Ray Geometry Research Articles

A model of radio scintillations in the deep Venus atmosphere: Application to the DAVINCI probe

Power fluctuations have been noted on radio signals propagating through the Venus atmosphere since the very first descent probe there (Venera 4) and have been observed as a routine feature in radio occultations, where the grazing ray geometry amplifies the effect of refractive scattering structures. Motivated by DAVINCI and other missions currently in development, a physical model of refraction variations in the Venus atmosphere is developed using the VEGA-2 high-resolution temperature profile down to the surface and other data, which suggest several distinct layers of more intense scattering. The resultant modeled radio scintillations are compared with observed scintillations and assessed for the DAVINCI relay link. High-time-resolution radio signal power measurements on the DAVINCI radio link promise to be an interesting probe of the Venus atmosphere.

Some Features of Scattering of a Plane ElectromaElectromagnetic Wave on a Plane Magnetodielectric Plate

The two-dimensional problem of scattering of a plane electromagnetic wave on a flat homogeneous magnetodielectric plate of finite dimensions is considered. The problem is solved by the method of integral equations for auxiliary surface currents. Algebraization of integral equations was carried out using the collocation method and overlapping three-step basis functions. The results characterizing the efficiency of the proposed algorithm are presented. The influence of the geometric and material parameters of the plate on its effective scattering surface (ESS) in the direction of wave incidence, which characterizes the effects of “invisibility” of the plate, is studied. It is shown that the minimum of the specified ESS is achieved at a plate thickness close to the thickness that ensures the in-phase geometry of the geometric-optical rays that have passed through the plate and the rays that have passed by the plate. The ESS of a plate made of a material with positive and negative refractive indices is compared.

Details study on the kinematic characteristics of manta ray section in flapping motion and exploring its application in wave glider propulsion system

It has always been a human challenge to inspire natural configurations and phenomena and benefit from their merits in improving the performances of man-made proposed aero/hydro vehicles. For example, the manta rays are known for their great swimming performances. To design and fabricate an underwater robot based on the manta ray geometry and its kinematic characteristics, it is important to initially study its hydrodynamic behavior and possibly arrive at some key design parameters, which can remarkably help to figure out an optimum geometry with high swimming performances. The main objective of this study is to focus on the merits of gliding motion inspired by the manta ray fish considering the real sea conditions. In this regard, two wave-glider configurations with specific submersible geometries are selected to practice the bases of this objective. They are the manta-glider, which has a complicated 3D configuration representing the real manta ray swimming behavior, and the wing-glider, which has much simpler configuration constructing from a flat and uniform wing span shape. The 3D unsteady incompressible Navier-Stokes equations are numerically solved to simulate the gliding motion performances of these two gliders. The results show that the maximum efficiency of manta-glider model is ηmax = 50 %, which is much higher than that of the wing-glider with ηmax = 36 %, within an operational range with a relatively constant significant wave height (SWH). Alternatively, the wing-glider efficiency is about 5 % higher than that of the manta-glider in cases with non-constant SWH values. Irrespective of their efficiencies, the interesting outcome of this study is that the manta-glider model shows fewer fluctuations and performs more stable conditions than a simplified glider model in energy-absorbing applications. Considering the achieved outcomes, this work also suggests a simple guideline, which is so beneficial to arrive at a suitable wave glider propulsion design.

Microlocal analysis of borehole seismic data

<p style='text-indent:20px;'>Borehole seismic data is obtained by receivers located in a well, with sources located on the surface or another well. Using microlocal analysis, we study possible approximate reconstruction, via linearized, filtered backprojection, of an isotropic sound speed in the subsurface for three types of data sets. The sources may form a dense array on the surface, or be located along a line on the surface (walkaway geometry) or in another borehole (crosswell). We show that for the dense array, reconstruction is feasible, with no artifacts in the absence of caustics in the background ray geometry, and mild artifacts in the presence of fold caustics in a sense that we define. In contrast, the walkaway and crosswell data sets both give rise to strong, nonremovable artifacts.</p>

Valuative Invariants with Higher Moments

In this article we introduce a family of valuative invariants defined in terms of the p-th moment of the expected vanishing order. These invariants lie between \(\alpha \) and \(\delta \)-invariants. They vary continuously in the big cone and semi-continuously in families. Most importantly, they give sufficient conditions for K-stability of Fano varieties, which generalizes the \(\alpha \) and \(\delta \)-criterions in the literature. They are also related to the \(d_p\)-geometry of maximal geodesic rays.

