Spherical Reflector Research Articles

Early history of Arecibo Observatory

Thank you for the article “The Arecibo Observatory: Fifty astronomical years” by Daniel Altschuler and Chris Salter (Physics Today, November 2013, page 43). I’d like to add a historical note.The first publication to discuss using a spherical reflector set in the ground and steered by a line source, as illustrated in the article’s figure 2, was published in May 1951 by engineers at the Air Force Cambridge Research Laboratories (AFCRL).11. R. C. Spencer, C. J. Sletten, J. E. Walsh, Correction of Spherical Aberration by a Phased Line Source, Air Force Cambridge Research Laboratories, Cambridge, MA (1951);http://www.dtic.mil/dtic/tr/fulltext/u2/a800275.pdf The Department of Defense was interested in using what would become the world’s largest antenna to better understand the ionosphere for long-range radar and communications. Thus in 1959 officials from the AFCRL and Cornell University, home to Arecibo designer William Gordon, signed a contract to build the observatory. The project was funded by the Advanced Research Projects Agency, with Philipp Blacksmith of the AFCRL named as the project officer.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. C. Spencer, C. J. Sletten, J. E. Walsh, Correction of Spherical Aberration by a Phased Line Source, Air Force Cambridge Research Laboratories, Cambridge, MA (1951);http://www.dtic.mil/dtic/tr/fulltext/u2/a800275.pdf, Google Scholar© 2014 American Institute of Physics.

Development of a Spherical Solar Collector with a Cylindrical Receiver

Solar energy can be used for substitution of the depleting fossil fuels in thermal applications and electricity generation through thermal route. For medium and high temperature applications, a system for collecting solar energy at high temperatures was developed and built in this research work. The system, built at the center of development of renewable energy of the Algiers, consists of a 2θm= 60o included angle, R0 = 0.90 m diameter spherical reflector with a cylindrical receiver filled with water, tracking reflector which moves into the focus following the sun's movement. The system is capable of heating water or other fluids to temperatures above 350oC, thus making it possible to obtain process heat for domestic use and to store solar energy in a compact and economical way. An analysis of the system's optical characteristics was performed to aid in the design of the spherical reflector and cylindrical receiver. The thermal performance of the system was analyzed. The effects of mirror reflection, concentration ratio, heat transfer to the fluid (water), incidence angle, size and form of the cylindrical receiver, environmental conditions (wind, ambient temperature), have been studied by means of thermal model.The performance of the spherical reflector was tested by the temperature of the water. Total efficiencies (solar to thermal) of ηth= 60% -70% were obtained for a wide range of temperatures up to 350oC. The results of the present study show that it is possible to use the spherical reflector for systems requiring process heat and make possible substantial utilization of solar energy and considerable savings relative to fossil energy in the sunny countries of the world.

DUAL-BAND DUAL-SENSE UNIDIRECTIONAL CIRCULARLY POLARIZED ANTENNA WITH CPW-FED FOR WIRELESS APPLICATIONS

A novel dual-band unidirectional circularly polarized (CP) antenna fed by coplanar waveguide (CPW) for wireless applications is proposed. The antenna configuration consists of a ring- shaped ground, an F-shaped central strip and a spherical cap reflector. The longer and shorter branches of the F-shaped central strip help to produce radiations at lower and higher frequencies. The CP characteristics are achieved by adding two solid arcs and a grounded tuning stub. Both simulated and measured results are given and analyzed. Measurement results show a 10 dB return loss with a bandwidth of 56% (2.15 GHz-3.83 GHz) at 2.45 GHz (ISM), and a bandwidth of 42.6% (4.67 GHz- 7.2 GHz) at 5.8 GHz (HiperLAN), a 3 dB axial ratio bandwidth of 15.1% (2.25 GHz-2.62 GHz), 4.1% (5.67 GHz-5.91 GHz). The maximum gains within the two CP bands are 8.7 dBic and 10.2 dBic, respectively.

