[ Overview | lucernhammer MT | Serenity | Galaxy | Orion | Lyra | Emerald ]
[ 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.

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:

• make_sphere.c

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.

• mie.m Computes the complex-valued scattered electric far field of a perfectly conducting sphere.
• mieLayeredTerms.m Computes the coefficients for a sphere having a number homogeneous dielectric layers, with or without a conducting core
• mieScatteredField.m Computes the complex-value scattered electric far field of a sphere using the coefficients pre-computed by mieLayeredTerms.m
• examples.m Driver script with several examples demonstrating the use of the above.

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)

• sphere_0.5m_20480.facet (10242 nodes, 20480 facets)
• sphere_0.5m_81920.facet (40962 nodes, 81920 facets)
• sphere_0.5m_327680.facet (163842 nodes, 327680 facets)
• sphere_0.5m_1310720.facet (655362 nodes, 1310720 facets)

• sphere_0.55m_20480.facet (10242 nodes, 20480 facets)
• sphere_0.55m_81920.facet (40962 nodes, 81920 facets)
• sphere_0.55m_327680.facet (163842 nodes, 327680 facets)

Conducting Sphere Backscattering RCS, 10 MHz - 2.0 GHz	Conducting Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz

Conducting Sphere VV Bistatic RCS, 1.0 GHz	Conducting Sphere HH Bistatic RCS, 1.0 GHz

Conducting Sphere VV Bistatic RCS, 2.0 GHz	Conducting Sphere HH Bistatic RCS, 2.0 GHz

Conducting Sphere VV Bistatic RCS, 4.0 GHz	Conducting Sphere HH Bistatic RCS, 4.0 GHz

Conducting Sphere VV Bistatic RCS, 8.0 GHz	Conducting Sphere HH Bistatic RCS, 8.0 GHz

• Mie Series MATLAB Data Script: generate_mie_pec.m

Multi-Frequency Back/Forward-Scatter Data:

• Galaxy Input File: pec_sphere_multifreq.galaxy
• Galaxy RCS File: pec_sphere_multifreq.rcs
• Mie Backscatter RCS File: pec_sphere_multifreq_bs.rcs
• Mie Forward-Scatter RCS File: pec_sphere_multifreq_fs.rcs

1.0 GHz Bistatic Data:

• Serenity Input File: pec_sphere_1.0ghz.serenity
• Serenity RCS File: pec_sphere_1.0ghz.rcs
• Galaxy Input File: pec_sphere_1.0ghz.galaxy
• Galaxy RCS File: pec_sphere_1.0ghz.rcs
• Mie RCS File: pec_sphere_1.0ghz.rcs

2.0 GHz Bistatic Data:

• Serenity Input File: pec_sphere_2.0ghz.serenity
• Serenity RCS File: pec_sphere_2.0ghz.rcs
• Galaxy Input File: pec_sphere_2.0ghz.galaxy
• Galaxy RCS File: pec_sphere_2.0ghz.rcs
• Mie RCS File: pec_sphere_2.0ghz.rcs

4.0 GHz Bistatic Data:

• Serenity Input File: pec_sphere_4.0ghz.serenity
• Serenity RCS File: pec_sphere_4.0ghz.rcs
• Galaxy Input File: pec_sphere_4.0ghz.galaxy
• Galaxy RCS File: pec_sphere_4.0ghz.rcs
• Mie RCS File: pec_sphere_4.0ghz.rcs

8.0 GHz Bistatic Data:

• Serenity Input File: pec_sphere_8.0ghz.serenity
• Serenity RCS File: pec_sphere_8.0ghz.rcs
• Galaxy Input File: pec_sphere_8.0ghz.galaxy
• Galaxy RCS File: pec_sphere_8.0ghz.rcs
• Mie RCS File: pec_sphere_8.0ghz.rcs

Lossless Dielectric Sphere Backscattering RCS, 10 MHz - 2.0 GHz	Lossless Dielectric Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz

Lossless Dielectric Sphere VV Bistatic RCS, 1.0 GHz	Lossless Dielectric Sphere HH Bistatic RCS, 1.0 GHz

Lossless Dielectric Sphere VV Bistatic RCS, 2.0 GHz	Lossless Dielectric Sphere HH Bistatic RCS, 2.0 GHz

Lossless Dielectric Sphere VV Bistatic RCS, 4.0 GHz	Lossless Dielectric Sphere HH Bistatic RCS, 4.0 GHz

Lossless Dielectric Sphere VV Bistatic RCS, 8.0 GHz	Lossless Dielectric Sphere HH Bistatic RCS, 8.0 GHz

• Mie Series MATLAB Data Script: generate_mie_lossless_dielectric.m

Materials Files:

• Materials Summary: materials.material_summary
• Interfaces Summary: dielectric_sphere.interface_summary
• Regions Summary: lossless_dielectric_sphere.region_summary

Multi-Frequency Back/Forward-Scatter Data:

• Galaxy Input File: lossless_dielectric_sphere_multifreq.galaxy
• Galaxy RCS File: lossless_dielectric_sphere_multifreq.rcs
• Mie Backscatter RCS File: lossless_dielectric_sphere_multifreq_bs.rcs
• Mie Forward-Scatter RCS File: lossless_dielectric_sphere_multifreq_fs.rcs

1.0 GHz Bistatic Data:

• Serenity Input File: lossless_dielectric_sphere_1.0ghz.serenity
• Serenity RCS File: lossless_dielectric_sphere_1.0ghz.rcs
• Galaxy Input File: lossless_dielectric_sphere_1.0ghz.galaxy
• Galaxy RCS File: lossless_dielectric_sphere_1.0ghz.rcs
• Mie RCS File: lossless_dielectric_sphere_1.0ghz.rcs

2.0 GHz Bistatic Data:

• Serenity Input File: lossless_dielectric_sphere_2.0ghz.serenity
• Serenity RCS File: lossless_dielectric_sphere_2.0ghz.rcs
• Galaxy Input File: lossless_dielectric_sphere_2.0ghz.galaxy
• Galaxy RCS File: lossless_dielectric_sphere_2.0ghz.rcs
• Mie RCS File: lossless_dielectric_sphere_2.0ghz.rcs

4.0 GHz Bistatic Data:

• Serenity Input File: lossless_dielectric_sphere_4.0ghz.serenity
• Serenity RCS File: lossless_dielectric_sphere_4.0ghz.rcs
• Galaxy Input File: lossless_dielectric_sphere_4.0ghz.galaxy
• Galaxy RCS File: lossless_dielectric_sphere_4.0ghz.rcs
• Mie RCS File: lossless_dielectric_sphere_4.0ghz.rcs

8.0 GHz Bistatic Data:

• Galaxy Input File: lossless_dielectric_sphere_8.0ghz.galaxy
• Galaxy RCS File: lossless_dielectric_sphere_8.0ghz.rcs
• Mie RCS File: lossless_dielectric_sphere_8.0ghz.rcs

Lossy Dielectric Sphere Backscattering RCS, 10 MHz - 2.0 GHz	Lossy Dielectric Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz

Lossy Dielectric Sphere VV Bistatic RCS, 1.0 GHz	Lossy Dielectric Sphere HH Bistatic RCS, 1.0 GHz

Lossy Dielectric Sphere VV Bistatic RCS, 2.0 GHz	Lossy Dielectric Sphere HH Bistatic RCS, 2.0 GHz

Lossy Dielectric Sphere VV Bistatic RCS, 4.0 GHz	Lossy Dielectric Sphere HH Bistatic RCS, 4.0 GHz

Lossy Dielectric Sphere VV Bistatic RCS, 8.0 GHz	Lossy Dielectric Sphere HH Bistatic RCS, 8.0 GHz

