Reflector Shape Research Articles

Reconstruction of reflecting structures from vertical seismic profiles with a moving source

When a vertical seismic profile (VSP) is recorded, the illuminated part of a reflector depends upon the shape and position of the reflector itself as well as on the seismic velocities and the positions of sources and receivers. A preferable arrangement for the investigation of structures of reflectors is to fix the receiver(s) at constant depth(s) in the well and move the source horizontally along a line at the Earth’s surface, usually called a “multioffset VSP” (MSP) or “walkaway VSP.” As a test of the resolution power of this survey geometry, synthetic records were generated from a subsurface model by inverse Kirchhoff migration. Three different methods were applied for the reconstruction. Wavefront construction leads to the correct shape of the reflectors, thus assuring the validity of the modeling method applied. Reflection‐point mapping delivered a near similarity to the model, but without focusing fault edges. Kirchhoff migration resulted in a detailed image of the reflectors with fault edges focused. Application of reflection‐point mapping and Kirchhoff migration to a real survey delivered results consistent with results from a survey at the Earth’s surface.

The response of wavelength shifting panels in large water Cherenkov systems

This paper describes a series of tests performed with a panel of Bicron wavelength shifting acrylic plastic (BC-480) coupled to an EMI 9623B photomultiplier tube. The aim was to effectively increase the cathode coverage and its sensitivity to incident Cherenkov radiation, so that such a system could be employed in a solar neutrino detector. Measurements of the uniformity and effective efficiency of the system have been made and compared with the results of various simulation runs. The effects of side mirrors, back reflector, water interface and possible shaping of the panel to enhance its response are also assessed.

Application of subcriticality measuring methods for studying the temperature effect of the reactivity of uranium-water lattice assemblies

This paper presents some results of investigations of the temperature dependence of the reactivity of the MATR-1 stand of the Physics Power Institute; two techniques were used: a pulsed neutron source and an expelled source. The proposed scheme of the investigations was checked in uranium-water assemblies in which a reflector is important for the reactivity balance. The kinetic parameters were assumed for U 235 in both the experiments and calculations. The calculations were made in the two-group diffusion approximation in two dimensional geometry with the FACTOR and DNESTR programs. The constnats of the thermal neutron group were determined taking into account the heterogeneous core structure by averaging over the space-energy distribution of the neutron flux in modeled Wigner-Seitz cells. Results show that the systematic application of subcriticality measuring methods allows the direct determination of the importance of the core and reflector shapes i nthe development of the temperature dependence of the reactivity.

Optimization of Imperfect Diffuse Reflectors

The collection of light by an absorbing body may be enhanced by partly surrounding it by a reflector. The authors examine what shape of imperfect diffuse reflector will lead to the maximum power transfer from a given lambertian source to a given absorbing body. Applying the calculus of variations to this problem yields a set of integro-differential equations. Some optimal reflector profiles obtained by numerical solution of these equations are presented.

Design method of four‐reflector type beam waveguide feeds

AbstractWe describe a design method for four‐reflector type beam waveguide feeds composed of a conical horn and four reflectors which are widely used for the first‐stage radiation system of earth station antennas in satellite communication. The relational equation between the design parameters is derived based on beam‐mode expansion and we specify the independent design parameters. We derive the relation between the design parameters and such performance characteristics as spillover loss, cross‐polarization component and frequency. As design criteria (I) we minimize the cross‐polarization component on the condition of maintaining the spillover loss within a tolerable level, and (II) we minimize the spillover loss on the condition of maintaining the cross‐polarization component with a tolerable level. In determining the size of reflectors under prescribed mechanical constraints we establish that the design parameters governing the size of the conical horn and the shape of reflectors can be determined uniquely. Examples of application of this design method are presented to show the effect of the design parameters and to increase the design efficiency.

Design and characteristics of sector/cosecant‐square shaped beam antenna

AbstractThe base station antenna for a subscriber radio system is required to have a beam with sector section in the horizontal plane and cosecant‐square beam in the vertical plane. This paper proposes a method for shaping the reflector surface of the antenna so that it forms the required beam in the two planes and also presents the experimental results for a test antenna. It is shown that adequate characteristics can be obtained by this shaping method even for a single reflector. In this method the central cross‐section curve obtained as a solution of a two‐dimensional problem is used as the initial condition and then the reflector coordinates are successively determined from the conditions of the elevation angle of the ray reflected at the surface. The test antenna is a 90° sector beam antenna with aperture of about 52δ in the vertical plane and about 43δ in the horizontal plane. The experimental results indicate a gain of 23.5 dB at the peak and more than 20 dB within an angle of 1.5° in the vertical plane. The antenna beam realizes a sectoral section in the horizontal plane and a cosecant‐square section in the vertical plane to a level as low as ‐10 dBi. The results demonstrate the effectiveness of the present reflector shaping method.

