y 
In 
1t 
as 
3) 
ce 
as 
4) 
This distribution is uni-modal, with mode = Arg(X), 
and shape controlled by |X{.Low [X| means flat 
distribution, high |X| means peaked distribution. 
Data from 1989 Maestro campaign provided an 
opportunity to investigate phase properties and 
hypothesis used for the model construction, which 
are in brief: once there exists a fixed phase 
difference between two polarizations, this will 
appear as the argument of the covariance between 
these two channels and this will also be the mode 
of this phase difference, provided |X| is large 
enough. In this paper uncalibrated data will be 
used for investigating the properties of phase 
Prior to any radiometric correction. In a 
subsequent paper it will be investigated how the 
calibration procedures can modify phase definition 
quality and discriminatory power. 
2. CHECKING PHASE PROPERTIES 
Observing the histogram of phases differences one 
can see what is the mode (within certain 
precision), and compare if this mode agree with the 
argument of the covariance or how the spread of the 
distribution depends on the correlation coeficient. 
However, when dealing with MSAR images, the number 
of channels combinations is high and visual 
inspection of histograms is not practical, besides 
the uncertainty of the method. An automatic method 
was chosen to find the mode for each calculated 
phase difference, by estimating the rate of an 
inhomogenous Poisson process by Jth waiting 
times[4]. 
For evaluating the flatness of the distribution, 
one can use the kurtosis, the normalized fourth 
moment of a distribution for which one possible 
estimate is: 
N ‚X 1% 
kurt(xi,...,xw) = DE E (5) 
i=l 
  
Kurtosis is a  nondimensional quantity which 
measures the relative sharpness or flatness of a 
distribution, being O (zero) for the gaussian 
distribution. Care is needed, because phase is 
periodic, so a convenient 2% window must be set, 
to calculate the moments. The mode is the natural 
choice to center this window. If a phase 
distribution is very peaked, the mean is expected 
to be near of the mode and the kurtosis a large 
positive value. If the distribution is flat, the 
mode and mean can be very different from the 
covariance argument (because of the instability of 
the situation), and the kurtosis will be negative. 
3. RESULTS 
The model described above was tested using 
relatively homogeneous areas from the UK test-site. 
Phase difference properties and quality were tested 
on a fairly large agricultural area in Reedham 
(four polarizations - C band)- 1 class only. The 
availability of ground data over the Feltwell test 
site allowed the study of phase difference 
discriminatory power and consistency. Four 
different crops and ground cover were defined using 
four polarizations and frequencies C and P: sugar 
beet (four test-sites), stubble (five test-sites), 
wheat (three test-sites) and potato (two 
test-sites). 
609 
Table 1 presents the modulus and argument of the 
correlation coefficient, the mode (31 wait times), 
the average around this mode, and the kurtosis for 
three channel combinations: HH-VV (S -S929), HV-VH 
and HH-HV - Reedham area. It is possible to observe 
that, contrary to that one can expect, the 
correlation coefficient between HV and VH is not 
ONE, probably due to cross-talk [5]. 
TABLE 1 
PHASE DIFFERENCES PROPERTIES AND QUALITY 
  
channels |p| Zp mode average  kurt 
HY-VH. 0.945. -73.100 .-—75.900 .-72.800. 8.930 
HH-VV-- 0.511 '-91.300 -96.400 ' -93.800 “0.020 
HH-Hv ^ 0.034 .-16.100 -139.700 -137.8900. -1.220 
  
  
  
The mode and average are consistent (similar) with 
the argument of covariance in the HH-VV and HV-VH 
cases, although the kurtosis is much higher for the 
HV-VH case.This is also coherent with the fact that 
the correlation is higher in the second case. In 
the HH-HV case, the argument of the correlation 
does not agree with the mode and average and the 
kurtosis is lower than -1.2 ( -1.2 is the lower 
theoretical value for kurtosis for  non-valley 
distributions - flat distribution case). So the 
general behavior is consistent with the model for 
phase difference distribution. 
Table 2 presents some phase differences for 
Feltwell area, frequencies C and P and Table 3 
presents the range of correlation coeficient for 
each class and channel combination. In general, it 
is possible to note that, although these test-site 
were not very large because of reduced field sizes, 
there is a relative stability of phase difference 
values within the same class and some divergence 
when comparing two distinct classes. Sugar beet is 
distinct from wheat and potato by ^70 degrees in 
HH-VVp . Stubble is distinct from other classes by 
720 degrees. 
  
  
  
  
  
TABLE 2 
PHASES DIFFERENCES 
classes HH-VVc HH-VVp HV-VHp 
-58.000 -36.300 69.500 
sugar -61.300 -29.600 67.500 
beet -60.900 733.200 69.700 
-60.900 -33.400 68.500 
745.000 764.800 68.100 
-40.700 -118.000 -115.000 
stubble 744.700 -80.100 106.000 
746.000 -78.600 70.700 
-47.600 -71.500 -88.700 
-55.600 -103.200 -1.200 
wheat -61.000 7104.200 -61.000 
-43.600 -103.000 63.700 
potato -64 .900 -104.300 71.700 
763.100 -102.000 68.800