New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).

Elimination of infinities in equivalent edge currents, part I: Fringe current components

An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

Optimal interpolation of radiated fields over a sphere

The scattering of electromagnetic plane wave by a perfectly conducting disk is formulated rigorously in a form of the dual integral equations (abbreviated as DIE). The unknowns are the induced surface current (or magnetic field) and the tangential components of the electric field on the disk. The solution for the surface current is expanded in terms of a set of functions which satisfy Maxwell's equation for the magnetic field on the disk and the required edge condition. At this step we have used the method of the Kobayashi potential and the vector Hankel transform. Applying the projection solves the rest of a pair of equations. Thus the problem reduces to the matrix equations for the expansion coefficients. The matrix elements are given in terms of the infinite integrals with a single variable and these may be transformed into infinite series that are convenient for numerical computation. The numerical results are obtained for far field patterns, current densities induced on the disk, transmission coefficient through the circular aperture, and radar cross section. The results are compared with those obtained by other methods when they are available, and agreement among them is fairly well.

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Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane

The geometrical theory of diffraction (GTD) (cf. [1], for example) may be applied advantageously to many axially symmetric reflector antenna geometries. The material in this communication presents analytical, computational, and experimental results for commonly encountered reflector geometries, both to illustrate the general principles and to present a compact summary of generally applicable formulas.

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The geometrical theory of diffraction for axially symmetric reflectors

A method is proposed for accurately calculating the radiation pattern of reflector antennas in the entire angular range from the main beam direction to the off axis region. The principle of the method is similar to the physical optics diffraction theory, and consists of the result obtained by conventional physical optics corrected with the contribution from the edge current calculated by the geometrical theory of diffraction. However, the edge current is expressed in a simple form by means of a local coordinate system defined by the peripheral line and the mirror normal at each edge point and of the incident electromagnetic vector components in reference to this coordinate system. Therefore, it is possible to treat an arbitrarily shaped mirror surface and an antenna with a primary radiator using an arbitrary pattern. It is confirmed that the results obtained by the present method approach those obtained by the physical optics method near the main beam and those obtained by the geometrical theory of diffraction at the off axis. Accuracy is tested by applying the present method to the problem of diffraction from a circular disk for which a rigorous solution exists. The present method makes unnecessary the distinction of the use of physical optics (main beam) and the geometrical theory of diffraction (off axis) performed so far, in an empirical manner. It is possible systematically to obtain the pattern near the first-third side lobes where two methods may be connected.

Radiation pattern analysis of reflector antennas

Equivalent edge currents, derived from the edge diffraction theory for a half-plane, are used to obtain the radiation patterns of a parabeloidal reflector antenna when illuminated by a source at the focus. Cylindrical wave diffraction coefficients are used. The method avoids infinities at caustics and shadow boundaries thus giving solutions which are finite everywhere. A slope-wave equivalent current correction term is applied when the illumination is tapered towards the edge of the reflector. Comparisons are given with the physical optics approach and experimental results.

G. James

Papers

Reflector antenna radiation pattern analysis by equivalent edge currents

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