Analysis of numerically specified multireflector antennas bykinematic and dynamic ray tracing

A technique for tracing rays and fields with several numerically specified reflectors by using geometrical optics (GO) is described. The ray paths are determined by launching individual rays from the feed point and following them by reflection from all the reflector surfaces to the output aperture of the last reflector. This procedure is referred to as kinematic ray tracing. Thereafter, the amplitude, phase and polarization of the E-field is traced along the ray paths to the aperture; this is referred to as dynamic ray tracing. The aperture field is then integrated to find the aperture efficiency, which is factorized into convenient subefficiencies. The technique has been implemented in a computer code that has been used to analyze the proposed new shaped-offset dual-reflector feed for the spherical reflector antenna at the Arecibo Observatory     

A shaped offset-fed dual-reflector antenna

A shaping scheme based on geometric optics for offset-fed dual-reflector antennas is presented. A ray tube emerging from a symmetric feed horn is transformed, after reflections, into a circular beam with a uniform phase and a prescribed radial power distribution on the aperture. In this scheme, Snell's law was not imposed on the main reflector. Based on this approximate solution, computer runs were taken for a 5.5-m dish baseline system, and very satisfactory results were obtained. The system so designed not only gives very low sidelobes but also provides a very high aperture efficiency. At 12 GHz an estimated 84 percent of aperture efficiency was achieved in spite of the severe constraint that the ray intersecting the edge of the main reflector meet a -10-dBi criterion.     

La synthèse d’antennes à deux réflecteurs conformés à alimentation décalée

A potentially economic method for upgrading the gain of the large earth reflector antenna Cassegrain system to a gain comparable to that obtainable with a dualshaped reflector antenna system is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a paraboloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna where the geometrical optics energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller subreflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

Synthesis of offset dual shaped subreflector antennas for control of Cassegrain aperture distributions

Many existing large ground reflector antennas have been designed as Cassegrain systems-i.e., paraboloid/hyperboloid combinations. Other large ground antennas are simply paraboloid designs. Upgrading the gain of these systems to a gain comparable to that obtainable with a dual shaped reflector antenna system has been an important and costly objective of many such ground stations. A potentially economic method for such an antenna upgrade is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a parabaloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna that was first presented by Galindo-Israel and Mittra in 1977. In that approximate formulation, the geometrical optics (GO) energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller (sub) reflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

Design of dual-reflector antennas with arbitrary phase and amplitude distributions

A synthesis method based on geometrical optics for designing a dual-reflector antenna system with an arbitrary phase and amplitude distribution in the aperture of the second reflector is presented. The first reflector may be illuminated by a pattern with an arbitrarily curved phase front. A pair of first-order ordinary nonlinear differential equations of the formdy/dx=f(x, y)are developed for the system. Questions concerning uniqueness, existence and bounds for the solutions can be answered. Calculations and numerical results for the design of a uniform amplitude and phase dual-reflector system are presented.     

A new transform relationship for interpreting axial fields near a focus

A new Fourier transform relationship is shown to apply between the axial distribution of a field near a focus and the field, averaged around the axis, in the aperture of the focussing device. If phase and amplitude are measured along the axis the transform gives the radial distribution in the aperture, averaged around the axis, of the field amplitude and of any deviations in phase from an ideally focussed wavefront. The transform is, therefore, useful in diagnosing surface errors in reflector antennas. It may also be of use in determining errors in optical aspheric lenses and mirrors where radial errors are more prevalent in manufacture than are azimuthal errors. If only axial power is measured, a Wiener-Khinchine relationship gives the autocorrelation of the averaged radial field distribution in the aperture. The autocorrelation by itself contains useful phase information and, in some instances, the averaged aperture field can be recovered from the autocorrelation through a process of modeling. Symmetry relationships are discussed together with a practical example where phase and amplitude in a radio telescope aperture are estimated by modeling from the autocorrelation function.     

Reflection-lobe dispersion in a phased-array antenna

Reflection lobes in phase-scanned arrays with traveling-wave feeds can significantly degrade sidelobe levels. These lobes can be dispersed if the regularity of the feed system can be destroyed. In this communication, an aperture phase distribution is described that provides the maximum reflection-lobe dispersion for an arbitrary reasonably smooth amplitude distribution. This phase distribution is an explicit function of the amplitude distribution. The theoretical limitations on reflection-lobe dispersion in one- and two-dimensional arrays are determined and compared with the calculated properties of a sample linear array. The edge effects are also indicated.     

