Geology Reference
In-Depth Information
circular polarizations are limiting cases of the more
general configuration of elliptical polarization.
In the general case of the elliptic polarization of the
signal, the ellipse that the tip of the electric field vector
traces in the plane perpendicular to the wave propagation
is known as the “polarization ellipse.” Its geometrical
parameters define the polarization state of the signal. The
two parameters that are commonly used are the orienta-
tion
ψ
and ellipticity
χ
(Figure 7.15). The orientation is
the angle of the semimajor axis, measured counterclock-
wise from the positive horizontal axis. It takes on values
between 0° and 180°. The ellipticity (also called eccentric-
ity) measures the degree to which the ellipse is oval
[
χ
= arctan (b/a)]. It takes values between −45° and +45°.
The zero value corresponds to linear polarization and the
±45° values correspond to circular polarization. Table 7.2
shows the relation between the phase difference between
the two orthogonal transmitted waveforms and the shape
of the resulting polarization ellipse. If the two compo-
nents of the transmitted signal are in‐phase, the polariza-
tion of the resultant signal becomes linear (
χ
= 0). As a
special case, to generate a linear polarization in the H
plane, the V component must be zero and vice versa
(not shown in the table). Obviously, to generate a linearly-
polarized signal at any angle other than 45° the two
components should not be equal. When the phase shift
increases to
π
/2 radians (between the two equally trans-
mitted waves), the ellipticity increases to 45° and the
polarization becomes circular. Only two values of the ori-
entation angle are shown in Table 7.2: 45° and 135°. Note
that for the circular polarization the orientation angle is
undefined. So far, operational imaging radar sensors
transmit linearly polarized waves, but future sensors will
transmit circular polarization (CP) waves.
In the classical literature, the polarization state of a
plane wave is expressed by a vector, known as the Stokes
vector. Its elements are a function of the orientation and
ellipticity of the signal and can be written as
2
2
EE
I
I
Q
U
V
v
h
0
0
2
2
EE
EE
I
I
cos os
sin os
sin
2
2
v
h
0
(7.1)
*
2
2
2
Re
vh
0
I
2
2
Im
EE
*
0
vh
where
I
0
,
Q
,
U
, and
V
are known as Stokes parameters.
For fully polarized wave, the Stokes parameters are
related by the equation
2
2
2
2
IQUV
0
(7.2)
Therefore, only three parameters of the Stokes vector
elements are independent. The parameter
I
2
represents the
total power in a completely polarized signal. For a partially
polarized wave, the total power is greater than the summa-
tion of the squares of the other three terms. The degree of
polarization
d
p
of a signal is then given by the ratio
y
E
y
a
E
2
2
2
QUV
I
χ
°
d
(7.3)
ψ
°
b
p
2
x
0
E
x
This parameter has been successfully applied for target
scattering characterization [
Touzi,
1992] from polarimet-
ric radar observations (section 7.6.2.3).
In radar terminology the term “depolarization” refers to
the situation when the dominant polarization of the scat-
tered signal is different than the polarization of the transmit-
ted signal. In the case of passive microwave only one signal
(i.e., the emitted signal) is involved. In this case depolarization
Figure 7.15
Polarization ellipse of polarized EM wave show-
ing its two characteristic parameters: the orientation
ψ
and
ellipticity
χ
.
Table 7.2
Phase shift (
Δϕ
) between the electric field of the two orthogonal transmitted EM components and the shape and
parameters of polarizat
i
on ellipse associated with the resulting wave.
Δ
φ
0
π
/8
π
/4
3
π
/8
π
/2
5
π
/8
3
π
/4
7
π
/8
π
Ψ
45°
45°
45°
45°
any
135°
135°
135°
135°
χ
0°
11°
23°
34°
45°
34°
23°
11°
0°
Shape