Non-scanning curvature measurement with a segmented ultrasonic annular array

The presentation describes an ultrasonic method for the determination of the curvature radius of an object without mechanical scanning. Instead of scanning, a segmented ultrasonic annular array is used, where the phase and amplitude differences on the different receivers are used to determine the curvature radius (spherical reflector) and the lengths of the semi-axes (ellipsoidal reflectors), respectively. Experimental results with spheres as reflectors are presented and the latest results on the determination of the length of the semi-axes with an ellipsoidal reflector are presented.

Determination of the size of spherical inclusions smaller than the width of the sound beam

The current presentation introduces a new method for the determination of the size of balls with a diameter from nearly a wavelength up to the width of the sound beam (and higher). The basic approach is to analyse the directional pattern of the reflectors, which depends on size and shape. If the reflector is centered on the acoustic axis of the transducer, small objects cause approximately the same omni-directional echo, so that no differentiation of objects on the receiver is possible. For non-axial acoustic irradiation of the reflectors, differences of the directional pattern appear. While scanning spherical reflectors, these variations can be detected with a special structured array. Therefore a 3 MHz annular array is used, whose outer rings are divided in additional segments.In this work first measurements of spheres with different sizes where done. The sphere diameters varied about one up to six wavelengths and the lateral size of the sound beam in the scan depth was 2.8 wavelengths. All measurements are combined with sound field simulations, to provide algorithms for the determination of the size of reflectors.

Electromagnetic field in the caustic region of a spherical reflector under oblique incidence using Maslov's method

A theoretical investigation is made for the problem of electromagnetic field focussing by wide angle spherical reflector receiving obliquely incident plane waves of linearly polarized monochromatic radiation. The Maslov's method has been applied to determine the electromagnetic fields in the caustic region of the reflector. High frequency field expression which contains caustic region is converted into caustic free field expression by transforming the situation into hybrid domain. The high-frequency field solution that contains the caustic region is obtained from geometrical optics. The defect in high frequency solution due to geometrical optics is overcome by Maslov's method. Two cases of polarization of the incident wave have been considered, namely, (1) with the field parallel and (2) perpendicular to the meridional plane of incidence. The numerical computations are made to study the behavior of field intensity in caustic region using Maslov's method. The analytical and numerical results obtained from Maslov's method are also compared with method of angular spectrum which are in agreement.

High-precision velocity measuring system for projectiles based on retroreflective laser screen

The flying velocity of projectile is a key parameter for evaluating weapon performances. Here we adopt retroreflective laser screen optoelectronic approach to realize real-time, non-contact, reproducible, high-precision measurement for projectile velocity. Two fan-shaped laser screens combining with retroreflective films construct the sensing area, the changed luminous flux while the projectile flying through the screens is converted by optoelectronic detect module, collected with high-speed data collecting module, saved and processed by software. We study the retroreflective light spots by imaging when a one-dimensional expanding line-shaped laser beam incidents the cone cube reflective sheeting and the glass microsphere retroreflective material respectively. Based on the study result, an off-axis inclined spherical reflector with a central laser-penetrating hole, combining with a line-shaped LD and a large area PD, is used to achieve the laser screen transmitting-receiving integration optoelectronic detection. For the purpose of high precision, we propose a maximum negative slope algorithm finding the optimal timing feature points to calculate the velocity. The self-comparison experimental data with 7.62mm projectile indicate that the measuring precision by this method can reach 0.19‰.

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.

Total Immersion

This article focuses on various aspects of immersive engineering and its application in a product lifecycle. Immersive engineering can shorten development time and reduce production and maintenance costs. Studies show that immersive engineering also improves resource utilization and material flow, increases producibility, and reduces rework and scrap. Various company case studies show that the benefits of immersive engineering include fewer injuries, lower cost of tooling changes, higher quality, and faster time to market. In order to prepare an immersive engineering simulation, tasks under study are performed or mimed by technicians and workers who wear a couple of dozen spherical reflectors or markers that enable the digital replication of their body movements—motion tracking. The advantage of immersive engineering is that issues involving quality, productivity, manufacturability, lifecycle costs, and ergonomics across broad spectrum can be discovered and addressed early, when changes are less costly than they are after a company has invested in tooling or made other commitments.

