Cone Of Rays Research Articles

Application of Lorentz geometry to refractive optical systems

Lorentz geometry represents the mathematical foundation of Einstein’s general relativity. From the concept of the cone of edge rays, it was introduced successfully in the study of homogeneous media nonimaging optics, Gutiérrez et al. (1996), Winston et al. (2005). In this paper we present a new Lorentzian geometry formalism to analyze optical systems with refractive elements. We have obtained the general system of partial differential equations and the integrability conditions to be fulfilled. This new mathematical formalism is the basis for a new optical technique to analyze the irradiance pattern produced by refractive optical systems. We apply this Lorentzian formalism to an optical media with exponential refraction index. Comparisons between irradiance patterns obtained by this formalism and by raytrace simulations are also presented.

Disguised assumptions and the conditions for validity of Debye integral representation of focused fields.

In the paper of Wolf and Li [Opt. Commun.39, 205 (1981)OPCOB80030-401810.1016/0030-4018(81)90107-3], a sufficient condition was obtained under which the Debye integral representation (DIR) may be expected to give a good approximation to the solution of a boundary value problem that is generally taken to represent a field in the region of focus. After a long calculation of the solid angle of the circular cone of rays over which the Debye integral extends, the validity condition of DIR reduces to the requirement that the Fresnel number of the diffracting aperture, when viewed from the geometrical focus, is much greater compared to unity. The current study removes the long calculation of the cones of rays and replaces it with an analysis of Debye's disguised assumption relating to a replacement of the actual (unknown) field emerging from the exit pupil by the unperturbed incident field.

Advancing Accuracy of Shooting and Bouncing Rays Method for Ray-Tracing Propagation Modeling Based on Novel Approaches to Ray Cone Angle Calculation

We propose and evaluate several improvements to the accuracy of the shooting and bouncing ray (SBR) method for ray-tracing (RT) electromagnetic modeling. We propose per-ray cone angle calculation, with the maximum separation angle between rays calculated for every individual ray, based on a set of local neighbors rather than a single global maximum. This allows the smallest theoretical error of the SBR method, adaptive ray spawning procedures, and a unique analysis of the effect of ray cone sizes on the accuracy of the method. For the conventional uniform angular distribution of rays, a less general and versatile but more expeditious approach, we derive an analytical expression for the optimal choice of cone angle to again maximize the overall accuracy of the SBR computation. Both approaches are derived using icosahedral ray spawning geometry and adjacent ray sets, which are also used for our double counted rays identification and removal technique that avoids complicated ray path searches. The results demonstrate that the advanced shooting and bouncing RT method--using both proposed ray cone generation approaches--can perform wireless propagation modeling of tunnel environments with the same accuracy as image theory RT, a dramatically less efficient but traditionally considerably more accurate solver.

Интерферометр для контроля углов клиньев

The paper considers an optoelectronic laser interferometer system to control wedge angles. This system records an interference pattern on an image sensor. The interferometer makes it possible to estimate the small angle of the wedge under investigation by the variation it introduces into the shape of the optical radiation wavefront, which the interferometer then converts into changing the size of the interference pattern. In the interferometer considered, the wedge under investigation refracts the incident ray cone. The error inherent in surface finishing causes the deformation of the working wavefront to be 2 to 4 times smaller as compared to the deformation in previously known control setups involving reflection from the wedge surfaces. The interferometer developed ensures highly accurate control of wedge angles at the surface polishing stage, including potential detection of wedge direction. If required, the interferometer may be used for comprehensive quality control of wedge manufacturing, assessing not only the surface nonplanarity, but also glass inhomogeneity; it may also be used to control prism angles

Cascaded diffraction in optical systems. Part II: example calculations.