Synthesis of multireflector antennas by kinematic and dynamic raytracing

A technique for synthesizing reflector surfaces that transform a known input ray-field (e.g., the radiation field of a feed) to a desired output ray-field (e.g. an aperture distribution) is presented. The synthesis problem is reduced to solving linear equations by local biparabolic expansions of the reflector surfaces. Because the solution is easier to control, this is advantageous compared to existing techniques based on solving nonlinear differential equations. The condition to obtain low cross polarization can therefore be readily included, and the requirements for an exact solution to exist can be found clearly. The latter has been the subject of discussion in the literature for several years. The synthesis technique is applied to a shaped-offset dual-reflector antenna and to the proposed dual-reflector feed of the spherical reflector antenna in Arecibo. In both cases circular and elliptical apertures are considered     

Offset dual-shaped reflectors for dual chamber compact ranges

The application of the theory of the synthesis of offset dual-shaped reflectors to the design of compact ranges is examined. The object of the compact range is to provide a uniform plane wave with minimum amplitude and phase ripple over as large a volume as possible for a given size reflector. Ripple can be lowered by reducing the edge diffraction from the reflector producing the plane wave. This has been done either by serrating or rolling the edge. An alternative approach is to use dual offset-shaped reflector synthesis techniques to produce a reflector aperture distribution that is uniform over most of the aperture, but with a Gaussian taper near the edge. This approach can be used together with rolling and/or serration if desirable. The amount of phase and amplitude ripple obtained with two different dual-shaped reflector designs is studied as a function of position in the plane wave zone and reflector size in wavelengths. The amount of both transverse and longitudinal (z-component) cross polarization is studied     

Shaped Circularly Symmetric Dual Reflector Antennas by Combining Local Conventional Dual Reflector Systems

This paper presents a geometrical optics (GO) shaping method for circularly symmetric dual reflector antennas. The method is a one step procedure obtaining a local dual reflector system including both reflector surfaces and caustic simultaneously, such that a given feed power is transformed through a corresponding local reflector system into a desired aperture distribution. A shaped reflector system consists of an electrically small section of distinctive local reflector surfaces and its own caustic. Each caustic location varies and explains how the power is redistributed through the shaped reflector system. Each local reflector system is found iteratively with a previously known local dual reflector system. Several nonlinear algebraic equations are formulated based on GO principals and geometrical properties of a dual reflector system. The method reduces the solution to one simple non-differential equation with one unknown in order to find a local dual reflector system. Physical Optics (PO) analysis is used to verify the solution.      

A scanning spherical tri-reflector antenna with a moving flatmirror

Spherical reflector systems can achieve pattern scanning without rotation of the main reflector through the use of multiple subreflectors that can move. Also, two subreflectors can be shaped to correct for spherical aberration and to control the aperture distribution on the spherical main reflector. In a previous paper (see ibid., vol.41, p.778, no.6, 1993) we introduced a method that offers both aperture phase and intensity control and scans the main beam without an accompanying movement of the illuminated area over main reflector. The method can overcome the poor aperture utilization problem common in spherical reflector antenna systems; however, it requires motion of the entire subreflector system, including the feed, during scan. In this paper we discuss a method that does not require motion of the subreflector system during scan. This method employs a flat mirror that creates a virtual image of the subreflector system. The motion of the subreflector system in the previous design is replaced by the motion of the virtual image that is controlled by the motion of the flat mirror. The new design offers simplified mechanical motion, while maintaining beam efficiency performance comparable to that of traditional spherical tri-reflector scanning antennas, but with some sacrifice in aperture efficiency and cross-polarization performance     

Application of complex ray tracing to scattering problems

Representations and geometric constructions associated with complex points, complex lines, and complex rays are introduced. They are applied to the problem of scattering of an evanescent plane wave by a conducting circular cylinder. This problem has an exact solution, which provides a check of the validity of complex ray tracing and suggests more general applications. An important role is played by the transformation that maps the point of reflection, on the complex extension of the scattering surface, onto the trace in real space of the complex reflected ray. For the particular problem considered, the phase and amplitude of the reflected field are computed and the "phase paths" and "phase fronts" are constructed. The reflected field and phase paths obtained in this manner are not to be taken in their entirety because some reflection points are not "illuminated" by the incident wave, and because the reflector may be only part of the cylinder. Tentative selection and truncation rules are used which yield good agreement with the exact solution over some regions. The disagreement, where it occurs, comes-as it does for real rays-from neglecting the diffracted field such as the creeping waves around smooth surfaces and, in the case of truncation, the edge waves from the discontinuity. Some consideration is given to scattering by an arbitrary smooth conductor. Some problems peculiar to the use of complex rays are stated.     

Numerical technique for shaping reflecting surfaces to synthesize antenna patterns

Algorithms for shaping offset dual reflector antenna surfaces are presented which use small areas of optimally tilted conic sections reported by Y. Mizugutch for starting up a numerical synthesis of reflector surfaces. A new ray ratio squared method is described for the precise control of antenna aperture amplitude distributions.     

High Order Modes in a Spherical Fabry-Perot Resonator

The accuracy of the approximate solution to the wave equation in the "large aperture" case was investigated. The measured distribution of energy in the various transverse modes corresponded to the Laguerre-Gaussian solutions; resonant frequencies, however, deviated from those predicted by the approximate theory by as much as 2 percent for high radial mode numbers. Two first order perturbation calculations, including a neglected term in the wave equation and the nonsphericity of constant phase surfaces, yielded resonant frequencies in agreement with experiment.     

