Merge branch 'feature/rcs'

Project.toml

@@ -1,7 +1,7 @@
 name = "SphericalScattering"
 uuid = "1a9ea918-b599-4f1f-bd9a-d681e8bb5b3e"
 authors = ["Bernd Hofmann <Bernd.Hofmann@tum.de> and contributors"]
-version = "0.7.0"
+version = "0.7.1"
 
 [deps]
 LegendrePolynomials = "3db4a2ba-fc88-11e8-3e01-49c72059a882"

README.md

@@ -40,7 +40,7 @@ The following aspects are implemented (✔) and planned (⌛):
 ##### Available quantities (where applicable):
 - ✔ Far-fields
 - ✔ Near-fields (electric & magnetic)
-- ⌛ Radar cross section (RCS)
+- ✔ Radar cross section (RCS)
 - ⌛ Surface currents
 - ✔ Scalar potentials 
 - ✔ Displacement fields 

docs/src/application.md

@@ -91,6 +91,80 @@ print("Far-field error: $diff_FF %\n")
     [CompScienceMeshes](https://github.com/krcools/CompScienceMeshes.jl) are used to define several functional tests.
 
 
+---
+## [Radar Cross Section](@id rcsApplication) 
+
+The monostatic and the bistatic [radar cross section (RCS)](@ref rcsPW) can be evaluated.
+
+### Monostatic RCS
+
+The monostatic radar cross section as a function of the sphere radius can be computed as follows (compare also the plot in [[1, pp. 352ff]](@ref refs)):
+```@example RCS
+using SphericalScattering
+using PlotlyJS
+
+f = 1e8
+c = 2.99792458e8    # speed of light
+λ = c / f
+
+RCS = Float64[]
+aTλ = Float64[]
+
+# --- compute RCS
+for rg in 0.01:0.01:3.0
+
+    a = λ*rg
+
+    monoRCS = rcs(PECSphere(radius=a), planeWave(frequency=f))
+
+    push!(RCS, monoRCS / (π * a^2))
+    push!(aTλ, rg)
+end
+
+# --- plot
+layout = Layout(
+    yaxis=attr(title_text="RCS / πa² in dB"),
+    xaxis=attr(title_text="a / λ")
+)
+
+plot(scatter(; x=aTλ, y=10*log10.(RCS), mode="lines+markers"), layout)
+t = plot(scatter(; x=aTλ, y=10*log10.(RCS), mode="lines+markers"), layout) # hide
+savefig(t, "monoRCS.html"); nothing # hide
+```
+
+```@raw html
+<object data="../monoRCS.html" type="text/html"  style="width:100%;height:50vh;"> </object>
+```
+
+### Bistatic RCS
+
+The bistatic radar cross section along a ϑ-cut can be computed as follows (compare also the plot in [[1, pp. 351ff]](@ref refs)):
+```@example RCS
+using StaticArrays
+
+# --- points
+ϑ = [i*π/500 for i in 0:500]
+φ = 0
+points_cart = [SphericalScattering.sph2cart(SVector(1.0, ϑi, φ)) for ϑi in ϑ]
+
+# --- compute RCS
+biRCS = rcs(PECSphere(radius=λ), planeWave(frequency=1e8), points_cart) / λ^2
+
+# --- plot
+layout = Layout(
+    yaxis=attr(title_text="RCS / λ² in dB"),
+    xaxis=attr(title_text="ϑ in degree")
+)
+
+plot(scatter(; x=ϑ*180/π, y=10*log10.(biRCS), mode="lines+markers"), layout)
+t = plot(scatter(; x=ϑ*180/π, y=10*log10.(biRCS), mode="lines+markers"), layout) # hide
+savefig(t, "biRCS.html"); nothing # hide
+```
+
+```@raw html
+<object data="../biRCS.html" type="text/html"  style="width:100%;height:50vh;"> </object>
+```
+
 
 
 ---

docs/src/manual.md

@@ -135,14 +135,31 @@ E  = field(sp, ex, ElectricField(point_cart))
 H  = field(sp, ex, MagneticField(point_cart))
 
