Efficient computation of the Fresnel-zone fields for circular aperture
s plays an important role in applications where the frequency, apertur
e size, and observation location axe such that the Fraunhofer approxim
ation is not justified. If an adequate approximation for the aperture
field distribution is known, then the standard procedure for computing
the Fresnel-zone field distribution involves a time-consuming numeric
al integration over the aperture field distribution. In this paper, we
will represent the Fresnel-zone field for some commonly used aperture
field distributions in terms of incomplete Weber integrals, thereby a
voiding the need for numerical integration. Since the incomplete Weber
integrals are related to the incomplete Lipschitz-Hankel integral of
the first kind, four Bessel series expansions are used to dramatically
reduce the computation time required to compute the Fresnel-zone elec
tric fields.