A. Prata

Derivation and application of the equivalent paraboloid for classical offset Cassegrain and Gregorian antennas

The equivalent paraboloid is derived for classical offset Cassegrain and Gregorian antennas. The important practical case of systems with circular exit apertures is discussed in detail, and a condition for a symmetric equivalent paraboloid is derived. For such systems, diffraction effects are investigated using tapered and scanned feeds to illuminate the equivalent paraboloid and the two-reflector system. >

A design procedure for classical offset dual reflector antennas with circular apertures

A geometrical optics procedure for designing electrically optimized classical offset dual reflector antennas with circular apertures is presented. Equations are derived that allow the size and spacing of the main and subreflectors of the antenna system, along with the feed horn subintended angle, to be used as input variables of the design procedure. The procedure, together with these equations, yields an optimized design, starting from general system requirements. The procedure is demonstrated by designing both an offset Cassegrain and an offset Gregorian antenna, and is validated by analyzing their radiation patterns using physical optics surface current integration on both the main and subreflectors. >

Generalized classical axially symmetric dual-reflector antennas

This work presents a generalized study of classical axially symmetric dual-reflector antennas. The antenna dishes are simply described by conic sections, arranged to reduce the main-reflector radiation toward the subreflector surface. The dual-reflector configuration provides a uniform-phase field distribution over the illuminated portion of the aperture, starting from a spherical-wave feed source at the antenna primary focus. All possible configurations are characterized into a total of four distinct groups. Simple closed-form design equations and the aperture field distribution are derived, in a unified way, for all these kinds of generalized antennas using the principles of geometrical optics. The formulation is applied in a parametric study to establish the configurations yielding maximum radiation efficiency (not including diffraction effects). The design procedure is exemplified in the synthesis of a novel configuration, which is further analyzed by the moment method.

Lenslet analysis by rigorous vector diffraction theory

The accurate analysis of the electromagnetic field scattered by lenslets of dimensions of the order of the wavelength is considered. Assuming plane-wave illumination of the lenslet, a pair of coupled integral equations is derived, starting from the Stratton–Chu solution of Maxwell’s time-harmonic equations. These equations are solved rigorously (in a numerical sense) to obtain the lenslet-scattered field. For comparison, an approximate vector formula based on the aperture field is also derived and is related to the ubiquitous Fres-nel–Kirchhoff scalar diffraction formula. These analytical techniques are then applied to representative lenslets with diameters in the 2–100-wavelength range. The results demonstrate useful focusing characteristics even at 2–wavelength diameters and confirm that, depending on the accuracy required, the approximate vector formula based on the aperture field can be successfully employed for determining the lenslet-scattering characteristics.

A self-checking predictor-corrector algorithm for efficient evaluation of reflector antenna radiation integrals

An efficient algorithm for numerically evaluating diffraction integrals is presented. The algorithm employs a predictor-corrector scheme combined with Ludwigs (1968) integration procedure. The predictor-corrector eliminates the amplitude and phase ambiguities present in the real+imaginary algebra used in machine calculations and provides accuracy self-checking capabilities. The end result is a reliable and efficient integration method that does not require independent integrand phase information, can handle arbitrarily shaped integration domains, and is capable of monitoring its own accuracy as the integration proceeds. The performance of the algorithm is investigated by computing, using the physical optics technique, the electromagnetic field scattered by representative reflector antenna geometries. These tests demonstrate that the proposed algorithm is particularly efficient in the analysis of multi-reflector systems. >

GO Shaping of Omnidirectional Dual-Reflector Antennas for a Prescribed Equi-Phase Aperture Field Distribution

A formulation is presented for shaping dual-reflector antennas designed to offer an omnidirectional coverage. The shaping procedure is based on geometrical optics (GO) principles and assumes a uniform phase distribution for the aperture field. Two distinct dual-reflector arrangements, based on the axis-displaced Cassegrain (ADC) and ellipse (ADE) configurations, are investigated. The GO shaping results are validated using the accurate analysis provided by the method-of-moments technique

The design of classical offset Dragonian reflector antennas with circular apertures

The vector aperture field of classical offset Dragonian dual-reflector antennas is derived using geometrical-optics concepts. This field then yields the equivalent paraboloid of the geometry. From these results, the conditions for an axially symmetric equivalent paraboloid, when a circular aperture is assumed, are obtained. A complete step-by-step geometrical-optics-based design procedure for optimum classical offset Dragonian antennas with circular apertures is then presented (i.e., zero geometrical-optics cross-polarization and minimum spillover). This procedure is demonstrated by two design examples.

Beam squint in axially symmetric reflector antennas with laterally displaced feeds

Numerical calculations have been carried out and the beam squint for circular polarized excitation has been measured using a 100 m telescope. The telescope was operated in the Gregorian mode, where the equivalent focal length equals 387.5 m. The feed horn was laterally displaced by 1.364 m from the optical axis at the system focus. Good agreement was obtained between the numerical calculations and the experimental results. The authors found a shift of the two radiation patterns of approximately=2 arcsec. The orientation of the beam squint in the configuration with a laterally displaced feed is different from the orientation in offset reflector antennas. >

Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes

A geometrical theory of aberrations for the vicinity of the focus of arbitrary off-axis sections of conic mirrors is derived. It is shown that an off-axis conic mirror introduces linear astigmatism in the image. However, in classical two-mirror telescopes this aberration can be eliminated by tilting the secondary parent mirror axis. It is also shown that the practical geometrical-optics performance of a classical off-axis two-mirror telescope with no linear astigmatism is equivalent to the performance of an on-axis system, proving that both systems have identical third-order coma. To demonstrate the applicability of the theory developed in a practical system, a fast (i.e., f/2), compact, obstruction-free classical off-axis Cassegrain telescope is designed.

A 94 GHz spaceborne cloud profiling radar antenna system

The CloudSat spacecraft, scheduled to launch in 2003, will carry a 94 GHz cloud profiling radar. The electrical design of its antenna system has been completed and is presented here. It consists of a quasi-optical transmission line that performs signal relaying and duplexing (using a Faraday rotator), and a collimating antenna that provides the required gain and spatial resolution. A shaped open Cassegrain collimating antenna is used because of its clear aperture, which allows for accurate electrical modeling, good performance, and significant reduction in implementation time and cost. The complete antenna system (horns to free space) has a worst case predicted gain of 63.1 dBi (59% efficiency) and exceeds the sidelobe envelope requirement of 50 dB below the peak gain at angles from boresight greater than 7 degrees.