125 
) ( 1 2f) 
f can be re- 
(6(T)) .y 
dT 
(T)) 
(13) 
gral are con- 
e convolution 
the radar 
pproximated 
n 
(14a) 
d for the 
(14b) 
Figure 3. Simulated radar return signal as a function 
of range distance from a homogeneous isotropically 
scattering flat surface in L-band at 61.5 degrees 
incidence angle and a 141 meter altitude. The big 
arrow at a range distance of 295 meter indicates the 
position of the centre of the beam, the small arrows 
the +/- 3 degrees and + /- 6 degrees beside centre 
points. 
Figure 5. In the multi-level model all scatterers 
within a certain layer of the forest canopy are 
assumed to be located on a single plane. In the 
4-level 9 meter spacing model all scatterers 
between 27 + 4.5 meter and 27 - 4.5 meter are 
assumed to be located on the 27 meter level, the 
scatterers of the 18 +/- 4.5 meter layer on the 
18 meter level, etc.. 
beam width, 
d with HH- 
nd with HH- 
ing surface the 
ons 13 and 14 
ce in 
osition of the 
e +/- 3 
points. The 
thin the 
eturns to 
tion of the 
approximate 
). A stand 
ield, mea- 
dence angle 
ferent return. 
■ time was less 
;nals are 
tand a simple 
the forest are 
:1 planes 
. stand of po- 
lelled as a 
:er intervals, 
is from each 
gnal of level 
is t, the 
me, the return 
: and has the 
:he one drawn 
■awn for a 
; compared 
field and 
id. As expec- 
ily matches the 
loplar return 
2 return from 
iutions from 
tear the 18 
■.he returns 
butions of 
eparated at 
(a) 
(b) 
Figure 4. (a) Measured returns from a grass field are 
drawn together with the simulated return of figure 3. 
The strong signal at the left is the calibration sig 
nal which is a part of the transmitted pulse fed 
directly back to the receiver through a delay line. 
The signal between 140 and 160 meter range distance 
is caused by the first hit on the ground. The grass 
field return between 200 and ~350 meter closely 
matches the simulated return. The signal peaks at 
range distances exceeding 350 meter are artifacts 
introduced by the receiver. 
(b) Measured returns from a poplar field 
are drawn together with the simulated return of 
figure 3. Note that also in this case the first hit 
on the ground is visible. 
Figure 6. Simulated radar return signals as a func 
tion of range distance from identical homogeneous 
isotropically scattering flat surfaces in L-band at 
61.5 degrees incidence angle. The height of flight 
is 141 meter above level 0, 132 (=141-9) meter above 
level 1, 123 (=141-18) meter above level 2 and 114 
(=141-27) meter above level 3. 
first glance. This is not the case however for the 
example in figure 4b. 
An objective way to separate returns from distinct 
levels is calculation through inversion of the multi 
level model. 
The return P r ^(t) for a forest modelled as a col 
lection of n equidistant scatter planes is formula 
ted as 
n-1 
P ,(t) = I A..P .(t) (15) 
rf . 1 n' 
1=0 
with P ro (t) is P r (t) as in formula 13 with the height 
h=h 0 , 
P ri (t) is P r (t) as in formula 13 and the height 
h=ho~i. d-^ 
and d^ is the distance between 2 levels. 
The coefficients A£ represent the strength of the 
contributions of each scatter plane to the return