Graphics Programs Reference
In-Depth Information
The vector defines the center of the 3 dB footprint at time . The cen-
ter of the array coincides with the flight path, and it is assumed to be perpen-
dicular to both the flight path and the line of sight
qt
()
t
c
ρ
t
()
. The unit vector
a
along the real array is
β
∗
a
x
β
∗
a
z
a
=
cos
+
sin
(12.73)
β
∗
where is the elevation angle, or the complement of the depression angle,
for the center of the footprint at central time
t
c
.
12.9.4. Slant Range Equation
Co
n
sider the geometry shown in
Fig. 12.16
and assume that there is a scat-
terer
C
i
within the
k
th
range cell. This scatterer is defined by
{
ampltiude phase elevation azimuth height
,
,
,
,
}
=
(12.74)
ô
i
{
a
i
,
φ
i
β
i
µ
i
,
,
,
}
The scatterer
C
i
(assuming rectangular coordinates) is given by
ô
i
a
z
C
i
=
h
tan
β
i
cos
µ
i
a
x
+
h
tan
β
i
sin
µ
i
a
y
+
(12.75)
β
i
=
β
k
+
ε
(12.76)
where
β
k
denotes the elevation angle for the
k
th
range
c
ell at the center of the
observation interval and
ε
is an incremental
a
ngle. Let
Oe
n
refer to the vector
between the
n
th
array element and the point
O
, then
Z
#N
D
ob
t
c
M
ρ
t
()
β
i
#1
h
v
O
X
(
000
,,
)
µ
i
C
i
Y
C
i
Figure 12.16. Scatterer
within a range cell.
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