
Benchmarking Tool
for Assessing the Accuracy of Solutions of Electromagnetic Scattering Problems
The page aims assessing the accuracy of electromagnetic scattering solutions of its users. User upload his/her solution's bistatic radarcrosssection (RCS) in an ASCII file, and gets plots of their solution and corresponding reference, along with RCS errors in various bistatic angular sectors.
Users can find relevant information below and can upload their results by going through the links on the bottom of the page.
Problem Types
We solved two classes of Helmholtztype scattering problems; involving extremelylarge perfectlyconducting (PEC) objects, and twolayered composite dielectric objects. The first class involves a conducting sphere and a NASA Almond geometries of various sizes, whereas the second class involves a twolayered dielectric sphere with various dielectric properties.
Extremelylarge Conducting Objects 
Composite Dielectric Objects 



Sphere 
NASA Almond 
Twolayered Sphere 
Dimensions
The PEC sphere has a radius of 0.3 m, and the NASA Almond has a length of 0.2523744 m. We solve the sphere at 20 GHz, 40 GHz, 80 GHz, 96 GHz, 120 GHz, 160 GHz, 180 GHz, 210 GHz, 260 GHz, 280 GHz, 340 GHz, 380 GHz, 440 GHz, 500 GHz, and NASA Almond at 112.5 GHz, 225 GHz, 450 GHz, 900 GHz, 1800 GHz, 2500 GHz frequencies.
The dielectric sphere has the inner surface radius of 0.5 m and the outer surface radius of 1 m and it is solved at 9.6 GHz. In other words, the inner and outer surfaces have radius of 16.011077 λ and 32.022153 λ, respectively, where λ is the wavelength of the illuminating planewave in freespace.
We took the speed of light as 299,792,458 m/s while calculating the dimensions in wavelength.
Illumination
All geometries are located at the origin and illuminated by a plane wave propagating in the x direction with the electric field polarized in the y direction. Note that, NASA Almond lies on the xy plane with its sharp end pointing in the +x direction. The case which NASA Almond is illuminated from its sharp edge, i.e., the planewave is propagating in the (θ,φ) = (π/2, 0) direction, is noted as headon illumination.
NASA Almond is also illuminated 30° from the x axis on the xy plane. In that case, the planewave is propagating in the (θ, φ) = (π/2, π/6) and polarized in the φ direction in spherical coordinates.
Numerical Results
We compute the farzone copolar electric field with its real and imaginary parts on the xy plane with the resolution of 0.1°.
Since geometries are symmetric with respect to the xz plane, if they are illuminated from the +x direction, the results will be symmetric with respect to the xz plane as well.
Therefore, for the PEC and dielectric spheres as well as the NASA Almond which is headon illuminated, the electric field is calculated at 1801 points on the xy plane from φ = 0 (backscattering direction) upto φ = π (forwardscattering direction).
But for NASA Almond which is illuminated from (θ, φ) = (π/2, π/6), the electric field is calculated at 3601 points on the xy plane from φ = 0 upto φ = 2π since the symmetry isn't exist. Specifically, we compute
where E_{φ} is the φ component of the electric field and φ[n] = (n1)π/1801 for n = 1, 2, ..., 1801 or φ[n] = (n1)π/3601 for n = 1, 2, ..., 3601) depends on the geometry.
Note that a is the radius of your sphere in meters, i.e, a = 0.3 for PEC sphere and a = 1 for dielectric sphere. If it is NASA Almond, make a = 1.
Resulting RCS values will be normalized (unitless) for PEC and dielectric spheres, but they will be in ms for NASA Almond.
Input File
The input file should be a plane text file which contains f[n] which is described above, with its real and imaginary parts.
That is, for the spheres and headonilluminated NASA Almond, and input file should contains 1801 rows and two columns, and for NASA Almond 30° illuminated, it should contains 3601 rows and two columns. Each row corresponds to a sample with its real and imaginary parts.
Error Calculation
We calculate errors by the formula given below. Note that for sphere problems, input data is compared with their corresponding analytical Mie series results; but for NASA Almond, it is compared with ABAKUS's computational MLFMA results.
According to the geometry, we display errors between some bistatic angle. Error ranges are given below.
Geometry 
error 1 (bistatic angle) 
error 2 (bistatic angle) 
error 3 (bistatic angle) 
PEC Sphere 
0°  30° 
0°  90° 
0°  180° 
NASA Almond (headon illuminated) 
0°  30° 
0°  90° 
0°  180° 
NASA Almond (30° illuminated) 
15°  45° 
0°  90° 
0°  360° 
Dielectric Sphere 
0°  30° 
0°  90° 
0°  180° 
Plotting
For spheres, we calculate RCS by the formula which is given below.
For NASA Almond, we multiply this value by π to prevent normalization.
We also plot +30° interval of backscattering and forward scattering area.
An example plot is shown below.
You can download a plot by the link below it on the result page. Sphere RCS values will be in dB (unitless) and NASA Almond RCS values will be in dBms.
Links
ExtremelyLarge Conducting Objects (Sphere & NASA Almond)
Composite Dielectric Objects (Twolayered Sphere)
Benchmark Composite Dielectric Sphere Results
ε_{r}(ε_{out}, ε_{mid}, ε_{in}), μ_{r}(μ_{out}, μ_{mid}, μ_{in})
 ε_{r}(1.0, 2.0, 3.0),
μ_{r}(1.0, 1.0, 1.0)
 ε_{r}(1.0, 2.0, 4.0),
μ_{r}(1.0, 1.0, 1.0)
 ε_{r}(1.0, 2.0, PEC),
μ_{r}(1.0, 1.0, 1.0)
 ε_{r}(1.0, 10.0, 20.0 & σ = 0.1 S/m),
μ_{r}(1.0, 1.0, 1.0)
 ε_{r}(1.0, 4.0+i0.01, 2.0+i),
μ_{r}(1.0, 1.0, 1.0)
 ε_{r}(1.0, 2.0, 10.0+i),
μ_{r}(1.0, 1.0, 1.0)

