Abstract
Abstract : The basic concepts of geometrical optics together with the additional assumption that lead to the 'geometrical optics approximation' are described here. The eikonal equation is derived and the relationship of exact electromagnetic theory in the limit as wavelength approaches limit of 0 to geometrical optics is made evident. The application of the 'geometrical optics approximation' to phase analysis and synthesis is described and an example of synthesis is presented. The concept of power flow in ray tubes is used to obtain approximations to power distributions in the antenna aperture, in the focal region, and in the far field. Ray analysis is used to determine those feed locations in the focal region that will most nearly collimate the far-field rays that lie in certain desirable planes. The Theorem of Malus is used to formulate the equal path length law and applications are given. Focal surfaces (or caustics) relative to a rectilinear congruence are defined and then used to present a geometrical optics description of the focal region. The equations of the focal surfaces of a paraboloid receiving a plane wave 20 degrees off-axis are calculated and photographs of three-dimensional models of the focal surfaces are shown.
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