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Using diffracted-field formulas the slope of the field is evaluated at the reflection boundary of an edge-induced shadow. Retaining high-frequency terms the wavelength dependency is (λ)-1/2 Using a formula for the field near the turning point of an inflected surface the slope of the field at the reflection boundary is evaluated. Retaining high-frequency terms, the wavelength dependency is (λ)-5/6 in this case. That is, the shadow for the surface-curvature-induced case gets sharper nearly twice as fast as for the edge-induced case as the frequency increases. This slope is a measure of spillover into the shadow region. [ABSTRACT FROM AUTHOR]

A JPL Fortran program for designing the main reflector and the subreflector of a Galindo-Williams system with a constant intensity over the aperture of the main reflector was modified for use on our computer system. Geometrical optics and conservation of energy are the basic laws used for designing this type of surface. The basic computation is a numerical solution of three simultaneous differential equations. The resulting subreflector is a type of inflected surface. Analysis of the fields scattered from such a surface using physical optics yields adequate results. Cubic-phase theory is numerically applied to the Galindo-Williams surface. Although the technique appeared to yield results accurate to within 10%-15%, the nearness of the edge to the turning point caused a coupling of the edge and turning-point solutions, which prevented higher accuracy. [ABSTRACT FROM AUTHOR]

The conventional Kouyoumjian transition function cannot be used to evaluate the diffracted field for a converging wave because its argument is imaginary, and the total field is not continuous at reflection and shadow boundaries. In order to find the diffracted field near the edge shadow of the inflected surface, Rusch's proposed edge-diffraction transition function for a converging wave is used. The argument of this transition function is real and produces a continuous total field at the boundaries. The diffracted field is then added to the geometrical optics field and compared favorably with physical optics. [ABSTRACT FROM AUTHOR]