[ Overview |
lucernhammer MT |
Serenity |
Galaxy |
Orion |
Lyra |
Emerald |
Sapphire ]
[ lucernhammer RCS Server |
Benchmark Data |
FAQ |
Ordering Information ]
[ Overview |
lucernhammer MT |
Serenity |
Galaxy |
Orion |
Lyra |
Emerald |
Sapphire ]
[ lucernhammer RCS Server |
Benchmark Data |
FAQ |
Ordering Information ]
Spheres
On this page are presented RCS data for a collection of conducting (PEC), fully dielectric, and composite (PEC/dielectric) spheres. The corresponding Mie series RCS, as well as MATLAB scripts for computing the Mie data, are also presented. Some of this data was seen previously in Section 7.9.1 of our book The Method of Moments in Electromagnetics, Third Edition, however only data from Galaxy was compared to the Mie series in that section.
All calculations were performed on a Dell Precision T7900 workstation running Ubuntu Linux, with dual twelve-core Intel Xeon CPUs (E5-2690 v3) at 2.6 GHz with 256 GB of RAM, and dual NVIDIA GTX 1080Ti GPUs, each with 12GB of onboard RAM. Serenity utilizes both GPUs.
Construction of Spherical Geometry Inputs
Construction of spherical boundary files for our Galaxy MoM/BoR solver is trivial; a simple MATLAB or C program can be written to output a closed half-circle with the required radius and point density. Thus, just the boundary files for each case are made availlable below.
Construction of spherical facet files for our Serenity 3D MoM solver is a bit more involved, as we require an algorithm that will produce triangles of near equilateral aspect ratio at increasing levels of density. To do so, we have written a C program that begins with a 20 sided polyhedron having equilateral triangular faces. These triangles are then recursively subdivided into more triangles, with all vertices projected to the desired radius. The results of this algorithm are illustrated below for the first 5 levels of recursion.
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| Level 1 (20 facets) | Level 2 (80 facets) | Level 3 (320 facets) | Level 4 (1280 facets) | Level 5 (5120 facets) |
This C program will output an .stl file of a sphere of radius 1, for a specified level of recursion. It is easily compiled on a Linux system, and is available below:
All facet files available below were constructed using this program, with subsequent scaling as necessary.
MATLAB Routines For the Mie Series
The analytic solution for electromagnetic scattering by conducting, dieletric and stratified (conducting/dielectric) spheres is well known and available via the Mie series. An excellent summary of the expressions for the Mie Series can be found in the following book:
G. T. Ruck, ed., Radar Cross Section Handbook. Plenum Press, 1970.
This book may be out of print, though used copies can probably be had via Amazon. These expressions are also summarized in our book The Method of Moments in Electromagnetics, Third Edition, with corrections to a few typos found in Ruck's book.
MATLAB scripts that implement these expressions for computing the far scattered field of various spheres are provided below, as well as a short driver script with several examples to illustrate how the scripts are used.
Each benchmark below will have a corresponding MATLAB script that generates the Mie series RCS for that test case. To use these, the above scripts must also be present.
