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ation. 
Fiaure .3. a) Coherent scattering of a square 10 A 
x 10 A with 625 scatterers. b) Same resolution cell 
but scatterers having random heights (Gaussian distr 
ibution with s = 0,3). 
Figure 4. Correction factor to take into account 
the effect of mutual coupling. 
The correction factor C is shown if fig. 4, for two 
different incidence angles, as a function of d/A. 
General conclusions, holding for all 0-values, are 
that C=1 for large d/A as well as for d/A = m/2 
(m = 1, 2, ....) whereas d/A=0 (coinciding scatter 
ers) results in C=l/2. It may be concluded from the 
figure that in practical situations d/A > 10 will 
make the coupling negligible. 
In fig. 3b we have considered the same resolution 
cell and the same number of scatterers as in fig. 3a. 
The difference is that the scatterers now have heights 
h^ which are taken randomly from the Gaussian distri 
bution 
p (h/A) = —exp {-(h/A) 2 /2s 2 } 
s/2tt 
with s = <(h/A) 2 > = 0,3. The characteristic differ 
ences between fig. 3a and fig. 3b are that, as a re 
sult of the introduction of random heights, the main 
lobe (0=0) becomes much smaller whereas, outside the 
main lobe, the regular interference pattern is re 
placed by a random amplitude structure. 
Obviously the calculation of the received power will 
give a different answer for each collection of heights 
and therefore it only makes sense to consider the en 
i. • ■ I ; i I ; = •> 
0. 30. 60. 90. 
0 - 
Figure 5. a) One-dimensional simulation L=10A, N=49 
and rms height variation 0.05. b) Same configuration 
but with rms height 0.1. Dotted lines represent 
h{ 1-exp (-p ) } . 
semble average, as was mentioned already in relation 
to eq.(2). Although not impossible it is rather time 
consuming to calculate this average for a two-dimen 
sional case like the one in fig.2.For this reason the 
averaging process was performed for a one-dimensional 
case. In fig. 5 there are 49 scatterers situated at 
regular distances on a line with a length of 10A. The 
heights are Gaussian distributed with rms height 
variations of 0.05 (fig. 5a) and 0.1 (fig. 5b). 
In both cases the average of 100 samples was calcu 
lated. It was demonstrated before (Krul 1979) that 
0° can be written as: 
0° = F(0) exp (-p 2 ) + h {1-exp(-p 2 )} (4) 
where 
p = 4tt cos 0 \/< (h/A) 2 >i 
The right hand side of eq. (4) consists of two terms, 
the ratio of which is determined by the parameter p. 
The first term is the so-called, coherent term that be 
comes dominant when the rms height (and p by that) is 
made small. For p=0 the result is equal to F(0) which 
corresponds with fig. 3a. The second term of eq. 
(4) is the one that remains for large values of p. 
This term represents the incoherent addition of the 
scattered contributions, it is indicated in fig. 5 
by dotted lines. Only for this term the result ex 
pressed by eq.(3) will hold. 
3 INSTRUMENTAL ASPECTS 
In the preceding section it was demonstrated that 
radar cross section is, with some restrictions, a 
useful concept to describe the received power for 
distributed targets. Since it is a step by step 
method it opens the way to calibrate the system. As 
a first step we calibrate the power relations by 
means of a technically well defined point target. 
After that suitable interaction models based on the 
multi-scatterer assumption are introduced. These 
simplified descriptions of the wave-target interac-' 
1035