Graphics Programs Reference
In-Depth Information
∑
Ex
1
x
2
y
1
y
2
(
,
,
,
)
=
Ex
1
x
2
y
1
y
2
α
l
β
l
(
,
,
,
;
,
)
(12.65)
all scatterers
All formulas for the 2-D case reduce to those of a linear array case by setting
and
N
y
=
1
α
=
0
.
The variable part of the phase given in Eq. (12.63) is proportional to the inte-
gers and . Therefore, after completion of the sequential fir-
ing, electric fields with paths of the same
(
x
1
+
x
2
)
(
y
1
+
y
2
)
,()
ij
sums, where
{
i
=
+
x
n
2
;
=
(
N
1
)
,
…
N
(
1
)
}
(12.66)
n
1
{
j
=
+
y
n
2
;
=
(
N
1
)
,
…
N
(
1
)
}
(12.67)
n
1
can be collected coherently. In this manner the 2-D information array
is computed. The coefficient sequence
is also computed. More precisely,
{
bm
x
(
,
m
y
)
;
(
m
x
,
m
y
)
=
0 …2
N
,
1
}
{
cm
x
(
,
m
y
)
;
(
m
x
,
m
y
)
=
0 …2
N
,
2
}
=
n
10…
N
for m
x
n
1
+
n
2
and m
y
=
n
1
+
n
2
(12.68)
=
,
1
,
and n
2
=
0 …
N
,
1
bm
x
(
,
m
y
)
=
bm
x
(
,
m
y
)
+
Ex
n
1
(
,
y
n
1
,
x
n
2
,
y
n
2
)
(12.69)
It follows that
cm
x
(
,
m
y
)
=
(
N
x
m
x
(
N
x
1
)
)
×
(
N
y
m
y
(
N
y
1
)
)
(12.70)
The processing of the complex 2-D information array is simi-
lar to that of the linear case with the exception that one should use a 2-D DFT.
After antenna gain and range attenuation compensation, scatterers are detected
as peaks in the 2-D amplitude spectrum of the information array. A scatterer
located at angles
{
bm
x
(
,
m
y
)
}
(
α
l
β
l
,
)
will produce a peak in the amplitude spectrum at
DFT indexes
(
p
l
,
q
l
)
, where
q
l
p
l
---
α
l
=
atan
(12.71)
λ
p
l
2
Nd
λ
q
l
2
Nd
sin
β
l
=
-------------------------
=
------------------------
(12.72)
cos
α
l
sin
α
l
Derivation of Eq. (12.71) is in Section 12.9.7.
12.9.3. Geometry for DFTSQM SAR Imaging
Fig. 12.14
shows the geometry of the DFTSQM SAR imaging system. In
this case,
t
c
denotes the central time of the observation interval,
D
ob
. The air-
craft maintains both constant velocity
v
and height
h
. The origin for the rela-
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