Facet Files Used In Runs Below (0.5m Radius iCOAT=5)
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Conducting Sphere Backscattering RCS, 10 MHz - 2.0 GHz |
Conducting Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz |
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| Conducting Sphere VV Bistatic RCS, 1.0 GHz | Conducting Sphere HH Bistatic RCS, 1.0 GHz |
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| Conducting Sphere VV Bistatic RCS, 2.0 GHz | Conducting Sphere HH Bistatic RCS, 2.0 GHz |
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| Conducting Sphere VV Bistatic RCS, 4.0 GHz | Conducting Sphere HH Bistatic RCS, 4.0 GHz |
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| Conducting Sphere VV Bistatic RCS, 8.0 GHz | Conducting Sphere HH Bistatic RCS, 8.0 GHz |
Multi-Frequency Back/Forward-Scatter Data:
1.0 GHz Bistatic Data:
2.0 GHz Bistatic Data:
4.0 GHz Bistatic Data:
8.0 GHz Bistatic Data:
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Lossless Dielectric Sphere Backscattering RCS, 10 MHz - 2.0 GHz |
Lossless Dielectric Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz |
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| Lossless Dielectric Sphere VV Bistatic RCS, 1.0 GHz | Lossless Dielectric Sphere HH Bistatic RCS, 1.0 GHz |
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| Lossless Dielectric Sphere VV Bistatic RCS, 2.0 GHz | Lossless Dielectric Sphere HH Bistatic RCS, 2.0 GHz |
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| Lossless Dielectric Sphere VV Bistatic RCS, 4.0 GHz | Lossless Dielectric Sphere HH Bistatic RCS, 4.0 GHz |
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| Lossless Dielectric Sphere VV Bistatic RCS, 8.0 GHz | Lossless Dielectric Sphere HH Bistatic RCS, 8.0 GHz |
Materials Files:
Multi-Frequency Back/Forward-Scatter Data:
1.0 GHz Bistatic Data:
2.0 GHz Bistatic Data:
4.0 GHz Bistatic Data:
8.0 GHz Bistatic Data:
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Lossy Dielectric Sphere Backscattering RCS, 10 MHz - 2.0 GHz |
Lossy Dielectric Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz |
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| Lossy Dielectric Sphere VV Bistatic RCS, 1.0 GHz | Lossy Dielectric Sphere HH Bistatic RCS, 1.0 GHz |
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| Lossy Dielectric Sphere VV Bistatic RCS, 2.0 GHz | Lossy Dielectric Sphere HH Bistatic RCS, 2.0 GHz |
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| Lossy Dielectric Sphere VV Bistatic RCS, 4.0 GHz | Lossy Dielectric Sphere HH Bistatic RCS, 4.0 GHz |
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| Lossy Dielectric Sphere VV Bistatic RCS, 8.0 GHz | Lossy Dielectric Sphere HH Bistatic RCS, 8.0 GHz |
Materials Files:
Multi-Frequency Back/Forward-Scatter Data:
1.0 GHz Bistatic Data:
2.0 GHz Bistatic Data:
4.0 GHz Bistatic Data:
8.0 GHz Bistatic Data:
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Lossless Coated Sphere Backscattering RCS, 10 MHz - 2.0 GHz |
Lossless Coated Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz |
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| Lossless Coated Sphere VV Bistatic RCS, 1.0 GHz | Lossless Coated Sphere HH Bistatic RCS, 1.0 GHz |
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| Lossless Coated Sphere VV Bistatic RCS, 2.0 GHz | Lossless Coated Sphere HH Bistatic RCS, 2.0 GHz |
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| Lossless Coated Sphere VV Bistatic RCS, 4.0 GHz | Lossless Coated Sphere HH Bistatic RCS, 4.0 GHz |
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| Lossless Coated Sphere VV Bistatic RCS, 8.0 GHz | Lossless Coated Sphere HH Bistatic RCS, 8.0 GHz |
Materials Files:
Multi-Frequency Back/Forward-Scatter Data:
1.0 GHz Bistatic Data:
2.0 GHz Bistatic Data:
4.0 GHz Bistatic Data:
8.0 GHz Bistatic Data:
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Lossy Coated Sphere Backscattering RCS, 10 MHz - 2.0 GHz |
Lossy Coated Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz |
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| Lossy Coated Sphere VV Bistatic RCS, 1.0 GHz | Lossy Coated Sphere HH Bistatic RCS, 1.0 GHz |
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| Lossy Coated Sphere VV Bistatic RCS, 2.0 GHz | Lossy Coated Sphere HH Bistatic RCS, 2.0 GHz |
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| Lossy Coated Sphere VV Bistatic RCS, 4.0 GHz | Lossy Coated Sphere HH Bistatic RCS, 4.0 GHz |
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| Lossy Coated Sphere VV Bistatic RCS, 8.0 GHz | Lossy Coated Sphere HH Bistatic RCS, 8.0 GHz |
Materials Files:
Multi-Frequency Back/Forward-Scatter Data:
1.0 GHz Bistatic Data:
2.0 GHz Bistatic Data:
4.0 GHz Bistatic Data:
8.0 GHz Bistatic Data: