Changes

[[Image:Splash-po.jpg|right|720px]]<strong><font color="#bd5703" size="4">Fast Asymptotic Solver For Large-Scale Scattering Problems</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link= An EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] </td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Primer Tutorial Gateway]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==

[[EM.Illumina ]] is a 3D electromagnetic simulator for modeling large free-space structures. It features a high frequency asymptotic solver based on Physical Optics (PO) for simulation of electromagnetic scattering from large metallic structures and impedance surfaces. You can use [[EM.Illumina ]] to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in the presence of large platforms.

[[EM.Illumina ]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when a full-wave analysis solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, EM.Illumina it assumes that a source like a short dipole radiator or an incident plane wave induces source generates currents on a metallic structure, which in turn reradiate into the free space. In the case of an impedance surface, both surface electric and magnetic current are induced on the surface of the scatterer. A challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries. The conventional physical optics method (GO-PO) uses geometrical optics ray Ray tracing from each source to the points on the scatterers to determine whether they fall into the are lit or shadow regions. But this can become shadowed is a time consuming task depending on the size of the computational problem. Besides GO-POTo avoid this difficulty, [[EM.Illumina also offers ]]'s simulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.

=== [[Image:Info_icon.png|30px]] Click here to lean more about the '''[[Basic Principles of Physical Optics as an Asymptotic Technique ===| Theory of Physical Optics]]'''.

Asymptotic methods are usually valid at high frequencies as k<subtable>0</subtr> R = 2&pi; R/&lambda;<subtd>0[[Image:Illumina L2 Fig title.png|thumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]]</subtd> >> 1, where R is the distance between the source and observation points, k<sub>0 </subtr> is the free-space propagation constant and &lambda;<sub>0 </subtable>is the free-space wavelength. Under such conditions, electromagnetic fields and waves start to behave more like optical fields and waves. Asymptotic methods are typically inspired by optical analysis. Two important examples of asymptotic methods are the Shoot-and-Bounce-Rays (SBR) method and Physical Optics (PO). The [[SBR Method|SBR method]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine of [[EM.Terrano]].  In the Physical Optics (PO) method, a scatterer surface is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currents. This concept is based on the fundamental equivalence theorem of electromagnetics and the Huygens principle. The electric surface currents are denoted by '''J(r)''' and the magnetic surface currents are denoted by '''M(r)''', where '''r''' is the position vector. According to the Huygens principle, the equivalent electric and magnetic surface currents are derived from the tangential components of magnetic and electric fields on a given surface, respectively. This will be discussed in more detail in the next sections. In a conventional PO analysis, which involves only perfect electric conductors, only electric surface currents related to the tangential magnetic fields are considered.

[[Image:MORE=== EM.png|40px]] Click here to lean more about Illumina as the '''[[Theory of Physical Optics]]'''Module of EM.Cube ===

== Building [[EM.Illumina]] is the high-frequency, asymptotic '''Physical Structure ==Optics Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. [[EM.Illumina]] shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

[[Image:PO18(1)EM.Illumina]]'s simulator is seamlessly interfaced with [[EM.png|thumb|250pxCube|EM.IlluminaCUBE]]'s Navigation Treeother simulattion engines.This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]]=== Grouping Objects By Surface Type ===, [[EM.Picasso]] or [[EM.Libera]].

EM[[Image:Info_icon.Illumina organizes physical objects by their surface typepng|40px]] Click here to learn more about '''[[Getting_Started_with_EM. Any object in Cube | EM.Illumina is assumed to be made of one of the three surface types:Cube Modeling Environment]]'''.

[[EM.Illumina can only handle surface and solid CAD objects]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. Only the outer surface of For simple scatterer geometries, [[Solid Objects|solid objectsEM.Illumina]] 's GO-PO solver is considered in the PO simulationfairly adequate. No line or [[Curve Objects|curve objects]] are allowed in But for complex geometries that involve multiple shadowing effects, the project workspace; or else, they will IPO solver must be ignored during the PO simulationutilized. You The IPO technique can define several PECeffectively capture dominant, PMC or impedance surface groups near-field, multiple scattering effects from electrically large targets with different colors and impedance valuesconcave surfaces. All the objects created and drawn under You have to remember that Physical Optics is a group share the same color and other propertiessurface simulator.  A new surface group can be defined by simply right clicking on one of the three '''This is not a problem for PEC''', '''PMC''' or '''Impedance Surface''' items in the '''Physical Structure''' section of the navigation tree and selecting '''Insert New PEC...''', '''Insert New PMC...'''objects, which have zero internal fields, or '''Insert New Impedance Surface...''' from the contextual menu. A dialog for setting up the group properties opens up. In this dialog even impedance surfaces, where you can change satisfy the name boundary conditions on one side of a surface only. PO analysis cannot handle the group or its colorfields inside dielectric objects. In the case of a surface impedance groupAdditionally, you can set the values for the real and imaginary parts of the '''Surface Impedance''' in Ohmsmost coupling effects between adjacent scatterers are ignored.