Modelling continuum intensity perturbations caused by solar acoustic oscillations

Context. Helioseismology is the study of the Sun’s interior using observations of oscillations at the surface. It suffers from systematic errors, for instance a center-to-limb error in travel-time measurements. Understanding these errors requires an adequate understanding of the nontrivial relationship between wave displacement and helioseismic observables (intensity or velocity). Aims. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which, in turn, perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship achieved to date between the wave displacement and the emergent intensity perturbation by solving the radiative transfer problem in the perturbed atmosphere. Methods. We derived an expression for the emergent intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying a first-order perturbation theory. As input perturbations, we considerd adiabatic modes of oscillation of different degrees in a spherically-symmetric solar model. The background and the perturbed intensities are computed by solving the radiative transfer equation considering the main sources of opacity in the continuum (absorption and scattering). Results. We find that for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity perturbations: the geometrical effects due to the wave displacement must always be taken into account as they lead to a difference in amplitude and a phase shift between temperature perturbations at the surface and emergent intensity perturbations. The closer to the limb, the greater the differences. For modes with eigenfrequencies around 3 mHz, we found that the radial and horizontal components of the wave displacement are important, in particular, for high-degree modes. Conclusions. This work presents improvements for the computation of the intensity perturbations, in particular, for high-degree modes. Here, we explain the differences in intensity computations seen in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase toward the limb. This should prove helpful when interpreting some of the systematic centre-to-limb effects observed in local helioseismology. The computations are fast (3 s for 2000 positions and one frequency for one core) and can be parallelised. This work can be extended to models of the line-of-sight velocity observable.

Structure From Motion on XSlit Cameras.

We present a structure-from-motion (SfM) framework based on a special type of multi-perspective camera called the cross-slit or XSlit camera. Traditional perspective camera based SfM suffers from the scale ambiguity which is inherent to the pinhole camera geometry. In contrast, an XSlit camera captures rays passing through two oblique lines in 3D space and we show such ray geometry directly resolves the scale ambiguity when employed for SfM. To accommodate the XSlit cameras, we develop tailored feature matching, camera pose estimation, triangulation, and bundle adjustment techniques. Specifically, we devise a SIFT feature variant using non-uniform Gaussian kernels to handle the distortions in XSlit images for reliable feature matching. Moreover, we demonstrate that the XSlit camera exhibits ambiguities in pose estimation process which can not be handled by existing work. Consequently, we propose a 14 point algorithm to properly handle the XSlit degeneracy and estimate the relative pose between XSlit cameras from feature correspondences. We further exploit the unique depth-dependent aspect ratio (DDAR) property to improve the bundle adjustment for the XSlit camera. Synthetic and real experiments demonstrate that the proposed XSlit SfM can conduct reliable and high fidelity 3D reconstruction at an absolute scale.

Refined Geometric Modeling of Laser Pulse Propagation in Airborne LiDAR Bathymetry

To achieve a geometrically accurate representation of the water bottom, airborne LiDAR bathymetry (ALB) requires the correction of the raw 3D point coordinates due to refraction at the air–water interface, different signal velocity in air and water, and further propagation induced effects. The processing of bathymetric LiDAR data is based on a geometric model of the laser bathymetry pulse propagation describing the complex interactions of laser radiation with the water medium and the water bottom. The model comprises the geometric description of laser ray, water surface, refraction, scattering in the water column, and diffuse bottom reflection. Conventional geometric modeling approaches introduce certain simplifications concerning the water surface, the laser ray, and the bottom reflection. Usually, the local curvature of the water surface and the beam divergence are neglected and the travel path of the outgoing and the returned pulse is assumed to be identical. The deviations between the applied geometric model and the actual laser beam path cause a coordinate offset at the water bottom, which affects the accuracy potential of the measuring method. The paper presents enhanced approaches to geometric modeling which are based on a more accurate representation of water surface geometry and laser ray geometry and take into account the diffuse reflection at the water bottom. The refined geometric modeling results in an improved coordinate accuracy at the water bottom. The impact of the geometric modeling methods on the accuracy of the water bottom points is analyzed in a controlled manner using a laser bathymetry simulator. The findings will contribute to increase the accuracy potential of modern ALB systems.

Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry

We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature K\"ahler metrics. We carry this out by exploring in detail the metric geometry of Mabuchi geodesic rays, and the uniform convexity properties of the space of K\"ahler metrics.

On Adiabatic Sound Propagation in a Shallow Sea with a Circular Underwater Canyon

An idealized problem of sound propagation in a shallow sea with a curved underwater canyon is considered. The canyon is a circular feature of the bottom relief which causes horizontal refraction of acoustic waves. The sound field computation method for a waveguide with an inhomogeneity of this type is considered, and the geometry of horizontal rays trapped by the canyon is studied. The computation method is based on the separation of variables in the equation for the mode amplitudes and representation of the solution in the form of a double series. This technique is rather general in nature, because it can be used to compute the field in any problem where the waveguide has rotational symmetry. Furthermore, it is also shown which terms of the series correspond to horizontal rays trapped by the canyon.