Boundary diffraction wave theory of resistive surfaces with edge discontinuities

The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numerically.

A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges

The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically.

Multifocusing revisited ‐ inhomogeneous media and curved interfaces*

ABSTRACTWe review the multifocusing method for traveltime moveout approximation of multicoverage seismic data. Multifocusing constructs the moveout based on two notional spherical waves at each source and receiver point, respectively. These two waves are mutually related by a focusing quantity. We clarify the role of this focusing quantity and emphasize that it is a function of the source and receiver location, rather than a fixed parameter for a given multicoverage gather. The focusing function can be designed to make the traveltime moveout exact in certain generic cases that have practical importance in seismic processing and interpretation. The case of a plane dipping reflector (planar multifocusing) has been the subject of all publications so far. We show that the focusing function can be generalized to other surfaces, most importantly to the spherical reflector (spherical multifocusing). At the same time, the generalization implies a simplification of the multifocusing method. The exact traveltime moveout on spherical surfaces is a very versatile and robust formula, which is valid for a wide range of offsets and locations of source and receiver, even on rugged topography. In two‐dimensional surveys, it depends on the same three parameters that are commonly used in planar multifocusing and the common‐reflection surface (CRS) stack method: the radii of curvature of the normal and normal‐incidence‐point waves and the emergence angle. In three dimensions the exact traveltime moveout on spherical surfaces depends on only one additional parameter, the inclination of the plane containing the source, receiver and reflection point. Comparison of the planar and spherical multifocusing with the CRS moveout expression for a range of reflectors with increasing curvature shows that the planar multifocusing can be remarkably accurate but the CRS becomes increasingly inaccurate. This can be attributed to the fact that the CRS formula is based on a Taylor expansion, whereas the multifocusing formulae are double‐square root formulae. As a result, planar and spherical multifocusing are better suited to model the moveout of diffracted waves.

Analysis of the High Frequency Field Expressions at the Caustic Region of a Spherical Reflector Placed in Chiral Medium

High frequency field expressions are derived around the caustic region of a spherical reflector placed in a homogenous, isotropic and reciprocal chiral medium. Firstly Geometrical Optics (GO) field expressions are derived for the spherical reflector placed in chiral medium. As the GO approximation fails at the vicinity of the caustic therefore, Maslov’s method has been used to find the field expressions which are also valid around the caustic region. Present work is an extension of previous work from two dimensional to three dimensional reflector. Some numerical results including line plots around the focal region of spherical reflector placed in chiral medium are obtained using the derived expressions.

On calculation of DGS diagrams of normal transducers for spherical and cylindrical reflectors

Formulas for the acoustic path were obtained and DGS diagrams were calculated in a general case and in a scalar approximation for a hollow spherical reflector positioned axially symmetrically relative to a normal transducer. The convergence of DGS diagrams to the asymptotic value determined by the formula for the far-field zone, the difference between them obtained using the reflection coefficients with exact and approximate accounting of the boundary conditions at the reflector, and the effect of a pulsed transmission-reception mode were studied. The DGS diagrams for a hollow circular cylindrical reflector (side drilled hole) were calculated using I.N. Ermolov’s method.

Temperature-stable and high Q-factor TiO2 Bragg reflector resonator

The highest Q-factor resonators employ whispering gallery modes in single-crystal sapphire but have poor temperature stability. Rutile was the first dielectric material used to construct a microwave dielectric resonator. However, its very high temperature coefficient of permittivity made it unsuitable for practical applications. This paper reports a high Q-factor (50 000) and temperature-stable spherical Bragg reflector resonator based on polycrystalline rutile operating at 29.9 GHz. Temperature stability is achieved by adjusting the electric filling factor of a spherical shell so that in combination with its highly negative temperature coefficient of permittivity, the effect of thermal expansion is exactly cancelled out.