<td> [[Image:PO19PO Ship Pattern.png|thumb|250pxleft|The PEC dialog.]] </td><td> [[Image:PO20.png550px|thumb|250px|The PMC dialogComputed radiation pattern of a short dipole radiator over a large metallic battleship.]] </td><td> [[Image:PO21.png|thumb|250px|The Impedance Surface dialog.]] </td>

=== Creating New Objects &amp; Moving Them Around =EM.Illumina Features at a Glance ==

You can move one or more selected objects to any material group. Right click on the highlighted selection <ul> <li> Metal (PEC) solids and select '''Move To &gt; Physical Optics &gt;''' from the contextual menu. This opens another sub-menu with a list of all the available surface groups already defined surfaces in [[PO Module]]. Select the desired surface group, free space</li> <li> PMC and all the selected objects will move to that group. The objects can be selected either impedance surfaces in the project workspace, or their names can be selected free space</li> <li> Import STL CAD files as native polymesh structures</li> <li> Huygens blocks imported from the Navigation Tree. In the latter case, make sure that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting a material group's name from the contextual menu. You can also move one or more objects from a PO surface group to [[EM.Cube]]'s other modules, or vice versa. In that case, the subfull-[[menus]] of the '''Move To &gt;''' item of the contextual menu will indicate all the [[EM.Cube]] wave modules that have valid groups for transfer of the selected objects. </li></ul>

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "=== Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units. Generation ===

# Setting the mesh <ul> <li> Physical Optics solution of metal scatterers and impedance surfaces</li> <li> Conventional Geometrical Optics - Physical Optics (GOPO) solver</li> <li> Novel iterative PO solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li> <li> Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li> <li> Frequency and angular sweeps with data animation</li> <li> Parametric sweep with variable object properties.or source parameters</li> <li> Multi-variable and multi-goal optimization of structure</li> <li> Remote simulation capability</li> <li># Generating the mesh. Both Windows and Linux versions of PO simulation engine available</li># Verifying the mesh.</ul>

The objects of your physical structure are meshed based on a specified mesh density expressed in cells/=== Data Generation &lambdaamp;₀. The default mesh density is 20 cells/&lambda;₀. To view the PO mesh, click on the [[File:mesh_tool_tn.png]] button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Discretization &gt; Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the PO mesh is displayed in the project workspace, [[EM.Cube]]'s mesh view mode is enabled. In this mode, you can perform view operations like rotate view, pan, zoom, etc. However, you cannot select or move or edit objects. While the mesh view is enabled, the '''Show Mesh''' [[File:mesh_tool.png]] button remains depressed. To get back to the normal view or select mode, click this button one more time, or deselect '''Menu &gt; Simulate &gt; Discretization &gt; Show Mesh''' to remove its check mark or simply click the '''Esc Key''' of the keyboard.Visualization ===

<ul> <li> Electric and magnetic surface current distributions on metallic or impedance surfaces</li> <li> Near field intensity plots (vectorial - amplitude &quotamp;Show Mesh&quot; generates a new mesh and displays it if there is none phase)</li> <li> Huygens surface data generation for use in the memory, or it simply displays an existing mesh in the memory. This is a useful feature because generating a PO mesh may take a long time depending on the complexity and size of objects. If you change the structure or alter the mesh settings, a new mesh is always generated. You can ignore the mesh in the memory and force other [[EM.Cube]] to generate a mesh from the ground up by selecting '''Menu &gt; Simulate &gt; Discretization &gt; Regenerate Mesh''' or by right clicking on the '''3modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2-D Mesh''' item of the Navigation Tree Cartesian and polar graphs</li> <li> Bi-static and selecting '''Regenerate''' from the contextual menu.monostatic radar cross section: 3D visualization and 2D graphs</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