On the Application of Asymptotic Formulae Based on the Modified Maslov Canonical Operator to the Modeling of Acoustic Pulses Propagation in Three-Dimensional Shallow-Water Waveguides

In this study a technique for the modeling of propagation of acoustic pulses in shallow-water waveguides with three-dimensional bottom inhomogeneities is described. The described approach is based on the ray theory of sound propagation and the method of modified Maslov canonical operator. Representation of acoustical field in terms of the canonical operator gives several important advantages in practical computations. In particular, it is possible to compute the time series of a pulse at a reception point located on the caustics of a family of rays. Besides, a significant part of calculations within the proposed approach can be performed analytically; therefore, overall computational costs are substantially reduced. As an example, sound propagation in a wedge-shaped waveguide representing a shelf area near the coast line is considered. The ray geometry in such a waveguide is discussed both in the isovelocity case and in the presence of the thermocline in the water column. For both cases, the time series of an acoustical pulse propagating along the track aligned along the isobaths (parallel to the apex edge of the wedge) is calculated.

Optics of fast magnetosonic waves

The geometry of fast magnetosonic rays in a low beta plane plasma is studied. The relevant ray equations turn out to form an analytic differential system, which in a number of cases yield explicit solutions. A combination of analytical and numerical techniques is used to study the behavior of rays, wavefronts and caustics; it turns out that null magnetic points and the boundary points of current sheets influence strongly their global geometry. The subject admits an interpretation in terms of classical optics, with a refraction index equal to the inverse of the magnetic field size.

Expansion of Wave Rays and Fronts in Media with Inhomogeneous Structure

In the article on the principles of Fermet, Huygens obtaine the differential equations in the form of Hamilton, which describe the ray trajectories and wave fronts in inhomogeneous media. Established that the vector of Poynting-Umov's determining the direction of energy propagation in inhomogeneous medium is coincident with the vector tangent to the ray. In the second part of the article established that the equations of the theory of rays' propagation in inhomogeneous media have the form of equations of nonlinear dynamics and describe the emergence of deterministic chaos in the geometry of rays for a wide variety of types of heterogeneous structures. In this case, the rays behave randomly and their description you must go to the description based on the theory of random functions and fields. In the third part of the paper is considered a model which is equivalent to the random medium and the calculation of the coordinates of the ray (the mathematical expectation and correlation functions). Understanding of these characteristics gives information about the behavior of the trajectories of the rays for these models of media. The description of the behavior of rays on the basis of the equations of statistical mechanics is discussed in the article for functions of Markov's type.

A Generic Multi-Projection-Center Model and Calibration Method for Light Field Cameras.

Light field cameras can capture both spatial and angular information of light rays, enabling 3D reconstruction by a single exposure. The geometry of 3D reconstruction is affected by intrinsic parameters of a light field camera significantly. In the paper, we propose a multi-projection-center (MPC) model with 6 intrinsic parameters to characterize light field cameras based on traditional two-parallel-plane (TPP) representation. The MPC model can generally parameterize light field in different imaging formations, including conventional and focused light field cameras. By the constraints of 4D ray and 3D geometry, a 3D projective transformation is deduced to describe the relationship between geometric structure and the MPC coordinates. Based on the MPC model and projective transformation, we propose a calibration algorithm to verify our light field camera model. Our calibration method includes a close-form solution and a non-linear optimization by minimizing re-projection errors. Experimental results on both simulated and real scene data have verified the performance of our algorithm.

Properties of Stimulated Emission of the РМ567 Dye in Pores of Anodized Aluminum Oxide

Properties of the stimulated emission of the РМ567 dye in porous aluminum oxide are investigated. It is established that when РМ567 molecules are doped into aluminum oxide pores, a small part of dye molecules forms aggregates. The quantum yield of fluorescence of РМ567 in Al2O3 is Ф f = 0.85. The stimulated emission of РМ567 in the Al2O3 film is observed in the short-wavelength maximum of the fluorescence band. The threshold of the stimulated emission is 2 MW/cm2. The kinetics of the decay of stimulated emission is measured. It is demonstrated that low-Q lasing of the stimulated emission of РМ567 in the film with Q ≥ 1·102 is caused by the fact that the geometry of rays in pores does not correspond to that of complete internal reflection, and hence, the radiative losses increase. The efficiency of lasing of РМ567 in Al2O3 is 0.3%.

Current sheets as waveguides for the fast magnetosonic wave

The geometry of rays and wavefronts associated to the fast magnetosonic wave is studied for a planar cold plasma, in an equilibrium where magnetic null points and current sheets are present. It is found (a) that null points attract rays and singular ones repel them, causing a characteristic evolution of wavefronts; and (b) that current sheets act as waveguides, directing both rays and wavefronts towards them. High frequency fast waves remain continuous when crossing the sheet; depending on the initial condition, these waves may become shocks before or after the sheet.