The current state of the reflector antenna art

The current state of the reflector antenna art is presented in the form of a review article, intended primarily for engineers who are new in the field. The properties of paraboloidal antennas are related to aperture efficiency, surface tolerance, feed defocusing, and aperture blocking. Other reflector shapes considered are offset-fed paraboloids, classical and offset Cassegrain systems, shaped-dual reflectors, and scanning reflectors. Properties of contoured-beam systems are reviewed. Structures and materials are reviewed for ground stations and satellite-borne reflectors. Emphasis is placed on specific hardware examples for each principle or concept. Near-field probing, dichroic surfaces, and techniques of surface metrology are presented as examples of promising areas for new developments.

An auditorium design based upon subjectively optimal acoustics for The Washington Center, Olympia, Washington, USA

Recently developed acoustical design criteria, derived from an exhaustive program of subjective testing at Kobe University and the University of Gottingen, have been applied to the acoustical design of The Washington Center, a multipurpose performing arts facility in Olympia, Washington, USA. In response to the programmatic emphasis on high‐quality acoustics for orchestral music, the architectural configuration progressed from a wide, single‐balcony scheme to one that is narrower with two balconies. The acoustical design effort was concentrated on the size and shape of wall reflectors, room asymmetry, and diffusing elements. The first reflection time delay, binaural dissimilarity, and total energy of the sound field were predicted with a computer model of the auditorium. Adjustments were made to the shape, cheeked by computer, and synthesized into the architectural design, arriving at optimum values for selected seat locations.

An extended model of the ultrasonic transducer

The linear model of the ultrasonic transducer has been extended to allow for the effects of diffraction, poor bonding and the various shapes of calibration reflectors. In this way the predictions of the model are brought closer into line with the practical results which would be obtained when transducers are calibrated. All of the common calibration targets are included in the model while, within the limitations outlined, the response of transducers to some natural defects could also be predicted.

Rotation and Shape of High Altitude Reflectors Controlled from the Ground

Passive, inverted-dish shaped communications mirrors made of a thin wire mesh may be maintained in a stationary position above most of the atmosphere by the pressure of reflected radiation beamed at the mirror from the ground. We show that by beaming at the mirror an appropriate mixture of linearly and circularly polarized radiation, and by inducing small periodic variations of the plane of polarization, one can monitor and sufficiently control wire orientation in the mirror, which allows one to reduce mirror weight and/or set the mirror in rotation. Mirror rotation in turn can modify mirror shape, open up flaps, and allow synchronized messages to be sent to prechosen locations.

Anti‐fading polygonal cylinder passive repeater

AbstractFor economical construction of general microwave communication channels passive repeaters are used. Effective improvement in avoiding momentary interruptions cannot be expected unless measures are adopted to prevent fading at passive repeaters and space diversity is employed at the antenna side.The radiation field of an aperture type antenna is represented by the product of the amplitude distribution and the phase distribution of the field at the aperture. Amplitude distribution has been the main area considered in analyses to date. This paper discusses a method for controlling the phase distribution and shows that this method is best suited to prevent fading. the method modifies the shape of a conventional flat reflector excited by plane waves into a polygonal cylinder which inscribes a shallow parabolic cylinder, so that a near‐axis directional beam is formed in even the direction of the first null point of the reflected waves. the level at the first null point of a polygonal cylindrical reflector designed to keep the gain reduction directly on the axis below about 1 dB agrees well with the predicted mean field intensity due to fading at a receiving point. the use of a polygonal cylinder reflector is economical and prevents momentary interruptions due to fading so that the communication channels remain stable and possess high quality with improved reliability.

Prediction of scattering cross-section reductions due to plate orthogonality errors in trihedral radar reflectors

A method is presented for the determination of the reduction in scattering cross-section levels due to angular errors between plates in trihedral radar corner reflectors. The method applies to any regular reflector shape and for any incident ray direction in the reflector main beam zone; it owes its viability to a recently developed technique for determining trihedral reflector effective areas. The analysis is not exact, but gives good agreement with experimental results for a wide range of reflector sizes.