Real imaging optical systems are in any case finite in diameter and therefore limit the ray cones coming from the various object points. The truncation of the ray cones generates edge diffraction effects, which have an impact on the point spread function and therefore on the resolution of the system. Traditionally real calculations of the diffraction effects are mostly simplified by assuming a truncation in the exit pupil only. In this hybrid approach, the light propagation therefore can be calculated by raytrace first, and the more cumbersome diffraction calculated is only performed between exit pupil and image plane. To come to a better quantitative understanding of the validity of this approximation, a more refined model is developed in an adjacent publication. Some example calculations for real setups and an overview about the order of magnitude of the cascaded diffraction effects are worked out in this contribution.

Geometric modeling of integration of solar energy in high-rise bio-climate buildings

A feature of high-rise buildings is their high energy consumption compared to buildings of lower height. The use of solar energy can reduce the energy load. An urgent task is to develop tools that can justify decision-making on the feasibility of integrating solar systems in the energy-efficient design of high-rise buildings.The article discusses the methods of geometric modeling in determining the effective solar radiation on the surfaces of high-rise bioclimatic buildings. The design of bioclimatic high-rise buildings is based on the principle of their maximum adaptation to the natural environment, which is considered at three levels: macroclimate, mesoclimate and microclimate.In geometric modeling of the integration of solar systems into a high-rise bioclimatic building at the macro level, a primary analysis is carried out regarding the potential of solar radiation in accordance with the geographical location of the high-rise buildings on the planet. Application of the geometric model of the diurnal cone of solar rays Φ, which was proposed by prof. А. Podgorny allows you to analyze changes in the duration of solar exposure for a given day of the year when changing the geographical location of the construction site on the planet.Geometric modeling of heliosystems at the meso and micro levels analyzes the potential for solar radiation of a high-rise building in accordance with its shape, position and shading. In the article, it is proposed that zones of effective solar radiation on the surfaces of tall buildings be determined by geometric modeling of the zones of formation of intrinsic and incident shadows, taking into account the dynamics of sunlight. Zones of constant, variable lighting, constant shading on the surface of a high-rise building determines the location of the rational arrangement of solar systems.

New species of Labiobulura (Nematoda: Ascaridida), and Dorcopsinema and Paralabiostrongylus (Nematoda: Strongylida) from Dorcopsis muelleri (Macropodidae) from Lengguru, West Papua, Indonesia

ABSTRACTA new species of the Subuluridae (Nematoda: Ascaridida) Labiobulura lengguruensis n. sp. is described from the caecum and colon and two new species of the Chabertiidae: Cloacininae (Nematoda: Strongylida) Paralabiostrongylus tuberis n. sp. and Dorcopsinema amplum n. sp. are described from the stomachof the macropodid marsupial Dorcopsis muelleri (Lesson, 1827) (Mammalia: Macropodidae) in Papua Indonesia. Labiobulura lengguruensis differs from all congeners in having a simple denticle associated with each labial lobe of the buccal capsule. Paralabiostrongylus tuberis can be distinguished from its congeners in by the position of the deirid and the form of the dorsal ray and genital cone. Dorcopsinema amplum can be distinguished from its congeners by the length of the spicule, the morphology of the appendages on the ventral lip of the genital cone, the position of the lateral branches of the dorsal ray, the shape of the female tail, the morphology of the vagina and the size of the eggs.The known nematode fauna of D. muelleri is summarised. The finding of three species of Dorcopsinema each in a different geographical locality suggests the possibility of allopatric speciation. A revised key to the species of Dorcopsinema is given.