To set == Building the PO mesh properties, click on the [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Discretization &gt; Mesh Settings... '''or right click on the '''3-D Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the value of '''Mesh Density''' to generate a triangular mesh with a higher or lower resolutions. [[PO Module]] offers two algorithms for triangular mesh generation. The default algorithm is '''Regular Surface Mesh''', which creates triangular elements that have almost equal edge lengths. The other algorithm is '''Structured Surface Mesh''', which usually creates a very structured mesh with a large number of aligned triangular elements. You can change the mesh generation algorithm from the dropdown list labeled '''Mesh Type'''. Another parameter that can affect the shape of the mesh especially in the case of [[Solid Objects|solid objects]] is the '''Curvature Angle Tolerance''' expressed in degrees. This parameter determines the apex angle of the triangular cells of the structured mesh. Lower values of the angle tolerance will results Physical Structure in more pointed triangular cellsEM.Illumina ==

<table><tr><td> [[Image:PO2.png|thumb|450px|Two ellipsoids of different compositions.]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh === The Variety of the two ellipsoidsSurface Types in EM.]] </td></tr></table>Illumina ===

The physical optics method assumes an unbounded, open{| class="wikitable"|-boundary computational domain, wherein the physical structure is placed against a free space background medium. As such, only finite! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-extent surfaces are discretized| style="width:30px;" | [[File:pec_group_icon. png]]| style="width:250px;" | [[Glossary of EM.Cube]]'s [[PO ModuleMaterials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]] uses a triangular | style="width:300px;" | Modeling perfect metal surfaces| style="width:250px;" | Solid and surface mesh to discretize all the surface and objects|-| style="width:30px;" | [[Solid Objects|solid objectsFile:pmc_group_icon.png]] in the project workspace. As mentioned earlier, [[Curve Objects| style="width:250px;" |curve objects]] (or wires) are not allowed in [[PO Module]]Glossary of EM. In the case of solidsCube's Materials, only the surface of the object or its faces are discretizedSources, as the interior volume is not taken into account in a PO analysis. In general, triangular cells are placed on the exterior surface of [[Solid ObjectsDevices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |solid objectsPerfect Magnetic Conductor (PMC) Surface]]. In contrast, [[Surface Objects|style="width:300px;" | Modeling perfect magnetic surfaces| style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:voxel_group_icon.png]] are assumed to be double-sided by default. The means that the PO mesh of a surface object indeed consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. | style="width:250px;" | [[Glossary of EM.Cube]]'s PO mesh has some more settings that allow you to treat all mesh cells as double-sided or all single-sided. This can be done in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented [[Materials, Sources, Devices & Other Physical Object Types#Impedance Surface Objects|surface objectsImpedance/Dielectric Surface]] only. In the single-sided case, it is very important that all the normals | style="width:300px;" | Modeling impedance surfaces as an equivalent to the cells point towards the source. Otherwise, the [[Surface Objectssurface of dielectric objects |style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:Virt_group_icon.png]] will be assumed to lie in the shadow region and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct | style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]] to reverse the direction | style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of the normal vectors at the surface of all the cells.objects|}

'''As a general rule, Click on each category to learn more details about it in the [[Glossary of EM.Cube]]'s PO mesh generator merges all the objects that belong to the same surface group using the Boolean Union operation.''' As a resultMaterials, overlapping objects are transformed into a single consolidated object. This is particularly important for generating a contiguous and consistent mesh in the transition and junction areas between connected objects. In generalSources, objects of the same CAD category can be Devices &quot;unioned&quot;. For example, [[Surface Objects|surface objectsOther Physical Object Types]] can be merged together, and so can [[Solid Objects|solid objects]]. However, a surface object and a solid in general do not merge. Objects that belong to different groups on the Navigation Tree are not merged during mesh generation even if they are all of PEC type and physically overlap.

