3.4 Scattering Cross Section of Simple Point Targets
41
Fig. 3.19 Electromagnetic
wave scattering on a flat
triangular plate
For γ 0 = θ 0 = 0 case, we obtain A =
4π
λ 2 a
2 b
2 regardless of polarization type of
incident wave (Fig. 3.19).
To find a RCS of a triangular plate at γ 0 and θ 0 arbitrary angles, it is reasonable to
use (3.22) relation. However, due to extreme awkwardness of obtained relations, we
confine to RCS examination at its determination in two mutually orthogonal planes,
perpendicular to plate surface γ 0 = 0 and γ 0 = π /3.
For the first case (horizontal plane, γ 0 = 0), we have:
A =
4π
λ 2 cos
2
θ 0
b
∫
0
dy
a−
ay
b
∫
−(a−
ay
b )
e
−2 jkx sin θ 0 dx
2
=
4π
λ 2 (ab)
2 cos
2
θ 0
sin(ka sin θ 0 )
ka sin θ 0
4
.
(3.51)
For the second case (vertical plane, γ 0 = π /2), we have:
A =
4π
λ 2 (ab)
2 cos
2
θ 0
sin(kb sin θ 0 )
kb sin θ 0
+
1 − sin 2(kb sin θ 0 )/2(kb sin θ 0 )
kb sin θ 0
.
(3.52)
The obtained formulas quite good correlate with experimental data.
In horizontal plane, the backscattering diagram (BSD) represents a quite rapid
(at change of observing angle) oscillating function; herewith, a width of main BSD
lobe in 0.5 level comprises 18λ/a [deg] and level of the first side lobe—26.6 dB. In
vertical plane, an opposite case, the BSD represents a monotone function with no
lobes. Width of the main lobe in 0.5 level at b > 6λ and a > 2λ condition equals to
31.5λ/b [deg]. If kb sin θ 0 > 2, then A =
4π
λ 2
ctgθ 0
kb
2
; however, an application area
of this formula is limited by angles θ 0 < 35
◦ .
Besides plates in shape of isosceles triangle, we can frequently meet in practice
plates in shape of right-angled triangle. Any triangles with a base and b height in
vertical plane also would have no-lobes BSD.
41
Fig. 3.19 Electromagnetic
wave scattering on a flat
triangular plate
For γ 0 = θ 0 = 0 case, we obtain A =
4π
λ 2 a
2 b
2 regardless of polarization type of
incident wave (Fig. 3.19).
To find a RCS of a triangular plate at γ 0 and θ 0 arbitrary angles, it is reasonable to
use (3.22) relation. However, due to extreme awkwardness of obtained relations, we
confine to RCS examination at its determination in two mutually orthogonal planes,
perpendicular to plate surface γ 0 = 0 and γ 0 = π /3.
For the first case (horizontal plane, γ 0 = 0), we have:
A =
4π
λ 2 cos
2
θ 0
b
∫
0
dy
a−
ay
b
∫
−(a−
ay
b )
e
−2 jkx sin θ 0 dx
2
=
4π
λ 2 (ab)
2 cos
2
θ 0
sin(ka sin θ 0 )
ka sin θ 0
4
.
(3.51)
For the second case (vertical plane, γ 0 = π /2), we have:
A =
4π
λ 2 (ab)
2 cos
2
θ 0
sin(kb sin θ 0 )
kb sin θ 0
+
1 − sin 2(kb sin θ 0 )/2(kb sin θ 0 )
kb sin θ 0
.
(3.52)
The obtained formulas quite good correlate with experimental data.
In horizontal plane, the backscattering diagram (BSD) represents a quite rapid
(at change of observing angle) oscillating function; herewith, a width of main BSD
lobe in 0.5 level comprises 18λ/a [deg] and level of the first side lobe—26.6 dB. In
vertical plane, an opposite case, the BSD represents a monotone function with no
lobes. Width of the main lobe in 0.5 level at b > 6λ and a > 2λ condition equals to
31.5λ/b [deg]. If kb sin θ 0 > 2, then A =
4π
λ 2
ctgθ 0
kb
2
; however, an application area
of this formula is limited by angles θ 0 < 35
◦ .
Besides plates in shape of isosceles triangle, we can frequently meet in practice
plates in shape of right-angled triangle. Any triangles with a base and b height in
vertical plane also would have no-lobes BSD.