Radar System Engineering

64 PROPERTIES OF RADAR TARGETS [SEC.3.3
of back scattering from a sphere of radius a small compared to the radar
wavelength. In this limiting case the incident field is considered homogeneous
over the extension of the target. In the homogeneous field the
—yct
sphere becomes an electric dipole with a dipole moment pe , where
(2)
and c is the dielectric constant. The field of this dipole, observed at a
distance r in the wave zone and in a direction perpendicular to the
polarization, is
‘(,–.()
~A
() 2 ek
Z-cl)
ART= : p—.
r
Thecross section is therefore
If It] >>1, which is true, for instance, for a raindrop, we obtain the
simpler expression
()
27ra ~
(5)
which in this form serves to compare the radar cross section with the
‘(geometric cross section’’ raz.
Forthe case of a metal sphere, onewould betempted touse the same
formula with [cl = CO. This, however, is not correct, because, in the
case of a conducting sphere, surface currents which have a magnetic
dipole moment are induced by the field. The radiation of both the
electric and the magnetic dipole must therefore be considered. We then
obtain
(4)
~=4—Ta~,
x’
(3)
(6)
3.3. Scattering of a Plane Wave by a Sphere.—The general problem
of scattering of a plane wa~e by a sphere is solved in detail in J. A.
Stratton’s book, Electromagnetic Theory (pages 563 ff), and references to
the original papers can be found there. The cross section for back
scattering from a metal spherel divided by ~az is plotted vs. a/X in Fig.
I P. J. Rubenstein, RL Report So. 42, .\pr. 3, 1943, \-umericalvalues for the
problem of scatteringfrom a dielectricspherecan be found for certainvalues of the
dielectric constant in the references given by Stratton, Electromagnetic Theory,
McGraw-Hill, New York, 1941,p. 563 ff. See also Robert JVeinstock,RRL Report