Graphics Programs Reference
In-Depth Information
2π
f
0
r
tt
t
2
ψ
⊥
=
2π
f
0
t
+
----
(12.101)
The instantaneous frequency for the
i
th
scatterer within the
k
th
range cell is
computed as
f
0
1
2π
d
ψ
)
ô
s
]
------
---
f
di
=
=
[
2
r
st
s
+
(
(
D
n
1
)
+
r
ô
st
(
D
n
2
)
(12.102)
ô
st
d
t
Substituting the actual values for
r
st
,
r
ô
st
(
D
n
1
)
,
r
ô
st
(
D
n
2
)
and collecting
terms yields
ô
s
ρ
2
2
v
sin
λ
β
k
β
∗
f
di
=
-------------------
--------------
(
hD
n
1
+
(
+
D
n
2
)
sin
)
s
(12.103)
t
()
ô
Note that if
=
0
, then
2
v
λ
f
di
=
------
sin
β
k
sin
µ
(12.104)
which is the Doppler value corresponding to a ground patch (see Eq. (12.49)).
The last stage of the processing consists of three steps: (1) two-dimensional
windowing; (2) performing a two-dimensional DFT on the windowed quadra-
ture components; and (3) scaling to compensate for antenna gain and range
attenuation.
12.9.7. Derivation of Eq. (12.71)
Consider a rectangular array of size , with uniform element spacing
, and wavelength . Assume sequential mode operation where
elements are fired sequentially, one at a time, while all elements receive in par-
allel. Assume far field observation defined by azimuth and
e
levation angles
. The unit vector
NN
×
d
x
==
d
y
d
λ
(
αβ
,
)
u
on the line of sight, with respect to
O
, is given by
u
βα
a
x
=
sin
cos
+
sin
βα
a
y
sin
+
cos
β
a
z
(12.105)
The
(
n
x
,
n
y
)
th
element of the array can be defined by the vector
N
2
1
N
2
1
da
x
da
y
en
x
(
,
n
y
)
=
n
x
-------------
+
n
y
-------------
(12.106)
where
(
n
x
,
n
y
=
0 …
N
,
1
)
. The one-way geometric phase for this element is
ϕ'
n
x
(
,
n
y
)
=
ku en
x
(
•
(
,
n
y
)
)
(12.107)
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