and the corresponding Mueller matrix of the cross
scattering mechanism can be written as,
if 50 00
gel pa
F:=|0 0 10/% (10)
010 9 1
3 ALGORITHM
The total Mueller matrix is the sum of the Mueller
matrices for the above individual mechanisms. This
gives,
ot] Umi
o2 Sit ar B+ an
a—1 , -1 5
fa = 2st ts (12)
a+} 2 B +1 43 2
foa = i 28 Sou $2415 (13)
. COSÔ Le T P à > x
[s = S + 75 + S3 + 54 (14)
sind a
fa = PT (15)
Cosd 3i 2 >
faa = rS TT P m 53 + Sa (16)
SE Ard: ud (17)
The left sides of (11)-(16) are the elements of the
Mueller matrix measured by the polarimetric radar
system. St (à? = 1,---,4) are the four unknowns to
be decided. The optimal solution of (11)-(17) can be
found using the WLS method. After the unknowns
are obtained. the simulated Muller matrix
F=Fi+F2+Fat Fa (18)
can be reconstructed, and the co- and cross-
polarisation responses predicted by the model are,
ob, =4m(SE +S: + 53) (19)
gy, = 4n(S}/a + 53/6 + S3) (20)
Ton = Thy = 47S; (21)
4 RESULTS AND DISCUSSIONS
In August-September 1993, the NASA /JPL AirSAR
quad-polarised system flew approximately 60 test sites
in Australia. Two of them are used to test the model.
One is the Gippsland site covered by native eucalypts,
farmland and pine plantations while the other, the
Sydney site, has typical urban features, such as com-
mercial and residential buildings or a mixture. An
ocean water area is also covered by the second site.
The incidence angle varies from about 30? in near
range to 60? in far range. Since the mean value elimi-
nates the speckle effects, and characterises the features
of the distributed targets, sub-blocks, normally more
than 2000 pixels, are used for the simulation. The size
of a pixel is about 6 x 6 m?.
To obtain the optimal decomposition, the values of
a, B and 6 have to be given. For forests in the first site,
we assume that the double bounce scattering is caused
by the trunk-ground structure. Therefore, œ = 4 and
ó — 150? are chosen. For the urban areas in the second
site, we assume that the double bounce scattering is
caused by both metallic and dielectric materials, thus
a = 2.5 and § = 165° are chosen. The choice of f is
a little more complicated, because it varies very much
with the incidence angle. In the simulation, B varies
in the region of 0.5 — 0.1 according to the incidence
angle and the dielectric constants.
In our simulation, all the weighting factors in the
method of WLS are chosen to be the same for sim-
plicity, resulting in the decomposed value being iden-
tical to the measured value for HV (VH) polarisation.
In the following examples, therefore, the decomposed
cross scattering components will not be mentioned fur-
ther.
1.0 Co- pol eo AN Cro- pol
2 (?
= = T o IARE
o bees
3 Bi = Up WS QUITS,
E RN NY
E UNUM MN E RSS AY
© HI PR S X um NSS ANY
2 RAN aa VID
Zp RES 5 RRA N
22 M NEE 09 x > WO
E 0) NS N ND
X 9 \ ^
XY
y Sa m =
Tm > TS
rr
HR
1] [UI
J UN UN
HI ATEN
DE
ZZ
7^
Es
=
Normalised o
Normalised o
[|
Till
UHI
ii
y kenn JI
ST 2H hy
UN
[]
7
7
L7
EL
LEE
=
4
ZZ
7
Z
É
2
à
N
EN
=
N
Zz
RLY
2
CH LA]
SUN N
SZ LM /]
N
Figure 1: Top: Measured P-band polarisation signa-
tures from buildings facing radar at incidence angle
of 309. Bottom: theoretical polarisation signatures by
single bounce scattering.
4.1
The backscattering from residential buildings in ur
ban areas could be dominated by a single bounce from
building roofs and/or a double bounce from the wall-
ground structures depending on buildings' orientation
and radar's incidence angle. Two groups of residential
buildings in the Sydney region are selected for compar
ison. These two groups of buildings are all facing radar
and similar to one another, except that the radar’s m-
Residential Buildings
198
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