=== Mesh Density &amp; Local Mesh Control Organizing Geometric Objects by Surface Type ===

EMYou can define several PEC, PMC or impedance surface groups with different colors and impedance values.Illumina applies All the mesh density specified in objects created and drawn under a group share the Mesh Settings dialog on same color and other properties. Once a global scale to discretize all new surface node has been created on the objects in navigation tree, it becomes the "Active" surface group of the project workspace. Although the mesh density , which is expressed always listed in cells per free space wavelength similar to full-wave method of moments (MoM) solvers, bold letters. When you have to keep in mind that draw a new CAD object such as a Box or a Sphere, it is inserted under the triangular currently active surface mesh cells in PO Modules act slightly differentlytype. The complex-valued, vectorial, electric and magnetic There is only one surface currents, '''J''' group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''MActivate''' are assumed to be constant on the surface item of each triangular cellthe contextual menu. On plates and flat faces or surfacesIt is recommended that you first create surface groups, and then draw new objects under the normal vectors to all the cells are identicalactive surface group. Incident plane waves or other types of relatively uniform source fields induce uniform PO currents on all these cellsHowever, if you start a new EM. ThereforeIllumina project from scratch, and start drawing a high resolution mesh may not be necessary on flat new object without having previously defined any surface or faces. Howevergroups, a high mesh density new default PEC surface group is very important for accurate discretization of curved objects like spheres or ellipsoidscreated and added to the navigation tree to hold your new CAD object.

You can lock the mesh density of any surface group [[Image:Info_icon.png|30px]] Click here to any desired value different than the global mesh density. To do so, open the property dialog of a surface group by right clicking on its name in the Navigation Tree and select learn more about '''Properties...[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]''' from the contextual menu. At the bottom of the dialog, check the box labeled '''Lock Mesh''' {{Note|In [[EM. This will enable the '''Density '''boxCube]], where you can set a desired valueimport external CAD models (such as STEP, IGES, STL models, etc. The default value is equal ) only to CubeCAD. From CubeCAD, you can then move the global mesh densityimported objects to EM.Illumina.}}

<td> [[ImageFile:PO6PO MAN1.png|thumb|450pxleft|Two overlapping PEC spheres480px|EM.]] </td><td> [[Image:PO7.png|thumb|450px|Trinagular surface mesh of the two spheresIllumina's navigation tree.]] </td>

== EM.Illumina's Excitation Sources ==

A short Hertzian dipole is the simplest way {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of exciting a structure in EM.Illumina. A short dipole source acts like an infinitesimally small ideal current Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon. To define a short dipole png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, follow these stepsSources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

* Right click Click on the '''Short Dipoles''' item each category to learn more details about it in the '''Sources''' section [[Glossary of the Navigation Tree and select '''Insert New Source..EM.Cube''' from the contextual menu. The Short Dipole dialog opens up.* In the '''Source Location''' section of the dialogs Materials, you can set the coordinate of the center of the short dipole. By defaultSources, the source is placed at the origin of the world coordinate system at (0,0,0). * * In the '''Source Properties''' section, you can specify the '''Amplitude''' in Amp, the '''Phase''' in degrees as well as the '''Length''' of the dipole in project units.* In the '''Direction Unit Vector''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipoleDevices & Other Physical Object Types]].

A short Hertzian dipole is the simplest way of exciting a structure in [[EM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated and displayed in Watts in the its property dialog. Your physical structure in [[EM.Illumina]] can also be excited by an incident plane wave. In particular, you need a plane wave source to compute the radar cross section of a target. The direction of incidence is defined by the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system. The default values of the incidence angles are &theta; = 180° and &phi; = 0° corresponding to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure that was previously analyzed in another [[EM.Cube]] computational module.

=== Plane Wave Sources =EM.Illumina's Simulation Data & Observables ==

Your physical structure in [[EM.Illumina can be excited by an incident plane wave]] does not produce any output data on its own unless you define one or more observables for your simulation project. In particular, a plane wave source is needed to compute The primary output data in the radar cross section Physical Optics method are the electric and magnetic surface current distributions on the surface of a targetyour structure. A plane wave is defined by its propagation vector indicating At the direction end of incidence and its polarization. a PO simulation, [[EM.Illumina provides ]] generates a number of output data files that contain all the computed simulation data. Once the following polarization options: TMzcurrent distributions are known, TEz, Custom Linear, LCPz [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and RCPzradar cross section (RCS).

The direction of incidence is defined through the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system[[EM. The values of these angles are set in degrees in Illumina]] currently provides the boxes labeled '''Theta''' and '''Phi'''. The default values are &theta; = 180° and &phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM_z and TE_z polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfiedfollowing observables: '''ê . ê''' = 1 and '''ê × k''' = 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message pops up. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to the normal incidence only (&theta; = 180°).

