By W. V. T. Rusch
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Inasmuch as both methods rely on the ray optics formulas for the source distributions, the results near the reflector axis are identical. 7 INTEGRAL AND GEOMETRICAL THEORIES OF SCATTERING 53 the contributions from the induced source distributions are virtually cancelled by the contribution from the primary source of illumination . It is in these rearward directions that contributions from the neglected currents on the back of the reflector, had they been included, would have been most significant in determining the resultant field.
The Keller geometrical theory of diffraction extends geometrical ray optics to include rays produced by scattering from sharp edges or points, or by incident rays which graze reflecting surfaces. These diffracted rays have many of the same properties as direct or reflected rays : (1) They travel in straight lines (in homogeneous media). (2) Their field strength is inversely proportional to the squareroot of the cross-sectional area of a tube of rays. (3) The phase is proportional to the length of the ray (relative to some arbitrary zero-phase point).
For example, the geometrically scattered field from a hyperboloid is derived from the surface integral by Rusch . 54 II EQUATIONS OF THE ELECTROMAGNETIC FIELD a stationary point to exist is that the field point be many wavelengths from the surface. The major contribution to the field comes from the immediate vicinity of the stationary point. Consequently, it is necessary to determine the source or equivalent-source distribution in an accurate, independent manner. In the event that the source distribution at the stationary point is unknown or known to be negligibly small, conventional geometrical-optics analysis is not applicable.