Geometry of reflector antennas

Abstract

In this chapter we deal with a description of the geometry of a paraboloid of revolution. We shall collect the geometrical relationships, which we need for the description of the electromagnetic radiation characteristics of the paraboloidal reflector antenna. Because many radio telescopes and communication antennas actually employ the Cassegrain or Gregorian layout, we include the formulas for those systems too. These are dual reflector systems, where a relatively small secondary reflector, placed near the focus of the primary paraboloid concentrates the received radiation in a secondary focus, located near or behind the vertex of the primary reflector. The Cassegrain employs a hyperboloidal secondary, while the Gregorian system uses an elliptical secondary reflector. One of the foci of these dual-focus conic sections coincides with the focus of the paraboloid, while the other provides the secondary focus at a convenient location. The great advantage from an operational viewpoint is the possibility to locate bulky receiving equipment behind the primary reflector. As we shall see later, there are also significant electro-magnetic advantages of the dual-reflector varieties.