Design of a Correcting Plate for Compensating the Main Reflector Distortions of a Dual Shaped System
We present a method of synthesizing a correcting.
geometrical optics↗
Engineering topics
Galindo-Israel, V.
Publications and source records attributed to Galindo-Israel, V..
Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations
In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.
Galindo-Israel, V.↗
Design considerations for the beamwaveguide retrofit of a ground antenna station
A primary requirement of the NASA Deep Space Network (DSN) is to provide for optimal reception of very low signal levels. This requirement necessitates optimizing the antenna gain to the total system operating noise level quotient. Low overall system noise levels of 16 to 20 K are achieved by using cryogenically cooled preamplifiers closely coupled with an appropriately balanced antenna gain/spillover design. Additionally, high-power transmitters (up to 400 kW CW) are required for spacecraft emergency command and planetary radar experiments. The frequency bands allocated for deep space telemetry are narrow bands near 2.1 and 2.3 GHz (Ka-band), 7.1 and 8.4 GHz (X-band), and 32 and 34.5 GHz (Ka-band). In addition, planned operations for the Search for Extraterrestrial Intelligence (SETI) program require continuous low-noise receive coverage over the 1 to 10 GHz band. To summarize, DSN antennas must operate efficiently with low receive noise and high-power uplink over the 1 to 35 GHz band.
Veruttipong, T.↗
Design considerations for the beam-waveguide retrofit of a ground antenna station
Retrofitting an antenna that was originally designed without a beam waveguide introduces special difficulties because it is desirable to minimize alteration of the original mechanical truss work and to image the actual feed without distortion at the focal point of the dual-shaped reflector. To obtain an acceptable image, certain Geometrical Optics (GO) design criteria are followed as closely as possible. The problems associated with applying these design criteria to a 34-meter dual-shaped DSN (Deep Space Network) antenna are discussed. The use of various diffraction analysis techniques in the design process is also discussed. GTD and FFT algorithms are particularly necessary at the higher frequencies, while Physical Optics and Spherical Wave Expansions proved necessary at the lower frequencies.
Veruttipong, T.↗
Low-loss off-axis feeds for symmetric dual-reflector antennas
Circularly symmetric, dual reflector, high gain antenna systems often require feeds placed off the system's axis because of the need for multiple feeds to use the reflector antenna. Also, the constraint requiring the hyperboloid or shaped subreflector to remain circularly symmetric is sometimes added. In a Cassegrainian system, the subreflector and feed may be rotated off axis around the paraboloid focus and retain main reflector focusing. However, substantial spillover results in considerable noise with a high gain/low noise temperature system. In a shaped system, the tilt of the shaped subreflector and feed together results in substantial defocusing as well as spillover noise. If the subreflector is tilted approximately one-half the angle of the feed tilt in either the Cassegrainian or the dual shaped reflector antenna, it is found that spillover and noise are substantially reduced with tolerable defocusing. An extensive numerical analysis of these effects was conducted to determine the characteristics of a planned 70-meter, dual shaped reflector versus Cassegrainian antenna and to gain some understanding of the cause of the observed effects.
Veruttipong, T.↗
Interpolation Methods for GTD Analysis of Shaped Reflectors
The finding of smooth analytic representations for antenna reflector surfaces which are prescribed only by discretized data obtained by various synthesis methods is examined. Frequently the data are distributed in a nonuniform grid and contain noise. The smoothness required is to C sub 1 for physical optics diffraction analysis and to C sub 2 for geometrical theory of diffraction (GTD) analysis. The GTD analysis approach requires a surface description which returns data very rapidly. Two methods of interpolation, the global and the local methods, are discussed. They each have advantages and disadvantages; characteristics are discussed and examples are presented.
Galindo-Israel, V.↗
Synthesis of offset dual shaped subreflector antennas for control of Cassegrain aperture distributions
The method presented for antenna upgrading 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 produce a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method is based on the approximate formulation for an offset dual shaped high gain antenna first presented by Galindo-Israel and Mittra (1977). It is pointed out that in their approximate formulation, the geometrical optics energy was scattered from a subreflector and then from a second large reflector, which reflected a uniform phase distribution. In the offset dual shaped subreflector (DSS) antenna proposed here, 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. The DSS synthesis is tested on the 210-ft-diameter Cassegrain antenna at Goldstone, California.
Galindo-Israel, V.↗
Shaped reflector beam waveguide and high gain antenna systems
In this paper the problem of synthesizing dual reflector antennas for both amplitude and phase control of the final aperture distribution is discussed. An approximate procedure for the offset synthesis problem is presented and applications of the procedure to the shaping of beam waveguides and reflectors for high-gain antenna systems are illustrated.
Galindo-Israel, V.↗
Far-Field Antenna Pattern From a Near-Field Test
Plane/polar geometry simplifies measurement of near-field data for this antenna and allows a determination of far-field pattern by Jacobi-Bessel series expansion of data. Measuring probe is an undersized, dielectrically loaded and open-ended waveguide with a far-field pattern similar to that of a small magnetic dipole in its forward directions, making it unnecessary to rotate probe in direction similar to antenna rotation.
