreGiardini-Naxos. The hypothesis is based on the study of tsunami arrival times [Platania, 1909; Baratta, 1910] and is supported, according to Billi et al. [2008], by inspection of: a multibeam morphobathymetry [Marani et al., 2004] and of a crustal-scale seismic profile [Scrocca et al., 2004]. [3] The arguments of Billi et al. [2008], however, have weak points that cast doubt on their interpretation. But most importantly, data collected in the last few years by the authors of this comment (A. Argnani and F. Chiocci), and work on tsunami modelling (S. Tinti and his group) cast further doubt on the proposed hypothesis that a large submarine landslide that was caused by the 1908 earthquake is located offshore Giardini-Naxos. These issues will be discussed in the following.

In Search of the 31 March 1761 Earthquake and Tsunami Source

Earthquake catalogs for the Iberian Peninsula report three strong- magnitude events in the eighteenth century: 27 December 1722, 1 November 1755, and 31 March 1761. These events have magnitudes greater than 7 and generated tsunamis that damaged the Portuguese coasts. However, their source areas are controversial because of the lack of detailed and coherent historical descriptions. The 31 March 1761 earthquake was felt in Lisbon at noon, alarming the inhabitants and throwing down ruins of the past 1 November 1755 earthquake. According to several sources the earthquake was followed by a tsunami that was observed as far as Cornwall (United Kingdom), Cork (Ireland), and Barbados (Caribbean). The Portuguese catalogs locate this event on the Horseshoe Abyssal Plain, south of Gorringe Bank, and attribute a magnitude of 7.5. The Caribbean tsunami catalog (Lander et al. , 2002) locates the event further north 37° N 10° W and estimates of its epicenter intensity as IX. In this study we present a reappraisal of the available historical reports concerning the 1761 event, a revision of the macroseismic intensities along Iberia, and the tsunami observations along the western Portuguese and Galicia coasts, England, Ireland, and the West Indies. With this dataset we use backward raytracing techniques to discuss the location of the event and its integration with one of the major tsunami generation areas in the western Portuguese margin. We conclude that the 31 March 1761 earthquake took place at 12:01 a.m. (Lisbon time). Its epicenter was located about 34.5° N 13° W and had a tsunami magnitude close to 8.5. Online material: Felt reports from the 31 March 1761 earthquake.

A numerical method to estimate time-varying values of diffuse irradiance on surfaces in complex geometrical environments

The estimation of diffuse irradiance that impinges on a window or photovoltaic panel is of major importance for the determination of their performance. The present paper introduces the concept of angular shading factors (ASF) for the calculation of time-varying diffuse irradiances to be performed without the need to repeat time consuming intereflection calculations at every time step. For the calculation of ASF, a Monte Carlo backward ray tracing technique was used. As a result, geometrically complex scenes consisting of surfaces with diffuse and specular reflectances, while transparent and translucent surfaces can be modeled as well. After that, the calculation of diffuse irradiance can be performed in a dynamic way, by taking into consideration the sky radiance distribution variability.

Constrains on the source of the 1755 Lisbon tsunami inferred from numerical modelling of historical data on the source of the 1755 Lisbon tsunami

The 1755 Lisbon tsunami was felt all over the North Atlantic, being one of the first major events of this kind relatively well documented by historical sources. However, in spite of the extensive research work on the historical reports by a considerable number of authors, the epicentre location of this event is still uncertain and its focal mechanism is still not well understood, implying a great uncertainty in the tsunami generating mechanism. The generally assumed epicentre, inferred from isoseismal maps, is located slightly north of the Gorringe Bank (SW Iberia) and the rupture mechanism has been assumed in the past to be similar to the well studied 1969.02.28 event. While all previous studies have used a seismic-based approach, this paper uses all that is known about the tsunami parameters at the coast — presented in a companion paper — to define the location and geometry of the tsunami source. For that purpose some backward ray-tracing techniques were developed and their results were used to define the initial fields in a number of shallow water simulations of the water height at the coastal locations where the most reliable historical data are available. The source parameters also took into account the estimated seismic energy released. The results obtained here suggest that the 1755 tsunami probably originated on the continental shelf, implying an epicentre area located between the Gorringe Bank and the Iberian coast, in a geodynamic context quite different from the one implied in the 1969.02.28 event. The amplitude of the initial movement in the source region, required by the shallow water simulations to account for the reported magnitudes, suggests an elongated but shallow rupture area, extending along the shelf. It is suggested that this location of the rupture would have significant implications in the geology of the region.

Visual Translucent Algorithm (Vista)

VISTA (VISual Translucent Algorithm) is a fast, 4-D cloudscape generator that includes simulation of haze and cloud- related visual phenomena such as cloud shadows, rainbows, and solar arcs. VISTA uses a meteorological sounding as input and produces cloud scenes using a backward ray tracing technique. The ray is checked for the first intersection of either 1) an opaque surface (thick cloud or surface), 2) a translucent layer, or 3) an optical refraction layer. Depending on the nature of this intersection, the specular reflection is calculated after taking into account direct illumination, if any. Placement of clouds depends on location of potential cloud layers, cloud domain characteristics, and gravity waves, while small (of order 1 meter) cloud structure is stochastically generated by a sawtooth generator. Background land surfaces can be deterministically (either real or hypothetical) input or can be stochastically generated.