the radar cross section concept. 
The radar cross section 0 is first defined for a, 
so-called, point target. In this case a is a hypo 
thetical area intercepting that amount of power which, 
when scattered isotropically, produces an echo with 
power P as received from the actual object. In for 
mula: 
2 -*"S 
a = lim 4td E .E * 
/e\e L * 
(1) 
where d is the distance between the radar and the 
point target, and E represents the incident electric 
field strength at the target whereas E is the field 
scattered by the object as it is received by the 
radar. For quite a large number of point targets 
(metal plates, metal or dielectric spheres etc) the 
radar cross section can be calculated. (Rugk 1970) 
dB 
-2«. 
Although the formal dimension of O' is in m one will 
often find that dB 1 s are used. This is explained by 
the fact that the received power for the unknown tar 
get is compared (on a logarithmic scale) with that 
for a garget with a well known cross section, e.g. 
a = lm . 
Obviously in radar remote sensing the targets can 
no longer be considered as point targets. In fact 
the radar is collecting the power scattered by a giv 
en area or volume, the so-called resolution cell, the 
dimensions of which are determined by the radar sys 
tem design (viz section 3). The usual subsequent 
assumption is then that the radar return of each 
resolution cell can be replaced by that of a collec 
tion of N point scatterers. In general the density 
of these scatterers will not be uniform since the 
distribution is determined by the characteristics 
of the object. 
According to eq. (1) the radar has to measure 
Figure 1. Introduction of 
differential radar cross 
section. 
Fiaure 3. a) Cc 
x 10 X with 62! 
but scatterers 
k^ution with s = 
Fiqure 2. Resolution cell to be con 
sidered for simulation. 
-+S ->s* 
E .E *. 
With the k-th scatterer giving rise to a field con- 
tribution u^ exp(jcf> k ) we may write: 
This equation will give a different answer for each 
resolution cell. Therefore it only makes sense to 
consider the ensemble average of eq.(2). 
Within the N-scatterer concept it is conceivable 
that each scatterer is the representation of a number 
of neighbouring elements that, in a given direction 
add more or less coherently. Therefore it can be 
argued that the radiation of the N scatterers can 
be added on an incoherent, or power, basis. Conse 
quently, only those terms of eq.(2) with k=£ will 
remain and the ensemble average is found to be: 
Figure 4. Corre 
the effect of e 
The correction 
different incic 
General conclus 
that C=1 for lc 
(m = 1, 2, . . . 
ers) results ir 
figure that in 
make the couplj 
In fig. 3b we 
cell and the Sc 
The difference 
which are te 
bution 
p (h/X) 
1 
51/27 
So far a number of assumptions were introduced in a 
rather heuristic way and the question arises whether 
the necessary conditions are really met in a practi 
cal situation. It is instructive to use simulation as 
a method to investigate these aspects further. The 
configuration to be considered for the simulation is 
presented in fig. 2. The resolution cell is supposed 
to be a square whereas the scatterers are positioned 
in a regular grid. For the sake of simplicity we will 
take all u independent of look angle (isotropic 
scattering) and equal to one. In a vertical plane 
through a row of scatterers we find to be composed 
of two terms. The first one represents the phase 
shift along the resolution cell and the second term 
gives the phase difference of the scatterer with 
height h^ with respect to that of a scatterer with 
zero height. 
It is useful for reference purposes to start with 
a calculation of the received power for the simple 
limiting case where all heights are equal to zero. 
In fig. 3a the result is given for a square of 10X 
x 10X with 625 scatterers. It turns out that this 
number of scatterers in combination with the area of 
the resolution cell gives rise to a new problem ori 
ginating from the fact that, by increasing the number 
of scatterers per unit area, the power absorbed from 
the incident radar beam, increases as well. The only 
way to prevent the absorbed power to become infinite 
is by changing the a -values. In a physical sense 
this change is effectuated by mutual coupling between 
the scatterers. 
By applying the energy conservation principle it 
can be shown for any pair of point scatterers that, 
due to coupling effects, their radar cross sections 
are modified by a factor: 
C = {l + cos(kdsinG)sin kd/(kd)} 
where k=2TT/X and 6 represents the incidence angle of 
the illuminating wave whereas d is the distance be 
tween the two scatterers under consideration. 
with s = /<(h/ 
ences between i 
suit of the int 
lobe (0=0) becc 
main lobe, the 
placed by a rar 
Obviously the 
give a differer 
and therefore j