• Mie Series MATLAB Data Script: generate_mie_lossy_dielectric.m

Materials Files:

• Materials Summary: materials.material_summary
• Interfaces Summary: dielectric_sphere.interface_summary
• Regions Summary: lossy_dielectric_sphere.region_summary

Multi-Frequency Back/Forward-Scatter Data:

• Galaxy Input File: lossy_dielectric_sphere_multifreq.galaxy
• Galaxy RCS File: lossy_dielectric_sphere_multifreq.rcs
• Mie Backscatter RCS File: lossy_dielectric_sphere_multifreq_bs.rcs
• Mie Forward-Scatter RCS File: lossy_dielectric_sphere_multifreq_fs.rcs

1.0 GHz Bistatic Data:

• Serenity Input File: lossy_dielectric_sphere_1.0ghz.serenity
• Serenity RCS File: lossy_dielectric_sphere_1.0ghz.rcs
• Galaxy Input File: lossy_dielectric_sphere_1.0ghz.galaxy
• Galaxy RCS File: lossy_dielectric_sphere_1.0ghz.rcs
• Mie RCS File: lossy_dielectric_sphere_1.0ghz.rcs

2.0 GHz Bistatic Data:

• Serenity Input File: lossy_dielectric_sphere_2.0ghz.serenity
• Serenity RCS File: lossy_dielectric_sphere_2.0ghz.rcs
• Galaxy Input File: lossy_dielectric_sphere_2.0ghz.galaxy
• Galaxy RCS File: lossy_dielectric_sphere_2.0ghz.rcs
• Mie RCS File: lossy_dielectric_sphere_2.0ghz.rcs

4.0 GHz Bistatic Data:

• Serenity Input File: lossy_dielectric_sphere_4.0ghz.serenity
• Serenity RCS File: lossy_dielectric_sphere_4.0ghz.rcs
• Galaxy Input File: lossy_dielectric_sphere_4.0ghz.galaxy
• Galaxy RCS File: lossy_dielectric_sphere_4.0ghz.rcs
• Mie RCS File: lossy_dielectric_sphere_4.0ghz.rcs

8.0 GHz Bistatic Data:

• Galaxy Input File: lossy_dielectric_sphere_8.0ghz.galaxy
• Galaxy RCS File: lossy_dielectric_sphere_8.0ghz.rcs
• Mie RCS File: lossy_dielectric_sphere_8.0ghz.rcs

Lossless Coated Sphere Backscattering RCS, 10 MHz - 2.0 GHz	Lossless Coated Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz

Lossless Coated Sphere VV Bistatic RCS, 1.0 GHz	Lossless Coated Sphere HH Bistatic RCS, 1.0 GHz

Lossless Coated Sphere VV Bistatic RCS, 2.0 GHz	Lossless Coated Sphere HH Bistatic RCS, 2.0 GHz

Lossless Coated Sphere VV Bistatic RCS, 4.0 GHz	Lossless Coated Sphere HH Bistatic RCS, 4.0 GHz

Lossless Coated Sphere VV Bistatic RCS, 8.0 GHz	Lossless Coated Sphere HH Bistatic RCS, 8.0 GHz

• Mie Series MATLAB Data Script: generate_mie_lossless_coated.m

Materials Files:

• Materials Summary: materials.material_summary
• Interfaces Summary: coated_sphere.interface_summary
• Regions Summary: lossless_coated_sphere.region_summary

Multi-Frequency Back/Forward-Scatter Data:

• Galaxy Input File: lossless_coated_sphere_multifreq.galaxy
• Galaxy RCS File: lossless_coated_sphere_multifreq.rcs
• Mie Backscatter RCS File: lossless_coated_sphere_multifreq_bs.rcs
• Mie Forward-Scatter RCS File: lossless_coated_sphere_multifreq_fs.rcs