 FF = field(sp, ex, FarField(point_cart))
-
 ```
 For the uniform field excitation, only the electric field as well as the scalar potential can be calculated:
 ```julia
 Φ = field(sp, ex, ScalarPotential(point_cart))
 ```
 
 
+---
+## Radar Cross Section
+
+To compute the bistatic [radar cross section (RCS)](@ref rcsPW), the function
+```julia
+σ = rcs(sp, ex, points_cart)
+```
+is provided. For the monostatic RCS, the function
+```julia
+σ = rcs(sp, ex)
+```
+is provided.
+
+!!! note
+    The RCS is (so far) only defined for a plane wave excitation.
+
+
+
 ---
 ## Conversion Between Bases
 

docs/src/planeWave.md

@@ -95,3 +95,21 @@ H  = field(sp, ex, MagneticField(point_cart))
 
 !!! note
     The total far-field is not defined (since the incident far-field is not defined).
+
+
+---
+## [Radar Cross Section](@id rcsPW)
+
+To compute the bistatic radar cross section (RCS) [[1, pp. 350ff]](@ref refs)
+```math
+\sigma (\vartheta, \varphi) = \lim_{r\rightarrow \infty} \left( 4 \pi r^2 \frac{{|e^\mathrm{sc}|}^2}{{|e^\mathrm{sc}|}^2} \right)
+```
+the function
+```julia
+σ = rcs(sp, ex, points_cart)
+```
+is provided. For the monostatic RCS, the function
+```julia
+σ = rcs(sp, ex)
+```
+is provided.

src/SphericalScattering.jl

@@ -43,6 +43,7 @@ export SphericalMode, SphericalModeTE, SphericalModeTM
 export PECSphere, DielectricSphere, LayeredSphere, LayeredSpherePEC
 export DielectricSphereThinImpedanceLayer
 export field, scatteredfield
+export rcs
 export sphericalGridPoints, phiCutPoints, thetaCutPoints
 
 
@@ -82,6 +83,7 @@ include("UniformField/scattered.jl")
 include("totalFields.jl")
 include("coordinateTransforms.jl")
 include("utils.jl")
+include("rcs.jl")
 
 if !isdefined(Base, :get_extension)
     include("../ext/SphericalScatteringExt.jl") # for backwards compatibility with julia versions below 1.9

src/rcs.jl

@@ -0,0 +1,50 @@
+
+"""
+    rcs(sphere::Sphere, excitation::PlaneWave, point_cart; parameter::Parameter=Parameter())
+
+Compute the bistatic radar cross-section (RCS). 
+"""
+function rcs(sphere::Sphere, excitation::PlaneWave, points_cart; parameter::Parameter=Parameter())
+
+    FF = scatteredfield(sphere, excitation, FarField(points_cart); parameter=parameter)
+
+    return 4π * norm.(FF) .^ 2 / abs2(excitation.amplitude)
+end
+
+
+
+"""
+    rcs(sphere::Sphere, excitation::PlaneWave; parameter::Parameter=Parameter())
+
+Compute the monostatic radar cross-section (RCS): the bistatic RCS solely for the incident direction of the plane wave. 
+"""
+function rcs(sphere::Sphere, excitation::PlaneWave; parameter::Parameter=Parameter())
+
+    point_cart = -excitation.direction
+
+    return rcs(sphere, excitation, [point_cart]; parameter=parameter)[1]
+end
+
+
+
+"""
+    rcs(sphere::Sphere, excitation::Excitation, point_cart; parameter::Parameter=Parameter())
+
+RCS only defined for plane waves, so far.
+"""
+function rcs(sphere::Sphere, excitation::Excitation, point_cart; parameter::Parameter=Parameter())
+
+    return error("The (bistatic) RCS is only defined for a plane-wave excitation (so far).")
+end
+
+
+
+"""
+    rcs(sphere::Sphere, excitation::Excitation; parameter::Parameter=Parameter())
+
+RCS only defined for plane waves, so far.
+"""
+function rcs(sphere::Sphere, excitation::Excitation; parameter::Parameter=Parameter())
+
+    return error("The (monostatic) RCS is only defined for a plane-wave excitation (so far).")
+end

test/utils.jl

@@ -39,3 +39,21 @@ end
     @test_nowarn plotffcut(norm.(FF), points_sph, normalize=true, scale="log", format="rectangular")
     @test_nowarn plotffcut(norm.(FF), points_sph, normalize=true, scale="linear", format="rectangular")
 end
+
+@testset "Radar cross section" begin
+
+    # --- monostatic RCS
+    @test_nowarn rcs(PECSphere(; radius=2.0), planeWave(; frequency=1e8))
+
+    @test_throws ErrorException("The (monostatic) RCS is only defined for a plane-wave excitation (so far).") rcs(
+        PECSphere(; radius=1.0), SphericalModeTE(; frequency=f)
+    )
+
+
+    # --- bistatic RCS
+    @test_nowarn rcs(PECSphere(; radius=2.0), planeWave(; frequency=1e8), [SVector(1.0, 0.0, 0.0)])
+
+    @test_throws ErrorException("The (bistatic) RCS is only defined for a plane-wave excitation (so far).") rcs(
+        PECSphere(; radius=1.0), SphericalModeTE(; frequency=f), []
+    )
+end