High-frequency diffraction of electromagnetic waves by a circular aperture in an infinite plane conducting screen

The scattering of plane electromagnetic wave of wave number
k
by a circular aperture of radius
a
in an infinitely conducting plane screen of zero thickness and infinite extent is considered. In the limit of large
ka
and at normal incidence, the ratio of the transmission cross section to the geometrical optical value
\pi a^{2}
, is found up to the order
(ka)^{-5^{j}2}
.