Graphics Programs Reference
In-Depth Information
)
2
8π
z
2
32
⁄
z
1
32
⁄
(
)
2
---------------------------------------
α
n
σ
θ
n
=
tan
(
sin
cos
θ
n
tan
α
(11.41)
9λ
n
sin
where is the wavelength, and , are defined in
Fig. 11.21
.
Using trigo-
nometric identities, Eq. (11.41) can be reduced to
λ
z
1
z
2
)
2
8π
z
2
32
⁄
z
1
32
⁄
(
sin
α
---------------------------------------
-------------------
σ
θ
n
=
(11.42)
9λ
)
4
(
cos
α
For non-normal incidence, the backscattered RCS due to a linearly polarized
incident wave is
2
λ
z
tan
8πθ
α
sin θα
θ
θα
cos
tan
------------------
------------------------------------------
σ
=
(11.43)
sin
sin
tan
+
cos
θ
where is equal to either or depending on whether the RCS contribu-
tion is from the small or the large end of the cone. Again, using trigonometric
identities Eq. (11.43) (assuming the radar illuminates the frustum starting from
the large end) is reduced to
z
z
1
z
2
λ
z
tan
8πθ
α
)
2
------------------
θα
σ
=
(
tan
(
)
(11.44)
sin
When the radar illuminates the frustum starting from the small end (i.e., the
radar is in the negative z direction in
Fig. 11.21
), Eq. (11.44) should be modi-
fied to
λ
z
tan
8πθ
α
)
2
------------------
θα
σ
=
(
tan
(
+
)
(11.45)
sin
For example, consider a frustum defined by ,
, . It follows that the half cone angle is .
Fig. 11.23a
shows a plot of its RCS when illuminated by a radar in the positive
z direction.
Fig. 11.23b
shows the same thing, except in this case, the radar is
in the negative z direction. Note that for the first case, normal incidence occur
at , while for the second case it occurs at . These plots can be repro-
duced using MATLAB function
Ðrcs_frustum_gui.mÑ
given in Listing 11.8 in
Section 11.9.
H
=
20.945
cm
r
1
=
2.057
cm
r
2
=
5.753
cm
10°
100°
80°
MATLAB Function Ðrcs_frustum.mÑ
The function
Ðrcs_frustum.mÑ
computes and plots the backscattered RCS of
a truncated conic section. The syntax is as follows:
[rcs] = rcs_frustum (r1, r2, freq, indicator)
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