International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
In the case that the phase angles are equal 5, #5, —> à = 0 the 
trace of the tip of the electric field vector E is a straight line. 
2.2 The Pauli decomposition approach 
If a scatterer is illuminated by an electromagnetic plane 
transmitted by an antenna, tfe incident wave at the scatterer is 
given by 
É" -hE? + VE" (11) 
and that induces currents in the scatterer, which in turn reradiate 
a scattered wave. In the far zone of the scatterer, the scattered 
wave can be considered as a plane wave. The scattering process 
can be modelled as a linear transformation, described by a 
matrix S. The received field is then given by: 
sopEnR epis $e] u 
zen elt 
vv 1 
| 
dé 
The [S] matrix is referred to as Jones matrix (Jones, 1941), and 
is a complex 2x2 matrix, containing information on the 
scatterer. Sy, and S,, are called co-polar and Spy and Syn cross- 
polar components. According to the reciprocity theorem, the 
cross-polar components are equal. 
Instead of the matrix notation, one may use a four element 
complex vector k , which contains complete information on 
the [S] matrix. 
(13) 
es Bis : Trace(|S]4)=[ky,k ka, k;1" 
where Trace ([S]) is the sum of the diagonal elements of [S] and 
V is a complete set of 2x2 complex basis matrices under a 
hermitian inner product. Any complete orthonormal basis set of 
four 2x2 matrices can be used. A basis which is more related to 
the physics of wave scattering, the Pauli basis, is formed by the 
Pauli spin matrices (Cloude, 1986). 
|l o] 276 11. 10 fl 
A 2 42| I | 
1 
| 
1109 y 14e [9 [Y 
The corresponding vector k, is then 
1 y 7 1 1 , 1 3 Y Y 5 
kp = [S hh + S , S hh 7 S , S hv + Su > (S, = S hv )l ( 13) 
2 
NZ 
The Pauli decomposition approach assigns the appropriate 
deterministic scattering mechanisms to each one of the four 
elementary scattering matrices. The basic scattering 
mechanisms are: isotropic surface, right wound helix and left 
wound helix. Consequently, the Pauli matrices can be 
interpreted as shown in table 2 (Hellmann, 1999). 
  
Pauli matrix | Scattering type Interpretation 
  
Surface, 
sphere,cornerreflectors 
odd-bounce 
d 
  
even-bounce dihedral 
0 
0 =] 
  
K I | even-bounce 45? titled dihedral 
| 0 titled 45° 
0 =i cross-polariser Not existent for 
0 backscattering 
  
  
i 
  
  
  
  
Table 2. Pauli matrices and their interpretation in the ( e e ) 
polarization basis 
3. INTERPRETATION OF THE POLARIMETRIC 
DATA 
3.1 Interpretation of polarization signatures 
A polarization signature is given by its 3-D presentation. X,P,Z 
axes are assigned to the ellipticity angle x, the orientation angle 
y, and the intensity of the co-polar or cross-polar components 
of the radar signal (Z). As mentioned previously, the ellipticity 
angle takes values in the interval [-45", 45°] and the orientation 
angle in the interval [0, 180^]. Polarization signatures were 
extracted for four land uses: urban, forest, vegetation, and 
smooth surfaces (roads, runways, etc). 
intensity for an ellipticity angle close to 45° and an orientation 
angle close to 180° (figure 3). This means that polarization is 
left hand circular (ie. the amplitudes of the co-polar 
components Sp, and S,, are equal and the relative difference 
angle close to 90°), and the orientation of the wave transmitted 
changes 180° relative to the orientation of the wave received. 
The above description fits well to the even-bounce scattering 
type of horizontal dihedrals, which correspond to the building- 
ground interaction that we encounter in urban areas. 
The signature of the urban class presents high values of 
In figure 3 we also observe very low values of intensity for an 
ellipticity angle close to 0° and an orientation angle close to 0". 
This means that in urban areas, polarization horizontally 
oriented, which is the dipole like scattering case, is missed. The 
low intensity values for an ellipticity angle close to -45° and an 
orientation angle close to 0° denote the surface scattering type 
of smooth surfaces (e.g. roads) found in the urban areas. 
     
(a) 
Figure 3. a) The co-polar and b) the cross-polar signature of the 
urban area 
Urban areas also have large cross-polar contribution (figure 3). 
The range entire of values of the ellipticity angle is encountered 
for high intensity of the cross-polar components and for an 
orientation angle close to a) 29°, and b) 162°. This proves that 
discontinuities of both scattering types, dihedrals and surfaces, 
result in random polarization ellipses. Those with an orientation 
282 
  
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Figure 5. 
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