Propagation properties of hollow conical double half-Gaussian beams

In this paper, we present a new hollow beams – hollow conical double half-Gaussian beams – and deduce the analytical equation of propagation and transformation of these through the paraxial optical system by using the Collins formula. By using the formula deduced, we calculate and analyze the propagation properties of these in free space. In an experiment, we have obtained hollow conical double half-Gaussian beams, which are cone-angle controllable by using the combinational optical system of the spherical reflector, reflecting positive-axis cone and zoom lens, and we obtain the beam loop of far field in different distances. The results show good coherence between theory and experiment. This paper will play a guiding role in the practical application of hollow conical double half-Gaussian beams.

Spherical Reflector in Chiral Medium Supporting Positive Phase Velocity and Negative Phase Velocity Simultaneously

Focused high frequency electromagnetic waves reflected from a PEC spherical surface placed in homogeneous, reciprocal and isotropic medium with high chirality parameter are analyzed. The value of the chirality parameter is set such that it simultaneously supports modes of negative and positive phase velocities. Present work is an extension of the previous work, in which the chiral medium supports only positive phase velocity. Using the previous derived expressions, line plots in the focal region are obtained.

Non-astigmatic imaging with matched pairs of spherically bent crystals or reflectors

This paper defines the exact conditions for the application of a previously proposed, general, non-astigmatic, imaging scheme, consisting of a matched pair of spherically bent crystals or reflectors, to x rays. These conditions lead to two specific experimental arrangements, of which one can provide large magnifications. Potential applications include the x-ray diagnosis of laser-produced plasmas and x-ray imaging of, e.g., biological samples, using the highly monochromatic radiation at synchrotron light sources. The results obtained for x rays are, however, valid for a wide spectrum of the electromagnetic radiation so that, for instance, an application of one of the imaging schemes to lithography in the EUV wavelength range should also be possible, if the spherically bent crystals are replaced by appropriate spherical reflectors. Also described is the design of an x-ray crystal spectrometer, which meets the here defined, necessary requirements for the observation of the x-ray spectra of helium-like argon.

A compensated spherical reflector antenna using sub‐reflectarrays

AbstractSpherical reflectors have been used as wide‐angle scanning antennas due to the unique geometric properties of the sphere. The inherent spherical aberration, however, causes considerable performance degradation. This article presents a novel sub‐reflectarray compensating technique to correct it. A microstrip reflectarray is a planar, inexpensive, passive device with unique capabilities of controlling reflection phases. By exploiting this feasible property, it is employed as an auxiliary phase corrector, and the phase errors caused by spherical aberration are compensated. Two examples, a 35‐m spherical reflector antenna at Ka‐band and a 1.5‐m breadboard spherical reflector, are presented, and simulation results show great performance improvement for both no scan and large scan cases. Because of the difficulty in measuring large reflector antennas at UCLA, it is part of future plan to collaborate with other institutions for the verification of the concept. However, we believe that the simulation results generated in this article should provide acceptable performance prediction of the proposed antenna design. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 577–582, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24088

Wide-angle point-to-point x-ray imaging with almost arbitrarily large angles of incidence

The paper describes a new scheme for wide-angle point-to-point x-ray imaging with almost arbitrarily large angles of incidence by a matched pair of spherically bent crystals to eliminate the astigmatism, which is a well-known imaging error of spherical mirrors. In addition to x rays, the scheme should be applicable to a very broad spectrum of the electromagnetic radiation, including microwaves, infrared and visible light, as well as UV and extreme UV radiation, if the crystals are replaced with appropriate spherical reflectors. The scheme may also be applicable to the imaging with ultrasound.