Spatial, polarization and angular characteristics of external conical refraction

Appearance of two rings of external conical refraction (ECR) is investigated theoretically within the plane-wave approximation. The hollow cone of ECR is the cone of normals inside a crystal. Due to a birefringence, two sets of isonormal waves are related to the cone. One set forms a filament of rays directed along the biradial, and the other set generates the hollow cone of rays. The apex angle of the cone is nearly twice as large as that of the cone of normals and its axis is close to the direction of the biradial. After leaving the exit facet of a crystal plate, the ray filament spreads into a cone again, and the ray cone gives rise to a second outer cone so that two nonconcentric rings appear at a screen behind the plate. Polarization states at the neighbouring points of the rings lying on one radius are mutually perpendicular. Numerical calculations were performed for crystals with moderate and large optical anisotropy, namely KGd(WO4)2, ammonium oxalate, L-N-(5-Nitro-2-peridyl)leucinol and sulfur. Dispersion of the angle of ECR, the apex angle of the cone of incident (from air) waves and the ray cone is calculated for three tungstate crystals, KGd(WO4)2, KLu(WO4)2, and KY(WO4)2.

Realistic cosmological measurement of distances in the Friedmann universe

We consider application of our development of Zeldovich’s ideas, presented in Ref. 1, for measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. To make a comparison with [Formula: see text]CDM we analyze ADD measurement in [Formula: see text]CDM model responsible for the later inflation (present accelerated expansion of the Universe). We also analyze a small deviation from equality in the distance duality relation induced by the fullness (by matter) of the cone of light rays (CLR) which is used for the ADD measurement method.

Development of Zeldovich’s approach for cosmological distances measurement in the Friedmann Universe

We present our development of Zeldovich's ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an open, spatially-flat and closed universe, and for any stress energy tensor. We solve the mentioned equations in terms of quadratures in a form suitable for further numerical investigations for the present universe filled by radiation, (baryonic and dark) matter and dark energy. We perform the numerical investigation in the absence of radiation, and show the strong dependence ADD on the filling of the cone of light rays (CLR). The difference of the empty and totally filled CLR may reach 600-700 Mps. for the redshift $f\simeq 3$.

Nonparaxial accelerating Bessel-like beams

A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories.

Bessel-like optical beams with arbitrary trajectories

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with pre-specified shape. These ray cones have circular bases on the input plane; thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between non-accelerating and accelerating optical waves that share diffraction-resisting and self-healing properties.

Axial-cones

Catadioptric imaging systems are commonly used for wide-angle imaging, but lead to multi-perspective images which do not allow algorithms designed for perspective cameras to be used. Efficient use of such systems requires accurate geometric ray modeling as well as fast algorithms. We present accurate geometric modeling of the multi-perspective photo captured with a spherical catadioptric imaging system using axial-cone cameras: multiple perspective cameras lying on an axis each with a different viewpoint and a different cone of rays. This modeling avoids geometric approximations and allows several algorithms developed for perspective cameras to be applied to multi-perspective catadioptric cameras. We demonstrate axial-cone modeling in the context of rendering wide-angle light fields, captured using a spherical mirror array. We present several applications such as spherical distortion correction, digital refocusing for artistic depth of field effects in wide-angle scenes, and wide-angle dense depth estimation. Our GPU implementation using axial-cone modeling achieves up to three orders of magnitude speed up over ray tracing for these applications.

Progresses in 3D integral imaging with optical processing

Integral imaging is a promising technique for the acquisition and auto-stereoscopic display of 3D scenes with full parallax and without the need of any additional devices like special glasses. First suggested by Lippmann in the beginning of the 20th century, integral imaging is based in the intersection of ray cones emitted by a collection of 2D elemental images which store the 3D information of the scene. This paper is devoted to the study, from the ray optics point of view, of the optical effects and interaction with the observer of integral imaging systems.

Double reflection and birefringence of a wave incident on the crystal boundary under the conditions of internal conical refraction

It is shown that a cone of rays undergoing internal conical refraction generates reflected ordinary and extraordinary rays at the crystal boundary, which form cylindrical surfaces. The cylinders formed by ordinary and extraordinary rays are, respectively, circular and elliptical. At the same intensity of rays forming the cone of internal conical refraction, the intensity distributions over the generatrices of these cylinders are different. A similar situation occurs also for refracted rays if a crystal is adjacent to an anisotropic medium.

