3.4 Scattering Cross Section of Simple Point Targets
39
A max =
4π
λ 2 a
2 b
2
=
4π S
2
λ 2 .
(3.42)
Pay attention that the last formula is correct for flat plates of any shape at normal
beam incidence. It is of interest to note that RCS of a flat plate opposed to RCS of
a ball depends both on wavelength λ and direction to the radar (γ 0 i θ 0 angles);
besides, it is proportional not to a geometrical area but to its square. The last is
connected with directivity of plate reflections contrary to indirect ball reflection. At
sliding incidence angles, we can obtain a good result for RCS using the following
formula:
A =
ab
2
λ
cos
2
α +
2π
3
(ka)
2
sin
2
α
,
(3.43)
where α = ka − 0.3π .
Area of sliding incidence angles distinct in that at changing of a longitudinal size,
the RCS oscillates with λ/3 period.
The given considerations show that metal sheets are unreasonable to use as
phantom targets imitating real objects as far as a little deviation of radiation direction
from a normal to a surface decreases a sheet RCS up to a zero. A phantom radar
target should have a considerable RCS value which is a little dependant on incidence
angle. Then, it would be well observed by radar. Angled reflectors with equal facet
forms, Luneburg lens etc., are used as radar phantom targets.
Flat circular plate RCS To find a RCS of a flat circular plate of ρ radius, in direction
determined by θ 0 angle, we can also use (3.22) formula where we should assume
that γ 0 = 0 and transfer to polar coordinates (r, γ ):
A =
4π
λ 2 cos
2
θ 0
2π
∫
0
ρ
∫
0
e
−2 jkr sin θ 0 cos γ r dr dγ
2
.
(3.44)
Employing a Bessel function representation, we obtain:
A =
4π
λ 2
πρ
2
2 cos
2
θ 0
2J (2kρ sin θ 0 )
2kρ sin θ 0
,
(3.45)
where J (·) is Bessel function of a first order.
Formula (3.45) gives satisfactory results only in ρ > 2λ and θ 0 < 45
◦ condition;
at θ 0 > 45
◦ , it gives not only numerically but qualitatively wrong results. In this
case, we can use the following representation:
A =
4π
λ 2
πρ
2
2
2J (2kρ sin θ 0 )
2kρ sin θ 0
2
+
2J 2 (2kρ sin θ 0 )
2kρ sin θ 0
2
,
(3.46)
39
A max =
4π
λ 2 a
2 b
2
=
4π S
2
λ 2 .
(3.42)
Pay attention that the last formula is correct for flat plates of any shape at normal
beam incidence. It is of interest to note that RCS of a flat plate opposed to RCS of
a ball depends both on wavelength λ and direction to the radar (γ 0 i θ 0 angles);
besides, it is proportional not to a geometrical area but to its square. The last is
connected with directivity of plate reflections contrary to indirect ball reflection. At
sliding incidence angles, we can obtain a good result for RCS using the following
formula:
A =
ab
2
λ
cos
2
α +
2π
3
(ka)
2
sin
2
α
,
(3.43)
where α = ka − 0.3π .
Area of sliding incidence angles distinct in that at changing of a longitudinal size,
the RCS oscillates with λ/3 period.
The given considerations show that metal sheets are unreasonable to use as
phantom targets imitating real objects as far as a little deviation of radiation direction
from a normal to a surface decreases a sheet RCS up to a zero. A phantom radar
target should have a considerable RCS value which is a little dependant on incidence
angle. Then, it would be well observed by radar. Angled reflectors with equal facet
forms, Luneburg lens etc., are used as radar phantom targets.
Flat circular plate RCS To find a RCS of a flat circular plate of ρ radius, in direction
determined by θ 0 angle, we can also use (3.22) formula where we should assume
that γ 0 = 0 and transfer to polar coordinates (r, γ ):
A =
4π
λ 2 cos
2
θ 0
2π
∫
0
ρ
∫
0
e
−2 jkr sin θ 0 cos γ r dr dγ
2
.
(3.44)
Employing a Bessel function representation, we obtain:
A =
4π
λ 2
πρ
2
2 cos
2
θ 0
2J (2kρ sin θ 0 )
2kρ sin θ 0
,
(3.45)
where J (·) is Bessel function of a first order.
Formula (3.45) gives satisfactory results only in ρ > 2λ and θ 0 < 45
◦ condition;
at θ 0 > 45
◦ , it gives not only numerically but qualitatively wrong results. In this
case, we can use the following representation:
A =
4π
λ 2
πρ
2
2
2J (2kρ sin θ 0 )
2kρ sin θ 0
2
+
2J 2 (2kρ sin θ 0 )
2kρ sin θ 0
2
,
(3.46)