To define {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source follow these steps|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}

* Right click Click on the '''Plane Waves''' item each category to learn more details about it in the '''Sources''' section [[Glossary of the Navigation Tree and select '''Insert New Source..EM.Cube''' The Plane wave Dialog opens ups Simulation Observables & Graph Types]].* In Current distributions are visualized on the Field Definition section surface of the dialogPO mesh cells, you can enter and the '''Amplitude''' magnitude and phase of the incident electric field in V/m and its '''Phase''' magnetic surface currents are plotted for all the objects. A single current distribution node in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by navigation tree holds the incident '''Theta''' and '''Phi''' angles current distribution data for all the objects in degreesthe project workspace. You can also set Since the '''Polarization''' currents are plotted on the surface of the plane wave and choose from individual mesh cells, some parts of the five options described earlierplots may be blocked by and hidden inside smooth and curved objects. * If the '''Custom Linear''' option is selectedTo be able to view those parts, you also need may have to enter freeze the X, Y, Z components of obstructing objects or switch to the '''E-Field Vector'''mesh view mode.

<td> [[FileImage:PO30PO38.png|thumb|360px390px|PO Module's Short Dipole Source dialog]] </td><td> [[File:PO29The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.png|thumb|420px|PO Module's Plane Wave dialog]] </td>

[[File:po_phys17{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.png|thumb|300px|PO Module's Huygens Source dialog]]}}

At the end of a full-wave simulation in the <table><tr><td> </td><td> [[EMImage:PO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.Cube]]'s FDTD, MoM3D, Planar or Physical Optics Modules, you can generate Huygens surface data</td><td> [[Image:PO44. According to Huygens' principle, if one knows the tangential electric and magnetic png|thumb|360px|Magnetic field components distribution on a closed surface, one can determine the total electric and magnetic fields everywhere inside and outside that closed surface. Huygens surfaces are defined around sensor plane above a structure for recording the tangential components of electric and magnetic fields at the end of full-wave simulation of the structuremetallic sphere. The tangential electric and magnetic fields are saved into ASCII data files as magnetic and electric currents, respectively. These current can be used as excitation for other structures. In other words, the electric and magnetic currents associated with a Huygens source radiate energy and provide the excitation for the [[PO Module]]'s physical structure.</td></tr></table>

In order You need to define a Huygens source, far field observable if you need want to have a Huygens data file plot the radiation patterns of '''your physical structure.HUY''' type. This file is generated as an output data file at the end of an FDTD, MoM3D, Planar or After a PO simulationis finished, if you have defined a Huygens Surface observable three 3D radiation patterns plots are displayed in one of those projects. When you define a Huygens source, you indeed import an existing Huygens surface into the project workspace and set it are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as an excitation sourcewell as the total far field.

To create a new Huygens source{{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, follow these steps:(0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

* Right click on the '''Huygens Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Import Huygens Source...''' from the contextual menu.<table><tr>* The standard <td> [[Windows]] Open Dialog opens up. The file type is set to '''.HUY''' by default. Browse your folders to find a Huygens surface data file with a '''.HUY''' file extensionImage:PO46. Select the file and click the '''Open''' button png|thumb|360px|3D radiation pattern of the dialog to import the data.* Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.* You can open the property dialog of parabolic dish reflector excited by a Huygens source by right clicking on short dipole at its name in the Navigation Tree and selecting '''Properties...''' From this dialog you can change the color of the Huygens source box as well as its location and orientation. You can enter new values for the X, Y, Z '''Center Coordinates''' and '''Rotation Angles''' of the Huygens box. You can also view the dimensions of the boxfocal point.]] </td>* By default, the Huygens data are imported as a single Huygens source. You can create an arbitrary array of Huygens sources for your PO project. To do so, in the &quot;Create Array&quot; section of the Huygens source dialog, enter desired values for the '''Number of Elements''' and '''Element Spacing''' along the X, Y and Z directions. You will see an array of wire-frame box appear in the project workspace.</tr></table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[File:PO34EM.png|400pxIllumina]] [[Filecan calculate two types of RCS for each structure:PO35'''Bi-Static RCS''' and '''Mono-Static RCS'''.png|400pxIn bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta; and &phi; are varied over the entire intervals [0°, 180°]and [0°, 360°], respectively, and the backscatter RCS is recorded.

