The high-frequency asymptotic solution of diffraction by a conducting subreflector is studied. By using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction, the scattered field is determined up to an including terms of order k^{-1/2} relative to the incident field. The key feature of the present work is that the surface of the subreflector is completely arbitrary. In fact, it is only necessary to specify the surface at a set of discrete points over a random net. Our computer program will fit those points by cubic spline functions and calculate the necessary geometrical parameters of the subreflector. In a companion paper by Y. Rahmat-Samii, R. Mittra, and V. Galindo-Israel, the scattered field from the submflector is used to calculate the secondary pattern of an arbitrarily shaped reflector by a series expansion method. Thus, in these two papers, it is hoped that we have developed a "universal" computer program that can analyze most dual-reflector antennas currently conceivable. It should also be added that our method of calculation is extremely numerically efficient. In many cases, it is one order of magnitude faster than the conventional integration method based on physical optics.

Diffraction by an arbitrary subreflector: GTD solution

Dual mode horns employed commonly as feeds for parabolic reflector antennas generate a radiation pattern that can be well-approximated by a Gaussian beam. To determine the far field of the antenna, it has been customary to perform integrations either of the physical optics currents on the reflector surfaces or of the ray optically determined field in the antenna aperture. These time-consuming integrations may be avoided if the Gaussian beam is tracked directly from the feed horn via subreflectors, if any, to the main reflector and then to the far zone. The tracking of such fields may be accomplished either by the complex-source point method or, in principle, by evanescent wave tracking. The former utilizes a complex coordinate space while the latter tracks fields entirely in the physical (real) coordinate space. For a parabolic antenna with an offset beam feed centered at the focus, both methods are examined here and an assessment is made of how the one can best complement the other. Numerical comparisons with results deduced elsewhere by a semi-heuristic procedure, and with experimental data, reveal the accuracy and versatility of the complex ray procedure.

Asymptotic analysis of parabolic reflector antennas

The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surface S_{a} that caps the reflector As a corollary to this equivalence theorem, the fields predicted by integration of the physical optics (PO) surface currents and the Kottler-Franz integration of the geometrical optics (GO) aperture fields on S_{a} agree to within the locally plane-wave approximation inherent in PO and GO Moreover, within the region of accuracy of the fields predicted by PO current or GO aperture field integration, the far fields predicted by the Kottler-Franz aperture integration are closely approximated by the far fields obtained from aperture integration of the tangential electric or magnetic field alone In particular, discrepancies in symmetry between the far fields of offset reflector antennas obtained from PO current and GO aperture field integrations disappear when the aperture of integration is chosen to cap (or nearly cap) the reflector

Equivalence of surface current and aperture field integrations for reflector antennas

A general theory of reflector antennas loaded by surface impedances is presented. Spatial variation of primary illumination is taken into account using a generalized slope diffraction coefficient. The theory is experimentally checked on surface loaded square plate scatterers and then used for computing the radiation diagram of parabolic and hyperbolic dishes. Computer programs and computed diagrams refer to the case of focal illumination and negligible tapering of primary illumination.

Rim loaded reflector antennas

Using recent developments of the geometrical theory of diffraction (GTD), the complete E - and H -plane patterns of Cassegrain antennas are computed. The pattern in the main beam region is computed by conventional aperture integration methods and the GTD analysis is used to evaluate the far-out lobes caused by spillover and by various edge diffraction processes. The effects of the edge curvature and surface curvature are included in the computations.

L. Peters

Papers

A GTD analysis of the far-out sidelobes of cassegrain antennas