Pattern characteristics of an antenna focused in the Fresnel region

This paper is an expansion of the theory of stationary aperture focusing as developed by Wehner and Bickmore. The field of a circular antenna focused in the Fresnel region is approximated in terms of finite Hankel transforms of the aperture amplitude function. Although the peak gain of the focused antenna is comparable to the Fraunhofer gain of an equivalent uniformly illuminated aperture, the pattern characteristics undergo second-order perturbations. A series solution for the pattern through the focal plane is given for an amplitude distribution expressible as a power series. The effect of amplitude taper is studied.