By W. V. T. Rusch
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Extra resources for Analysis of Reflector Antennas
It is generally considered to be sufficiently far from the aperture to permit the following approximations in the amplitude factors of the integrand ofEq. 521-3) The phase factor e~3kr must involve a higher-order approximation, however, than Eq. 521-2). Although the field points are at great distances from the aperture, nevertheless the path length from the center of the planar aperture to a point directly in front of the aperture, for example, is significantly different (in wavelengths) from the path length from the edge of the aperture to that point.
The currents which excite the scattered field are induced on the conducting surface by an incident wave assumed to be of a known amplitude, phase, and polarization everywhere in space. The "physicaloptics" approximations to the induced surface currents are valid when the transverse dimensions of the reflector, the radii of curvature of the reflector, and the radius of curvature of the incident wave front are all much larger than a wavelength. The closed reflecting surface S is divided into a region (or regions) S\ which is illuminated by direct rays from the source, and a region (or regions) £2 which is geometrically shadowed from direct rays from the source.
14). 51-2) ♦This assumption has eliminated edge contributions, which are probably significant within a few wavelengths of the edge. The subsequent formulas are therefore valid only for " l a r g e " apertures. Il 36 FIG. 14. EQUATIONS OF THE ELECTROMAGNETIC FIELD Kirchhoff scalar theory—planar aperture. where a coordinate system has been defined such that z = 0 is the plane of the aperture, (£, 17, 0) are the coordinates of a point in the aperture, (x,y, z) are the coordinates of the field point P.
Analysis of Reflector Antennas by W. V. T. Rusch