Through-Wall Imaging With UWB Radar System - KEMT FEI TUKE

4.2 Measurements of the Wall Parameters by Reflectometry 62
Propagation time [ns]
17.7
22.2
26.6
31.1
35.5
40.0
44.4
48.8
Wall-Air interface
Next wall
out of interest
Air-Wall interface
50 100 150 200 250 300 350 400
Propagation time [ns]
4.4
8.8
13.3
17.7
22.2
26.6
Next wall
out of interest
Wall-Air interface
Air-Wall interface
Clutters
50 100 150 200 250
Number of impulse responses
Number of impulse responses
a) Measured data without crosstalk b) After synchronization and normalization
Fig. 4.2.4: B-scans, antennas were moved from 0.5 m to 1.5 m from the wall. a)
Measured data, oversampled and without crosstalk. b) After synchronization and
normalization, next wall is 1.8 m from measured wall.
4.2.4 Algorithm Description
As mentioned above, the first step is to determine the reflection coefficient Γ of
the outer surface in order to be able to determine the wall permittivity. Since the
incident wave is not known in practice, a reference measurement hm(n) was made
beforehand and stored in the device memory. For that purpose, we used a large
sheet of metal Γ = −1 and measured the reflection at 1 m distance. Since we have
supposed wall parameters as frequency independent, we are able to determine Γ
of the first surface from the peak values of the measured data:
Γ = − �h1(n)� ∞
�hm(n)� ∞
= − �h(n)�∞ . (4.2.5)
�hm(n)�∞ The reflection coefficient of a wall is always negative (compare (4.2.1) and see Fig.
4.2.5). The infinity norm is a positive number, hence the minus in (4.2.5). The
determination of h(n) has to be done carefully by using the same wall distance for
synchronization as in the hm(n) measurement in order to respect the spreading
loss of the waves. However, a distance measurement to the wall is not required, it
can be easily obtained from position of h1(n).
Now, we can calculate the wall permittivity:
εrw =
(1 − Γ)2
(1 + Γ) 2
(4.2.6)