Deconvolution and the seismic theory of inverse scattering

In the seismic theory of inverse scattering, the problem is to infer the shape, size, and constitutive properties of reflectors from scattering measurements recorded at or near the earth's surface. Specifically, the geophysical inverse scattering problem is concerned with the identification of the elastic parameters associated with a linear three-dimensional wave equation, which is an approximate model for the propagation of seismic waves. For the three-dimensional acoustic wave model with ideal conditions e.g., noise-free data and no limitations on array aperture and temporal bandwidth, formal solutions exist (See Gel'fand and Levitan (1951); Agranovich and Marchenko (1963); Moses (1956); Newton (1980); and Silvia and Weglein (1981)). When these ideal conditions are not met, as is the case in the actual seismic reflection experiment, some type of regularization technique must be used in order to stabilize the inversion of a certain matrix equation. This paper discusses the seismic signal processing technique of deconvolution and how it relates to the formal theory of inverse scattering.

A New Method for Computer Aided Design of Luminaire Reflectors

This method consists of two stages. In the first stage, an approximate shape for the reflector is designed which provides a candlepower distribution by the reflector as close to a required distribution as possible within a range of dimensional limits. The required candlepower distribution and the range are given by input data. In the second stage, a precise prediction of the candlepower distribution of the designed reflector is made, considering the luminance distribution on a lamp surface to be non-uniform. The authors obtain the optimum reflector shape by repeated iterations of these stages, modifying the reflector shape based on the results of the candlepower distribution calculations, then recalculating the candlepower distribution for the new shape, until the candlepower distribution becomes satisfactory.

Optimum shape of a Kirkpatrick-Baez x-ray reflector supported at discrete points for on-axis performance

Nested flat plates bent into the Kirkpatrick-Baez parabolic geometry and supported at discrete points are one means of obtaining large area grazing incidence x-ray optics with good angular resolution. A method for optimizing the on-axis resolution combining finite element and ray trace techniques with selective masking is presented. The optimally determined supported point location technique can lead to greatly reduced in situ labor costs.

High efficiency and low sidelobe design for a large aperture offset reflector antenna

A design method giving high efficiency and low sidelobes is discussed for large aperture offset reflector antennas. A new reflector shaping technique using the subreflector and the beam waveguide reflector with the parabolic main reflector is proposed to simplify the main reflector manufacturing process. The effectiveness of the technique is confirmed by the model experiments. One problem with this reflector shaping technique is that the subreflector edge level cannot be controlled independently of the main reflector edge level. By investigating the relation between the gain reduction and the subreflector edge level, which affects the wide-angle sidelobe levels, the realizable characteristics of antennas are studied. In order to decrease the subreflector edge level without reducing the aperture efficiency, a technique using an extended reflector is also proposed. Its effectiveness is shown by theoretical and experimental investigations.

Quantitative evaluation of surface shape of medium size optical paraboloidal reflectors

A kinematic chain guided pneumatic displacement gauge system has been proposed to determine quantitatively the surface shape of medium size paraboloidal reflectors. Linear motion lower kinematic pairs have been synthesized in the form of kinematic linkage chain which generates the parabolic curve of predetermined geometry to be used as reference for observation purposes.

Truncation of nonimaging cusp concentrators

Truncation of nonimaging cusp reflectors which concentrate sunlight onto cylindrical receivers leads to collector designs which are more cost effective through substantial reductions in mirror height and length with small reductions in concentration ratios. In this paper, reflector shapes for truncated nonimaging cusp concentrators having various acceptance angles are presented, as well as curves for height/aperture and mirror arc length/aperture ratios versus concentration ratio. In addition to their general utility in concentrator design, the latter curves have special significance for thermoformed plastic reflector substrates. The reflector height/aperture ratio is the “draw”, and the reflector arc length/aperture ratio is the “stretch” to which the material is subjected during forming. With this information, important considerations in plastics fabrication can be addressed easily in the early design stages.

Open resonators with apertures in reflectors

A theoretical analysis is made of resonators with two mirrors having apertures of different dimensions and shape. The problem is reduced to integral equations of quasioptics. The solution of these equations, including two-dimensional systems (when the shape of the aperture differs from the reflector shape), is obtained applying the perturbation theory. The resultant simple expressions for the principal characteristics of the oscillation modes are sufficiently accurate in a wide range of resonator geometries of practical interest. Further progress is reported of the application of the perturbation method to open resonators.

Properties of caustics from conic reflectors 1: Meridional rays

General relations for the caustic surfaces obtained by illuminating an ellipsoid, paraboloid, or hyperboloid reflector by a point-light source, lying along the principal axis of the reflector, were derived. A thorough study of the evolution of caustics with the particular type of reflector, as well as with the relative position of the point-light source and the reflector, was undertaken. Interesting laws for the shape, position, and properties of the caustics were derived, depending on the shape of the particular reflector used, its aperture, and the relative position of the light source and the reflector. These properties may be useful for the creation of wide angle all-reflective multimirror systems designed for definite limits of distances and which, by adjacent pairs of reflectors, present only a limited and reduced amount of third-order aberrations.