Chapter 3: Vehicle-Mounted GPR System for Landmine Detection

3.3 Image Reconstruction 37
N
1
Q() r = ∑Qn
() r . (3.4)
N n = 1
According to Eqs. (3.3) and (3.4), the weighting factor is defined as the ratio
Q()
r
Wn
() r =
Q () r
n
(3.5)
With the weighting factor, the balanced traces sˆ( r ,) t are calculated as
sˆ (,) r t = s (,) r t ⋅W
() r . (3.6)
n n n
Next, these traces for each antenna combination are stacked to reduce incoherent
clutter and noise. Since these traces have different offset (antenna separation), their
time axes are not the same. To compensate the axes, normal move out (NMO) is
performed, and then the traces are stacked.
where
s (,) r t = ∑ sˆ
(, r τ ), (3.7a)
CMP n n
n=
1
N
air soil
⎛Ln
L ⎞
n
τ
n
= 2⎜
+ ⎟, (3.7b)
⎝ c 1 ε ⎠
air
L and L soil are the path lengths in the air and soil, respectively. c is the
velocity of the electromagnetic wave in the air, and ε is a permittivity of the soil.
This process virtually constructs a monostatic radar signal measured at the CMP
position from bistatic signals as illustrated in Fig. 3.11. Then migration is performed
for the stacked signals. Here diffraction stacking is used as a migration technique.
The amplitude at a position r ′ = { x′ , y′ , z′
} in the three-dimensional image is given
by
where
i( r′ ) dxdys ( r , τ ′), (3.8a)
= ∫∫
CMP
2 ′ −
τ ′ = r r , (3.8b)
1 ε
and r = { x, yz , } is the position signal acquired, i.e., the CMP position.