Rahmat-Samii, Y.↗
Synthesis of offset dual reflector antennas transforming a given feed illumination pattern into a specified aperture distribution
The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed which realizes an exact aperture phase distribution and an aperture amplitude distribution that is accurate to within an arbitrarily small numerical tolerance. However, this procedure does not always yield a smooth solution, i.e., the reflector surfaces thus realized may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, only the requirement for the aperture amplitude distribution is relaxed, and the condition on the aperture phase distribution is continued to be satisfied exactly.
Mittra, R.↗
Recent advances in electromagnetic synthesis and analysis of dual-shaped reflector antennas
Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.
Galindo-Israel, V.↗
Scan performance of dual offset reflector antennas for satellite communications
The basic numerical steps of a method to analyze dual offset reflector antennas are reviewed. The technique employs an alternative approach to calculating the secondary pattern of an arbitrarily shaped offset dual reflector antenna, and is based on the application of the geometrical theory of diffraction from the subreflector and physical optics (PO) scattering from the main reflector. The PO integral is evaluated using the Jacobi-Bessel series expansions, and numerical results are presented for the off-axis scan performance of an offset clear aperture Cassegrain antenna. Results indicate that the equivalent paraboloid concept can be used to determine the location of displaced feed and define the local optimal focal plane, and the scan performance of the Cassegrain reflector can be improved if the feed is located on the true opimal surface.
Rahmat-Samii, Y.↗
A new look at Fresnel field computation using the Jacobi-Bessel series
Computational procedures that would be useful in finding the Fresnel field from a knowledge of the Jacobi-Bessel expansion of the far field are considered. The range of validity of the Fresnel approximation is carefully examined by comparing it with the exact closed form solution for the uniform circular aperture. Also investigated numerically, and in great detail, is the range of validity (over theta) of the Fresnel small angle (FSA) approximation. For moderate sized apertures as small as 10 wavelengths, it is found that the FSA approximation is very accurate to angles as wide as four or more sidelobes (as seen in the far zone). A very efficient computational method is shown to exist for the radiation integral in the form of a single series expansion that is analytically continuous and convergent for a wide range of observation points in three-dimensional space.
Galindo-Israel, V.↗
A new approach for synthesizing dual reflector antennas
It is pointed out that the offset geometry for dual reflector antennas is attractive for satellite communications where low side lobes are necessary to achieve good isolation between adjacent main lobes operating over the same frequency band. A description is presented of a new, numerically rigorous technique for synthesizing dual offset reflectors. The objective of the synthesis procedure is to transform a given primary feed pattern into a desired aperture distribution through two reflections in an offset dual reflector system. It is found that a given specification for the aperture distribution does not always lead to a smooth solution for the two surfaces. In this event, the so-called energy condition on the specified amplitude distribution is relaxed, and an approximate solution which satisfies the energy condition only within a certain numerical tolerance is derived.
Mittra, R.↗
Plane-polar Fresnel and far-field computations using the Fresnel-Wilcox and Jacobi-Bessel expansions
It is pointed out that the computation of the Fresnel fields for large aperture antennas is significant for many applications. The present investigation is concerned with an approach for the effective utilization of the coefficients of the Jacobi-Bessel series for the far-field to obtain an analytically continuous representation of the antenna field which is valid from the Fresnel region into the far field. Attention is given to exact formulations and closed form solutions, Fresnel and Fresnel small angle approximations, aspects of field expansion, the accuracy of the Fresnel and Fresnel small angle approximations, and the Jacobi-Bessel expansion applied to the Fresnel small angle approximation.
Rahmat-Samii, Y.↗
Shaped reflector antenna analysis using the Jacobi-Bessel series
A vector radiation integral is derived for an offset shaped reflector illuminated by an arbitrarily located and oriented source. A procedure for expressing the integral in terms of a series of the Fourier transforms of an effective aperture distribution is discussed. The Jacobi-Bessel series is used to evaluate the Fourier transforms. Numerical results are presented for different reflector configurations and source locations.
Rahmat-Samii, Y.↗
A plane-polar approach for far-field construction from near-field measurements
The planar configuration with a probe scanning a polar geometry is discussed with reference to its usefulness in the determination of a far field from near-field measurements. The accuracy of the method is verified numerically, using the concept of probe compensation as a vector deconvolution. Advantages of the Jacobi-Bessel series over the fast Fourier transforms for the plane-polar geometry are demonstrated. Finally, the far-field pattern of the Viking high gain antenna is constructed from the plane-polar near-field measured data and compared with the previously measured far-field pattern.
Rahmat-Samii, Y.↗
An efficient technique for the computation of vector secondary patterns of offset paraboloid reflectors
A series approach for the rapid computation of the vector secondary pattern of offset paraboloid reflectors wherein the feed is displaced is presented. We show that the Jacobi polynomial series method, which has been demonstrated to provide an efficient means for evaluating the radiation integral of symmetric paraboloid reflectors, can be extended to the case of an offset paraboloid without compromising the ease or speed of computation. The analysis leading to the series formula is also useful for deriving an analytic expression for the optimum scan plane for the displacement of the feed. Representative numerical results illustrating the application of the method and the properties of the offset paraboloid are presented.
Mittra, R.↗