Radar System Engineering

CHAPTER 3
PROPERTIES OF RADAR TARGETS
SIMPLE TARGETS
BY A. J. F. SIEGERII, L. N. RIDENOUR, AND M. H. JOHNSON1
3.1, Cross Section in Terms of Field Quantities. -In the preceding
chapter the quantity “cross section of a target” was introduced phenomenologically.
Theoretical considerations which in certain cases
will allow the prediction of the value of these quantities from the known
properties (shape, material) of the target will be presented in this chapter.
The following considerations will be restricted to cases where the individual
target is sufficiently small, compared with the distance from the
transmitter, to permit the incident electromagnetic field at the target to
be approximated by a plane wave propagating in the direction of the
target away from the transmitter; this is chosen as the z direction.
The problem of finding the cross section then reduces to the mathematical
problem of finding that solution of Maxwell’s equations which
at large distances from the target reduces to the incident plane wave
and at the target fulfills the proper boundary conditions.
Suppose a solution of this problem has been found. .\t large distances
from the target the component of the electric field parallel to the receiving
% – Cf)
dipole can be written in the form Eoe :(2 – co +s~ + terms
r
decreasing faster than r–l, where En is the amplitude of the incident plane
wave, S/r is the amplitude of the only important part of the scattered
wave, A the radar wa~-elength, c the velocity of light, and t the time.
Usually 13, and S contain complex phase factors; S is in general a function
of the scattering angles. In the following discussion the symbol SE is
used to denote the value of S in the direction of the receiver. In terms
of Eo and S~, the cross section u defined in Sec. 2.3 is given by
(1)
3-2. Rayleigh Scattering from a Small Sphere.—As an illustration of
the use of this equation, we shall derive the Rayleigh law for the case
1Sections3.1-3.4 and 3.6 by .!. J, F, Siegert,3,5 by L, X. Ridenoar, and 3.7 b.v
11. H. Johnson.
63