Radar echo variations of a large rough sphere

The effect of surface roughness on the radar backscattering cross section of a perfectly conducting nominally spherical target is examined by applying the Kirchhoff method. It is shown that, for the type of roughness and sphere size to which the Kirchhoff method is applicable, the standard deviation of the cross section increases with frequency according to the law
2\sqrt{2} \sigma_{0} k\zeta
until the first Fresnel zone reduces in size to the scale length of the roughness. At this point a knee in the curve occurs and its further course is determined by a more detailed statistical description of the surface. Here
\sigma_{0}
is the nominal cross section,
\zeta
is the standard deviation of the surface height
h
and
k=2\pi/\lambda
, where
\lambda
is the wavelength. The average cross section is shown to be given by
\sigma_{0}[1+0 \{(kh)^{3}\}]
. Some experimental results are reported which support the theoretical conclusions.