1.0 GHz Bistatic Data:

• Serenity Input File: lossless_coated_sphere_1.0ghz.serenity
• Serenity RCS File: lossless_coated_sphere_1.0ghz.rcs
• Galaxy Input File: lossless_coated_sphere_1.0ghz.galaxy
• Galaxy RCS File: lossless_coated_sphere_1.0ghz.rcs

2.0 GHz Bistatic Data:

• Serenity Input File: lossless_coated_sphere_2.0ghz.serenity
• Serenity RCS File: lossless_coated_sphere_2.0ghz.rcs
• Galaxy Input File: lossless_coated_sphere_2.0ghz.galaxy
• Galaxy RCS File: lossless_coated_sphere_2.0ghz.rcs

4.0 GHz Bistatic Data:

• Serenity Input File: lossless_coated_sphere_4.0ghz.serenity
• Serenity RCS File: lossless_coated_sphere_4.0ghz.rcs
• Galaxy Input File: lossless_coated_sphere_4.0ghz.galaxy
• Galaxy RCS File: lossless_coated_sphere_4.0ghz.rcs

8.0 GHz Bistatic Data:

• Galaxy Input File: lossless_coated_sphere_8.0ghz.galaxy
• Galaxy RCS File: lossless_coated_sphere_8.0ghz.rcs

Lossy Coated Sphere Backscattering RCS, 10 MHz - 2.0 GHz	Lossy Coated Sphere Forward-Scattering RCS, 10 MHz - 2.0 GHz

Lossy Coated Sphere VV Bistatic RCS, 1.0 GHz	Lossy Coated Sphere HH Bistatic RCS, 1.0 GHz

Lossy Coated Sphere VV Bistatic RCS, 2.0 GHz	Lossy Coated Sphere HH Bistatic RCS, 2.0 GHz

Lossy Coated Sphere VV Bistatic RCS, 4.0 GHz	Lossy Coated Sphere HH Bistatic RCS, 4.0 GHz

Lossy Coated Sphere VV Bistatic RCS, 8.0 GHz	Lossy Coated Sphere HH Bistatic RCS, 8.0 GHz

• Mie Series MATLAB Data Script: generate_mie_lossy_coated.m

Materials Files:

• Materials Summary: materials.material_summary
• Interfaces Summary: coated_sphere.interface_summary
• Regions Summary: lossy_coated_sphere.region_summary

Multi-Frequency Back/Forward-Scatter Data:

• Galaxy Input File: lossy_coated_sphere_multifreq.galaxy
• Galaxy RCS File: lossy_coated_sphere_multifreq.rcs
• Mie Backscatter RCS File: lossy_coated_sphere_multifreq_bs.rcs
• Mie Forward-Scatter RCS File: lossy_coated_sphere_multifreq_fs.rcs

1.0 GHz Bistatic Data:

• Serenity Input File: lossy_coated_sphere_1.0ghz.serenity
• Serenity RCS File: lossy_coated_sphere_1.0ghz.rcs
• Galaxy Input File: lossy_coated_sphere_1.0ghz.galaxy
• Galaxy RCS File: lossy_coated_sphere_1.0ghz.rcs

2.0 GHz Bistatic Data:

• Serenity Input File: lossy_coated_sphere_2.0ghz.serenity
• Serenity RCS File: lossy_coated_sphere_2.0ghz.rcs
• Galaxy Input File: lossy_coated_sphere_2.0ghz.galaxy
• Galaxy RCS File: lossy_coated_sphere_2.0ghz.rcs

4.0 GHz Bistatic Data:

• Serenity Input File: lossy_coated_sphere_4.0ghz.serenity
• Serenity RCS File: lossy_coated_sphere_4.0ghz.rcs
• Galaxy Input File: lossy_coated_sphere_4.0ghz.galaxy
• Galaxy RCS File: lossy_coated_sphere_4.0ghz.rcs

8.0 GHz Bistatic Data:

• Galaxy Input File: lossy_coated_sphere_8.0ghz.galaxy
• Galaxy RCS File: lossy_coated_sphere_8.0ghz.rcs