Geology Reference
In-Depth Information
As the equation implies that the scattering from the target is
isotropic,
σ
is considered to represent the cross section of an
equivalent isotropic scatterer that would be required to gen-
erate the same power density as observed by the receiver.
One of the problems of using the concept of radar cross
section is its dependence on the surface area of the imaged
footprint (i.e., the ground resolution of the sensor).
Therefore, when radar sensors of different resolutions
view the same surface, then
σ
may be different. A more
useful quantity is obtained by dividing
σ
by the area of the
observed terrain. This parameter is called backscatter
coefficient or “sigma naught”
σ
0
. It is a dimensionless
quantity, which can be treated as an intrinsic property of
the surface. Moreover, if the ground target is composed of
a large number of distributed scattering elements as
opposed to a single element, then the integration of scat-
tered differential power from all scattering elements within
the resolution cell can be written as
rather than linear scale. When averaged over a number of
pixels (sampling area), the average must be calculated
from the values in the linear power scale then converted
to decibels using the equation
(7.68)
0
0
10log( )
linear
10
The standard deviation of
σ
0
over the sampling area is
expressed in decibels using the equation
0
0
Mean
SD
linear
linear
0
SD
10 log
(7.69)
dB
10
Mean
0
linear
Figure 7.28 shows the configuration of a side looking
RAR system. The successive pulses illuminate a strip
across the swath with width
S
, given by
h
Wh
PG
R
A
R
ds
(7.70)
(7.67)
r
2
tt
0
r
S
cos/
p
r
cos
2
A
4
2
4
2
0
r
r
where
W
is the antenna width,
λ
is the wavelength of
the transmitted signal,
h
is the altitude of the platform,
and
θ
r
is bean width of the transmitted signal in the range
direction. According to the above equation, a 2.1 m width
L‐band antenna (
λ
=27 cm) transmitting radar pulses
from 800 km altitude at
θ
r
= 20° will cover a swath width
of 100 km. Return signals from sequential pulses are pro-
cessed separately. When the next pulse is transmitted, the
radar will have moved forward a small distance and a
slightly different strip of terrain will be imaged. These
sequential strips of terrain will then be recorded side by
side to build up the image in the azimuth. The signal
This is a model for distributed target. This equation
shows that the backscatter coefficient is a statistical
measurement that represents the average power returned
from the distributed scattering elements. It can be con-
ceived as the ratio of the statistically averaged scattered
power density to the average incident power density. The
backscatter coefficient is determined by the surface
roughness, the physical and electrical properties of the
scattering elements, as well as the radar parameters;
namely the wavelength, polarization, and the local inci-
dence angle of the incident signal. Since values of
σ
0
are
usually very small, they are presented in decibels (dB)
(a)
(b)
(c)
L
V
θ
a
h
/cos(
θ
a
)
h
h
Slant range
Ground
range
X
r
X
a
S
Figure 7.28
Viewing geometry of a side‐looking real aperture radar: (a) a 3D perspective, (b) a projection in the
range plane, and (c) a projection in the azimuth plane. The spatial resolutions in the range and azimuth direc-
tions are
X
r
and
X
a
; respectively. The drawing is not to scale.
