IEEE Geoscience and Remote Sensing Magazine - March 2013 - 16
Table 3. POLARIMETRIC RADAR OBSERVABLES AND PARAMETERS DERIVED FROM THE ELEMENTS
OF THE SCATTERING MATRIX [S] [5], [15], [38]-[41].
2 # 2 Sinclair Matrix
Radar Observables
Application Examples
Scattering amplitude (complex)
and scattering power
S ij
v 0ij = 4r| S ij S *ij |
Classification/segmentation (texture based)
Change detection (multitemporal analysis)
Glacier velocities (feature tracking)
Ocean wave and wind mapping
Coherent scatterers
Total power
TP = S HH 2 + 2 S XX 2 + S V V
Amplitude ratios
0
v 0HH /v 0VV , v 0XX /v VV
, v 0XX / (v 0HH + v V0 V )
Dry/wet snow separation
Soil moisture and surface roughness estimation (bare surfaces)
Polarimetric phase differences
{ HHVV = { HH - { VV
Thin sea ice thickness
Crop types identification
Forest/nonforest classification
Helicity
Hel = | S LL | -| S RR |
Man-made target identification
independent parameters in form of six independent matrix
elements: Three real diagonal power elements and three
off-diagonal complex cross-correlations.
Symmetry assumptions about the distribution of elementary scatterers within the resolution cell simplify the
scattering problem and reduce the number of independent
parameters of [T] (or [C]) allowing qualitative and quantitative conclusions about the scattering behavior [35], [42],
[43]. Besides reciprocity, three special cases of symmetry are
important in radar remote sensing applications: Reflection,
rotation and azimuthal symmetry. Reflection symmetric
media are characterized by a symmetry plane that contains
the line-of-sight so that for any scatterer located at one side
of the plane a mirrored scatterer at the other side of the plane
exists. In this case the correlation between the co- and crosspolarized elements becomes zero. The resulting [T] matrix
contains only five independent parameters in form of three
real diagonal elements and one single non-zero complex
off-diagonal element (i.e., the correlation between the copolarized elements). The majority of natural distributed
scatterers is reflection symmetric. In the case of rotation
symmetry, the spatial distributions of elementary scatterers
do not change when rotated about the line-of-sight (LOS)
axis. Accordingly, the scattering behavior of such media is
invariant under the line-of-sight rotations and the resulting
coherency matrix contains only three independent parameters in form of two independent real diagonal elements and
one non-zero imaginary off-diagonal element. This is typical for gyrotropic random media, as given for example by a
random distribution of helices. When both, reflection and
rotation symmetry applies, the medium is said to be azimuthally symmetric: All planes including the line-of-sight
are reflection symmetry planes. Consequently, all three offdiagonal elements of the coherency matrix become zero,
and only two diagonal elements are independent, the number of independent parameters reduces to 2. This is the case
for volumes consisting of random distributions of ellipsoids.
Compared to the elements of the scattering matrix
[S], the coherency (or covariance) matrix elements have a
16
Classification/segmentation
Feature tracking
2
reduced resolution because of the spatial averaging (i.e.,
multi-looking), indicated by 1 g 2, performed for the
formation of [T]. Despite the higher radiometric resolution
achieved, this loss in resolution may be critical especially
for point scatterers but also for applications on distributed
scatterers. This can be partially compensated by using adaptive (edge and point scatterers preserving) filters to perform
the required multi-looking [15], [44].
The set of observables derived from the coherency (or
covariance) matrix contains, in addition to the observables
derived from [S], the correlation coefficients between different polarizations, which are given by
c HHVV =
c LLRR =
1 |S HH S *VV| 2
1 |S HH S *HH| 21 |S VV S *VV| 2
1 |S LL S *RR| 2
,
*
1 |S LL S *LL| 21 | S RR S RR
|2
(13)
where S LL and S RR are the circular left-left and circular
right-right (complex) scattering amplitudes that can be
expressed as a linear combination of the scattering amplitudes of the scattering matrix [S] measured in the H - V
basis (cf. (10)) as
1
S LL = 2 (S HH + 2iS XX - S VV )
1
S RR = 2 (S VV + 2iS XX - S HH) .
(14)
and whose application examples are summarized in Table 4.
B. Interpretation and Decomposition
of Scattering Processes
The main objective of scattering decomposition approaches
is to break down the polarimetric backscattering signature
of distributed scatterers which is in general given by the
superposition of different scattering contributions inside
the resolution cell into a sum of elementary scattering
contributions. The most common elementary scattering
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