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In-Depth Information
12.7. SAR Imaging Using Doppler Processing
It was mentioned earlier that SAR imaging is performed using two orthogo-
nal dimensions (range and azimuth). Range resolution is controlled by the
receiver bandwidth and pulse compression. Azimuth resolution is limited by
the antenna beamwidth. A one-to-one correspondence between the FFT bins
and the azimuth resolution cells can be established by utilizing the signal
model described in the previous section. Therefore, the problem of target
detection is transformed into a spectral analysis problem, where detection is
based on the amplitude spectrum of the returned signal. The FFT frequency
resolution
∆
f
is equal to the inverse of the observation interval
T
ob
. It follows
that a peak in the amplitude spectrum at
k
1
∆
f
indicates the presence of a scat-
terer at frequency
f
d
1
=
k
1
∆
f
.
For an example, consider the scatterer
C
i
within the
kth
range bin. The
instantaneous frequency
f
di
corresponding to this scatterer is
1
2π
d
ψ
2
v
λ
------
------
f
di
=
=
f
0
τ
t
µ
µ
i
=
sin µ
i
β
i
(12.49)
d
t
This is the same result derived in Eq. (12.23), with
µ
i
=
∆θ
. Therefore, the
scatterers separated in Doppler by more than
∆
f
can then be resolved.
Fig. 12.12
shows a two-dimensional SAR image for three point scatterers
located 10 Km down-range. In this case, the azimuth and range resolutions are
equal to 1 m and the operating frequency is 35GHz.
Fig. 12.13
is similar to Fig.
12.12, except in this case the resolution cell is equal to 6 inches. One can
clearly see the blurring that occurs in the image. Figs. 12.12 and 12.13 can be
reproduced using the program
Ðfig12_12_13.mÑ
given in Listing 12.1 in Sec-
tion 12.10.
12.8. Range Walk
As shown earlier, SAR Doppler processing is achieved in two steps: first,
range gating and second, azimuth compression within each bin at the end of the
observation interval. For this purpose, azimuth compression assumes that each
scatterer remains within the same range bin during the observation interval.
However, since the range gates are defined with respect to a radar that is mov-
ing, the range gate grid is also moving relative to the ground. As a result a scat-
terer appears to be moving within its range bin. This phenomenon is known as
range walk. A small amount of range walk does not bother Doppler processing
as long as the scatterer remains within the same range bin. However, range
walk over several range bins can constitute serious problems, where in this
case Doppler processing is meaningless.
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