Optical Fresnel-Zone gain of a rectangular aperture

An equation for the on-axis gain of a uniformly illuminated rectangular aperture is derived which is valid in the "Optical Fresnel Zone." This equation is formulated in terms of the ordinary radiation field gain multiplied by a correction factor which depends upon the aperture dimensions and the distance, R, from the aperture at which the gain is measured. A table of the function [C2(v)+S(v)]/v2 is given; C(v) and S(v) being the Fresnel integrals. The gain of a square aperture (LXL meters) in the Fresnel-zone region is compared with the gain of a circular aperture and it is shown that for apertures of equal Gsquare < Gcircle when (L2/λ)