Reflector antenna fields--An exact aperture-like approach

A new computational approach is presented which allows fast analysis of radiation from large reflector antennas. For an aperture a Fourier transform (FT) relationship does exist between far-field and aperture distribution. Accordingly, the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe (Shannon-Whittaker theorem applied at Nyquist rate). The finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a FT. In order to overcome this difficulty a new pseudosampling expansion, which explicitly takes into account the extra factor, is developed. For parabolic reflector the sampling functions are related to the Fresnel integrals, and the far field can be exactly reconstructed in terms of aperture far-field samples, which can be computed using the fast Fourier transform (FFT). Numerical computations and error analysis show the excellent performance of the method, which can be generalized to deal with arbitrary reflector surfaces and near-field evaluation.     

Synthesis of a laterally displaced cluster feed for a reflector antenna with application to multiple beams and contoured patterns

When a feed is displaced from the focus of a reflector, phase distortion results in the effective aperture distribution, which in turn gives rise to secondary beam distortion. In multiple beam or contour beam antennas, the feed normally consists of an array of identical elements located on a triangular lattice. Taking advantage of this arrangement, a "cluster" of feed elements instead of a single element may be used to control each beam. By adjusting the relative excitations of the elements in a cluster, the aperture phase distortion due to the feed displacement may be partially compensated. Two general methods for synthesizing the excitations for a laterally displaced feed cluster are presented. In the first method the excitations are chosen to minimize the weighted phase error in the effective aperture by analytical means. The second method determines the excitations by a gradient optimization algorithm which minimizes the weighted error between an objective and the actual power patterns in the secondary pattern space. The first method is roughly two orders of magnitude more efficient computationally than the gradient optimization algorithm, but not as flexible in application or as precise. Numerical results are presented for cluster feed designs and their application to the synthesis of contour patterns.     

The effects of the truncation and curvature of periodic surfaces: astrip grating

Equations are outlined for surfaces which are finite and curved in two dimensions (only locally periodic), as well as infinitely periodic in one dimension but truncated and curved in the second dimension. By removing the periodicity, a truncated strip-grating results and the scattered fields as well as an associated reflection coefficient are calculated. These numerically rigorous calculations are compared against two approximate solutions. The comparison is intended as a check of the approximate solutions toward their application, in particular, in the analysis of surfaces which are finite and curved in two dimensions. In general, the edge currents always differed from the currents induced on an infinite grating, while the interior strip currents on a finite grating (depending on the excitation wavelength) may or may not differ from those of an infinite grating. It is concluded that if a more accurate calculation of the spectral response is to be found, the interior currents must be better approximated     

Nonconfocal multimode resonators for masers

The case of a resonator composed of two concave spherical reflectors separated by an arbitrary distance is examined. The general problem of the electromagnetic field distribution over the nonconfocal aperture is first formulated by means of the Huygens principle. The solution of the resulting integral equation is obtained analytically in the highly nonconfocal limit. It was found that when the reflector spacing d is much larger than the radius of curvature b of the reflectors, the aperture field distribution is in the form of traveling waves. For arbitrary d/b, the eigenvalues and eigenfunctions of the lowest order mode is obtained by numerical solution using the IBM 7090 computer. The diffraction loss was found to increase rapidly when d→2b and a geometrical interpretation of this behavior is given. Furthermore, it was found that as the spacing departs from the confocal value, the apertures are no longer surfaces of constant phase. The optimum spacing for maximum Q of the resonator is also obtained.     

Classical axis-displaced dual-reflector antennas for omnidirectional coverage

The aim of this work is to discuss the synthesis and performance of classical dual-reflector antennas suited for an omnidirectional coverage. The reflector arrangements are axially symmetric with surfaces of revolution generated by axis-displaced conic sections, established from geometrical-optics (GO) standpoints to achieve omnidirectional radiation characteristics. Closed-form equations are derived for the design of all possible reflector configurations. The vector GO aperture field is also obtained, yielding an approximate analysis by the aperture method. Some pertinent geometrical characteristics and efficiency curves are then presented and discussed for several antenna configurations fed by transverse electromagnetic coaxial horns (for vertical polarization). A practical antenna design is conducted and analyzed by the method-of-moments technique, demonstrating the accuracy of the efficiency analysis yield by the aperture method for moderately large antenna apertures.     

A scattering matrix-based beamformer for wide-angle scanning in hybrid antennas

This paper presents a new approach to beamforming in hybrid antennas. Using a scattering matrix model for the hybrid antenna system, a bidirectional transformation is developed that relates the signals at the hybrid system feed to the signals that would be present in a planar array at the location of the reflector aperture. For example, the received fields at the feed of a hybrid antenna system may be transformed into the fields at the reflector aperture, and these reflector aperture fields may then be processed as if they were received by a planar or linear array. Similarly, the desired field or current distribution across the reflector aperture when transmitting may be transformed into the required field or current distribution at the hybrid system feed. This method allows standard linear or planar array analysis and synthesis techniques to be used with the hybrid system. Examples are provided for transmit and receive weight synthesis.