Figure: (Left) A rotated imported Huygens sourceTo calculate RCS, and (Right) An array of imported Huygens sources defined first you have to excite define an RCS observable instead of a PEC boxradiation pattern. At the end of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

[[File:PO27.png|thumb|400px|== Discretizing the Physical Structure in EM.Illumina's Simulation Run dialog.]]To open EM.Illumina's Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Run...'''or use the keyboard shortcut '''Ctrl+R'''. To start the simulation click the '''Run''' button of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, displays the running time and shows the percentage of completion for certain tasks during the PO simulation process. A prompt announces the completion of the PO simulation. At this time, [[EM.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by a plane wave source.==

=== Setting EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The Numerical Parameters ===mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]</td></tr></table>

[[File:PO28.png|thumb|350px|Since EM.Illumina's Simulation Engine Settings dialog.]]Before you run is a PO simulationsurface simulator, you can change some only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO simulation engine settingsanalysis. While in By contrast, surface CAD objects are assumed to be double-sided. In other words, the [[default PO Module]]'s '''Simulation Run Dialog'''mesh of a surface object consists of coinciding double cells, click one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina'''Settings''' button next s mesh generator has settings that allow you to the '''Select Engine''' dropdown listtreat all mesh cells as double-sided or all single-sided. In You can do that in the Physical Optics Engine Mesh Settings Dialog, there are two options for dialog by checking the boxes labeled '''Solver Type''': '''IterativeAll Double-Sided Cells''' and '''GOPOAll Single-Sided Cells'''. The default option This is Iterativeuseful when your project workspace contains well-organized and well-oriented surface CAD objects only. The GOPO solver is a zeroIn the single-order PO simulator sided case, it is very important that uses Geometrical Optics (GO) all the normals to determine the lit and shadow cells in point towards the structure's meshsource. For Otherwise, your surfaces fall in the termination of the IPO solvershadow region, there are two options: '''Convergence Error''' and no currents will be computed on them. By checking the box labeled '''Maximum Number of IterationsReverse Normal'''. The default Termination Criterion is based on convergence error, which has a default value of 0you instruct EM.1 and can be changed Illumina to any desired accuracy. The convergence error is defined as reverse the L2 norm direction of the normalized residual error in normal vectors globally at the combined '''J/M''' current solution surface of all the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by &eta;₀ in the residual error vectorcells.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EMImage:Info_icon.Cubepng|30px]]'s PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''ConstantClick here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''ConstantCube.27s_Mesh_Generators | Working with Mesh Generator]]'''.

<table><tr><td> [[Image:po_phys52POShip1.png|thumb|300px600px|EM.Illumina's Frequency Settings dialogGeometry of a metallic battleship model with a short horizontal dipole radiator above it.]]</td>You can run </tr><tr><td> [[EMImage:POShip2.Cube]]'s PO simulation engine in png|thumb|600px|Trinagular surface mesh of the sweep mode, whereby a parameter like frequency, plane wave incident angles or a user defined variable is varied over a specified range at predetermined samplesmetallic battleship model. The output data are saved into data files for visualization and plotting. [[EM.Cube]]'s [[PO Module]] currently offers three types of sweep:</td></tr></table>

To run a PO sweep, open the '''Simulation ''''''Run Dialog''' and select one of the above sweep types from the '''Simulation Mode''' dropdown list of this dialog=== EM. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode dropdown list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the projectIllumina's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:Simulation Modes ===

# Fix mesh at Once you have set up your structure in [[EM.Illumina]], have defined sources and observables and have examined the highest frequency.# Fix quality of the structure's mesh at the center frequency, you are ready to run a Physical Optics simulation.# Re-mesh at each frequency[[EM.Illumina]] offers five simulation modes:

You can {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the physical structure "As Is"| style="width:80px;" | Single run an angular sweep only if your project has a plane wave excitation. In this case, you have to define a plane wave source with | style="width:250px;" | Runs at the default settingscenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. During an angular sweep, either Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the incident theta angle or incident phi angle is varied within operating frequency of the PO solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified rangeset of frequency samples| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The other angle remains fixed at Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value that is specified in (s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the '''Plane Wave Dialog'''center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. You have to select either '''Theta''' Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or '''Phi''' as more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the '''center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep Angle''' in ]]| style="width:270px;" | Varies the Angle Settings Dialog. You also need value(s) of one or more project variables to set generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the start and end angles as well as the number of angle samples.center frequency fc| style="width:80px;" | None|}

