Geology Reference
In-Depth Information
carries information from every resolution cell along the
swath. This is indicated by the gray strip in Figure 7.28a.
Locations of each cell can be identified using the return
time of the signal.
The time
Δt
between the echoes from two points at dis-
tance
X
from each other in the ground range direction is
2
X
c
t
sin
(7.71)
r
Azimuth
The range resolution
X
r
is the minimum distance between
two points that can be separated in the received signal. It
is the distance that the ground cell is “seen” during pulse
width
τ
. This infinitesimal distance measures
cτ
, where
c
is the speed of light. According to equation (7.71)
X
r
is
given by
Figure 7.29
Scene from an airborne RAR, showing significant
distortion due to the much coarser resolution in the azimuth
direction (resolutions are 30 m and 5 km in range and azimuth
directions, respectively).
thousand echoes can be processed while assuming the sat-
ellite has not moved. This requires, of course, a relatively
high pulse repetition frequency (for ERS SAR it was
1400 Hz).
Figure 7.30 shows the first and last beams that illumi-
nate a marked ground target. The string of dots along the
satellite path represents positions at which the SAR
transmits pulses. A few thousand transmitted pulses
usually “see” the same ground cell (its size is determined
by the resolution of the sensor). As the platform contin-
ues to move forward, all echoes from the target (one echo
per pulse from successive pulses) are recorded during the
entire time that the resolution cell is viewed by the sensor.
The point at which the target leaves the view of the last
beam determines the length of the simulated or synthesized
(virtual) antenna
L
SA
. This technology is called “synthetic
aperture” because the scattering from the illuminated
ground cell continues to be included in the “collection” of
the return signals as the satellite travels along a linear
distance equivalent to the angular beam width
θ
a
:
c
X
2
sin
(7.72)
r
r
For a pulse width of 5 × 10
−8
and
θ
r
= 20°, the range resolu-
tion from equation (7.72) is
X
r
= 22 m. This is reasonable.
However, the azimuth resolution
X
a
is much bigger as
depicted in Figure 7.28. It is equal to the width of the
footprint because the echoes from all the points within
each stripe with width equal to the spatial resolution in
the range direction (the gray stripe Figure 7.28a) are
returned to the antenna at the same time.
Xh hL
a
a
/cos
/ os
(7.73)
where
L
and
θ
a
are the antenna length and the beam
width in the range plane, respectively. For
h
=800 km,
λ
=23 cm (L‐band),
L
=12 m, and
θ
=20°, equation (7.73)
gives
X
a
= 16.3 km. This is a very coarse resolution. In
order to have
X
a
=100 m, an antenna length of 1958 m is
required. Of course, this is not practical and that is what
prohibits the use of RAR when fine resolution in the azi-
muth direction is required. An example of a scene
acquired by an airborne RAR is shown in Figure 7.29
where the coarse resolution in the azimuth direction is
clearly visible.
L
R RL
/
(7.74)
SA
a
where
L
is the physical length of the antenna. The
exposure time
T
e
for a given target to remain within the
successive illuminating beams is given by
Synthetic Aperture Radar
Synthetic aperture radar is
based on the concept of combining signals from all radar
pulses that view the same ground resolution cell (or tar-
get) as the satellite passes over it. The collection of these
beams start with the first beam that “sees” the ground cell
and ends with the last beam that sees it. An important
fact that allows the utilization of this concept is that
radar pulses travel between the radar antenna to the tar-
get at the speed of light, which is five orders of magnitude
faster than the speed of the satellite. Therefore, several
TLVRLV
e
SA
/
/
(7.75)
In SAR, both the target's position and the ground
resolution in the range direction are determined from
the return time of the echo [equation (7.71)]; i.e., similar
to RAR. However, the resolution in the azimuth direction
is determined using one of the following two approaches,
which lead to the same result. The two approaches
are called synthetic array and Doppler frequency. In the
first approach
X
a
is derived by substituting the beam