Designing reflectors to generate a line-shaped directivity diagram

A novel method of designing a mirror surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the mirror surface for an arbitrary illuminating beam wavefront is derived as an envelope of a parametric family of surfaces. Each surface in the family transforms the input beam into a beam with plane wavefront of desired direction. For the spherical illuminating beam the mirror surface is given as the envelope of the family of rotational paraboloids. The envelope is represented as a family of curves given by the intersections of paraboloids with circular cones of rays from the point source.

Half-plane diffraction in a chiral medium

An exact, closed-form solution is presented for the problem of diffraction of an electromagnetic plane wave by a perfectly conducting half-plane embedded in a chiral (optically active) medium. The direction of incidence is arbitrary (3D case). The fundamental feature of the problem is its two-mode character. A chiral medium is isotropic but handed and supports two modal fields propagating with distinct velocities. The modes couple at the screen and its edge. Arising phenomena are exemplified by the two cones of diffracted rays and the excitation of lateral waves at the half-plane. The problem is a generalization of the previously solved 2D case of normal incidence and this motivates the adopted approach via the modal Hertz potentials. A subtle role in this context is played by the modal ghost potentials, i.e. peculiar potentials corresponding to the zero electromagnetic field. The mathematical core structure underlying the problem is defined by a boundary value problem for two scalar functions satisfying distinct Helmholtz equations and subject to a pair of boundary conditions at the half-plane. Required solutions to this problem are obtained with the aid of the Wiener–Hopf technique. The main result of the paper consists in showing how to generate, via relevant operators, the 3D electromagnetic solution from three appropriate solutions to the core problem. These solutions are, in essence, available from the 2D case. Basic properties of the solution are briefly discussed. Definitions of the diffraction coefficients indicate the canonical role of the problem for a geometrical theory of diffraction in chiral media.

Large volume growth and finite topological type

It is shown in this paper that a complete noncompact n n -dimen- sional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than 2 − 1 / n 2-1/n .

SOUND DIRECTIVITY GENERATED BY HELICOPTER ROTORS USING WAVE TRACING CONCEPTS

Results are presented from a study of directivity and sound focusing effects generated by helicopter rotors encountering parallel and oblique blade vortex interactions (BVI). The primary analysis is performed by using wave tracing to determine ray cones and acoustic lines from source points on the rotor with supersonic trace (phase) velocities. The results are compared and contrasted to predictions made from a numerical solution of the Ffowcs-Williams Hawkins equation. Sample problems considered include parallel and oblique BVI with an isolated line vortex, and interactions with self-generated epicycloidal vortices in forward flight. It is confirmed that the BVI process can produce strong directivity and clusters of focused sound waves in the far field. The trace velocity and wave tracing technique is shown to have potential applications for studies in noise reduction and/or noise directivity modifications using passive devices such as blade tip sweep. It is also shown that the numerically efficient nature of determining the primary acoustic lines with the trace velocity method can allow regions with strong directivity to be efficiently mapped out using redistributive observer point techniques.

Reflection shadow imaging of crystal surface by low-voltage point-reflection electron microscopy

We present experimental observations of low-voltage point-projection electron microscopy (PPM) in the reflection geometry (point-reflection electron microscopy (PRM)) and their interpretations. The cone of rays originating from an electron-field-emitter tip placed near the surface of a bulk crystal is Bragg reflected, and shadow images of the surface form inside each Bragg-reflected order. Shadow images of the cleaved GaAs (1 0 0) surface were obtained, using electrons of a few hundred volts kinetic energy. They are images of the same surface, projected from different virtual source directions beneath the surface. Reflected line patterns were also observed. Their origins are given, based on results from simulation and three-dimensional electron ray-tracing calculations. The instrument is promising for obtaining simple LEEM-type and stereographic images of crystal surface, since the shadow image in each reflected Bragg disk provides a projection of the surface from a different perspective.