In a parametric sweep, one or more user defined You can set the simulation mode from [[variablesEM.Illumina]] are varied at 's "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the same time over their specified rangesother simulation modes in the above list are considered multi-run simulations. This creates If you run a parametric space with simulation without having defined any observables, no data will be generated at the total number end of samples equal to the product of the number of samples for each variablesimulation. The user defined [[variables]] In multi-run simulation modes, certain parameters are defined using [[EM.Cube]]'s '''[[Variables]] Dialog'''. For varied and a description collection of [[EMsimulation data files are generated.Cube]] [[variables]]At the end of a sweep simulation, please refer to you can graph the &quot;Parametric Modeling, Sweep &amp; [[Optimization]]&quot; section of [[simulation results in EM.Cube]] Manual Grid or see you can animate the &quot;Parametric Sweep&quot; sections of 3D simulation data from the FDTD or [[Planar Module]] manualsnavigation tree.

== Working with = Running A Single-Frequency PO Simualtion Data Analysis ===

[[File:PO37.png|thumb|300px|PO Module's Current Distribution dialog.]]<table><tr><td> [[Image:PO38Illumina L1 Fig10A.png|thumb|500pxleft|480px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]]At the end of a PO simulation, [[EM.Cube]]Illumina's PO engine generates a number of output data files that contain all the computed simulation data. The main output data are the electric and magnetic current distributions. You can easily examine the 3D color-coded intensity plots of current distributions in the project workspace. Current distributions are visualized on the surface of the PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order to view these currents, you must first define a current distribution observable before running the PO simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the Simulation Run dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[PO Module]] you can define only one current distribution node in the Navigation Tree, which covers all the objects in the project workspace. After a PO simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of each of the electric and magnetic surface current components (X, Y and Z) as well as the total current magnitude. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -p and p. Note that sometimes the current distribution plots may hide inside smooth and curved objects, and you cannot see them. You may have to freeze such objects or switch to the mesh view mode.</td></tr></table>

=== Near Field Visualization Setting The Numerical Parameters ===

[[Image:PO42(4).png|thumb|300px|Before you run a PO Module's Field Sensor dialog]][[Image:PO43.png|thumb|400px|Near field plot simulation, you can change some of electric field on a sensor planethe PO simulation engine settings.]][[Image:PO44.png|thumb|400px|Near field plot of magnetic field on a sensor plane.]]While in the [[EM.CubeIllumina]] allows you 's '''Simulation Run Dialog''', click the '''Settings''' button next to visualize the near fields at a specific field sensor plane'''Select Engine''' dropdown list. Calculation of near fields In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a postzero-processing process order PO simulator that uses Geometrical Optics (GO) to determine the lit and may take a considerable amount shadow cells in the structure's mesh. For the termination of time depending on the resolution that you specifyIPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. To define The default Termination Criterion is based on convergence error, which has a new Field Sensordefault value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, follow these steps:the magnetic currents are scaled by &eta;₀ in the residual error vector.