Opticks : GPU Optical Photon Simulation for Particle Physics using NVIDIA® OptiX™

Opticks is an open source project that integrates the NVIDIA OptiX GPU ray tracing engine with Geant4 toolkit based simulations. Massive parallelism brings drastic performance improvements with optical photon simulation speedup expected to exceed 1000 times Geant4 when using workstation GPUs. Optical photon simulation time becomes effectively zero compared to the rest of the simulation. Optical photons from scintillation and Cherenkov processes are allocated, generated and propagated entirely on the GPU, minimizing transfer overheads and allowing CPU memory usage to be restricted to optical photons that hit photomultiplier tubes or other photon detectors. Collecting hits into standard Geant4 hit collections then allows the rest of the simulation chain to proceed unmodified. Optical physics processes of scattering, absorption, scintillator reemission and boundary processes are implemented in CUDA OptiX programs based on the Geant4 implementations. Wavelength dependent material and surface properties as well as inverse cumulative distribution functions for reemission are interleaved into GPU textures providing fast interpolated property lookup or wavelength generation. Geometry is provided to OptiX in the form of CUDA programs that return bounding boxes for each primitive and ray geometry intersection positions. Some critical parts of the geometry such as photomultiplier tubes have been implemented analytically with the remainder being tessellated. OptiX handles the creation and application of a choice of acceleration structures such as boundary volume hierarchies and the transparent use of multiple GPUs. OptiX supports interoperation with OpenGL and CUDA Thrust that has enabled unprecedented visualisations of photon propagations to be developed using OpenGL geometry shaders to provide interactive time scrubbing and CUDA Thrust photon indexing to enable interactive history selection.

A prototype optical-CT system for PRESAGE 3D dosimeter readout

This work introduces the Duke Integrated-lens Optical Scanner (DIOS), a prototype optical-CT system designed for convenient and low-cost readout of PRESAGE 3D dosimeters. A key novelty of the DIOS is the incorporation of a multi-purpose light-collimating tank (the LC-tank). The LC-tank collimates light from a point source, maintains parallel ray geometry through a dosimeter mounted inside the tank, and refocuses emergent light onto a CCD detector. A second purpose is to dramatically reduce the amount of refractive matched fluid required in prior optical-CT scanners. This is achieved by substituting large quantities of refractive-matched fluid with solid RI-matched polyurethane. The advantages of DIOS include eliminating the need for expensive telecentric lenses, and eliminating the impracticality of large volumes of RI matched fluid. The DIOS is potentially more susceptible to stray-light artifacts. Preliminary phantom testing shows promising agreement between PRESAGE/DIOS readout and prior commissioned optical-CT scanners, as well as with Eclipse dose calculations.

Time-domain Helmholtz-Kirchhoff integral for surface scattering in a refractive medium.

The time-domain Helmholtz-Kirchhoff (H-K) integral for surface scattering is derived for a refractive medium, which can handle shadowing effects. The starting point is the H-K integral in the frequency domain. In the high-frequency limit, the Green's function can be calculated by ray theory, while the normal derivative of the incident pressure from a point source is formulated using the ray geometry and ray-based Green's function. For a corrugated pressure-release surface, a stationary phase approximation can be applied to the H-K integral, reducing the surface integral to a line integral. Finally, a computationally-efficient, time-domain H-K integral is derived using an inverse Fourier transform. A broadband signal scattered from a sinusoidal surface in an upwardly refracting medium is evaluated with and without geometric shadow corrections, and compared to the result from a conventional ray model.

Gimbal Influence on the Stability of Exterior Orientation Parameters of UAV Acquired Images.

In this paper, results from the analysis of the gimbal impact on the determination of the camera exterior orientation parameters of an Unmanned Aerial Vehicle (UAV) are presented and interpreted. Additionally, a new approach and methodology for testing the influence of gimbals on the exterior orientation parameters of UAV acquired images is presented. The main motive of this study is to examine the possibility of obtaining better geometry and favorable spatial bundles of rays of images in UAV photogrammetric surveying. The subject is a 3-axis brushless gimbal based on a controller board (Storm32). Only two gimbal axes are taken into consideration: roll and pitch axes. Testing was done in a flight simulation, and in indoor and outdoor flight mode, to analyze the Inertial Measurement Unit (IMU) and photogrammetric data. Within these tests the change of the exterior orientation parameters without the use of a gimbal is determined, as well as the potential accuracy of the stabilization with the use of a gimbal. The results show that using a gimbal has huge potential. Significantly, smaller discrepancies between data are noticed when a gimbal is used in flight simulation mode, even four times smaller than in other test modes. In this test the potential accuracy of a low budget gimbal for application in real conditions is determined.