* Right click on You can also use higher- or lower-order integration schemes for the '''Field Sensors''' item in the '''Observables''' section calculation of the Navigation Tree and select '''Insert New Observable.field integrals.[[EM.Cube]]'''* The '''Label''' box allows you to change the sensor’s name. you can also change s PO simulation engine uses triangular cells for the color mesh of the field sensor plane using the '''Color''' button.* Set the '''Direction''' physical surface structures and rectangular cells for discretization of the field sensorHuygens sources and surfaces. This is specified by the normal vector For integration of the sensor plane. The available triangular cells, you have three options are : '''X7-Point Quadrature''', '''Y3-Point Quadrature''' and '''ZConstant''', with the last being the default option.* By default [[EM.Cube]] creates a field sensor plane passing through the origin For integration of coordinates (0rectangular cells,0too,0) on the XY plane. You can change the location of the sensor plane to any point by typing in new values for the X, Y and Z you have three options: '''Center Coordinates9-Point Quadrature'''. You can also change these coordinates using the spin buttons.* The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These numbers determine the resolution of near field maps. Keep in mind that large numbers of samples may result in long computation times. After closing the Field Sensor Dialog, a new field sensor item immediately appears under the '''Observables4-Point Quadrature''' section in the Navigation Tree. Once a PO simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation Tree. These include the magnitude and phase of all three components of '''EConstant''' and '''H''' fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the project workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -p and p.To display the fields properly, the structure is cut through the field sensor plane, and only part of it is shown. If the structure still blocks your view, you can simply hide or freeze it. You can change the view of the field plot with the available view operations such as rotate view, pan, zoom, etc.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}} === Visualizing 3D Radiation Patterns === [[File:PO45.png|thumb|300px|PO Module's Radiation Pattern dialog]] Unlike the FDTD method, Physical Optics is an open-boundary technique. You do not need a far field box to perform near-to-far-field transformations. Nonetheless, you still need to define a far field observable if you want to plot radiation patterns. A far field can be defined by right clicking on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and selecting '''Insert New Radiation Pattern...''' from the contextual menu. The Radiation Pattern dialog opens up. You can accept most of the default settings in this dialog. The Output Settings section allows you to change the '''Angle Increment''' in the degrees, which sets the resolution of far field calculations. The default value is 5 degrees. After closing the radiation pattern dialog, a far field entry immediately appears with its given name under the '''Far Fields''' item of the Navigation Tree. After a PO simulation is finished, three radiation patterns plots are added to the far field node in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the total far field defines as: :<mathtable>|\mathbf{E_{ff,tot}}| = \sqrt{ |E_{\theta}|^2 + |E_{\phi}|^2 }</mathtr><!--[[File:FDTD129.png]]--td> The 3D plots can be viewed by clicking on their name in the navigation tree. They are displayed in [[EM.Cube]]'s project workspace and are overlaid on the project's structure. The view of a 3D radiation pattern plots can be changed with the available view operations such as rotate view, pan, zoom, etc. If the structure blocks the view of the pattern, you can simply hide the whole structure or parts of it. The fields are always normalized to the maximum of the total far field. A legend box appears in the upper right corner of the 3D radiation plot, which can be moved around by clicking and dragging with the left mouse button. The calculated Directivity of the radiating structure is displayed at the bottom of the legend box. It is important to note that if the PO structure is excited by an incident plane wave, the radiation patterns indeed represent the far-zone scattered field data. [[File:PO46PO28.png|500px]] Figure: 3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point. === Radar Cross Section === [[File:PO47.pngthumb|thumbleft|300px480px|PO ModuleEM.Illumina's RCS Simulation Engine Settings dialog]] When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Cube]] calculates the radar cross section (RCS) of a target, which is defined in the following manner: :<math> \sigma_{\theta} = 4\pi r^2 \dfrac{ \big| \mathbf{E}_{\theta}^{scat} \big| ^2} {\big| \mathbf{E}^{inc} \big|^2}, \quad \sigma_{\phi} = 4\pi r^2 \dfrac{ \big| \mathbf{E}_{\phi}^{scat} \big| ^2} {\big| \mathbf{E}^{inc} \big|^2}, \quad \sigma = \sigma_{\theta} + \sigma_{\phi} = 4\pi r^2 \dfrac{ \big| \mathbf{E}_{tot}^{scat} \big| ^2} {\big| \mathbf{E}^{inc} \big|^2} </mathtd><!--[[File:FDTD130.png]]--/tr> Three RCS quantities are computed: the &theta; and &phi; components of the radar cross section as well as the total radar cross section, which are dented by &sigma;<sub>&theta;</subtable>, &sigma;_&phi;, and &sigma;_tot. In addition, [[EM.Cube]]'s [[PO Module]] calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta; and &phi; are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.

At the end of a PO simulation, the thee RCS plots &sigma;<subhr>&theta;</sub>, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the Navigation Tree. These plots are very similar to the three 3D radiation pattern plots. You can view them by clicking on their names in the navigation tree. The RCS values are expressed in m². For visualization purposes, the 3D plots are normalized to the maximum RCS value, which is also displayed in the legend box. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time.

[[FileImage:PO48Top_icon.png|500px30px]]'''[[EM.Illumina#Product_Overview | Back to the Top of the Page]]'''

Figure[[Image: RCS of a PEC sphere illuminated by an laterally incident plane waveTutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

<p>&nbsp;</p>[[Image:BACKBack_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''