Changes

== An EM.Illumina Primer == === EM.Illumina in a Nutshell === EM.Illumina is a 3D electromagnetic simulator for modeling large free[[Image:Splash-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 platformspo.jpg|right|720px]] EM.Illumina provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, EM.Illumina assumes that a source like a short dipole radiator or an incident plane wave induces 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 tracing from each source to the points on the scatterers to determine whether they fall into the lit or shadow regions. But this can become a time consuming task depending on the size of the computational problem. Besides GO-PO, EM.Illumina also offers 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. === Physical Optics as an Asymptotic Technique === Asymptotic methods are usually valid at high frequencies as k<substrong>0</sub> R font color= 2&pi; R/&lambda;<sub"#bd5703" size="4">0Fast Asymptotic Solver For Large-Scale Scattering Problems</subfont> >> 1, where R is the distance between the source and observation points, k<sub>0 </substrong> is the free-space propagation constant and &lambda;₀is 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.png|40px]] Click here to lean more about the '''[[Theory of Physical Optics]]'''. == Building the Physical Structure == [[Image:PO18(1).png|thumb|250px|EM.Illumina's Navigation Tree.]]=== Grouping Objects By Surface Type === EM.Illumina organizes physical objects by their surface type. Any object in EM.Illumina is assumed to be made of one of the three surface types: # Perfect Electric Conductor (PEC)# Perfect Magnetic Conductor (PMC)# Generalized Impedance Surface EM.Illumina can only handle surface and solid CAD objects. Only the outer surface of [[Solid Objects|solid objects]] is considered in the PO simulation. No line or [[Curve Objects|curve objects]] are allowed in the project workspace; or else, they will be ignored during the PO simulation. You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under a group share the same color and other properties.  A new surface group can be defined by simply right clicking on one of the three '''PEC''', '''PMC''' or '''Impedance Surface''' items in the '''Physical Structure''' section of the navigation tree and selecting '''Insert New PEC...''', '''Insert New PMC...''', or '''Insert New Impedance Surface...''' from the contextual menu. A dialog for setting up the group properties opens up. In this dialog you can change the name of the group or its color. In the case of a surface impedance group, you can set the values for the real and imaginary parts of the '''Surface Impedance''' in Ohms.  

<td> [[Imageimage:PO19Cube-icon.png|thumblink=Getting_Started_with_EM.Cube]] [[image:cad-ico.png |250pxlink=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png |The PEC dialoglink=EM.Tempo]] </td><td> [[Imageimage:PO20prop-ico.png|thumblink=EM.Terrano]] [[image:static-ico.png |250pxlink=EM.Ferma]] [[image:planar-ico.png |The PMC dialoglink=EM.Picasso]] </td><td> [[Imageimage:PO21metal-ico.png|thumb|250px|The Impedance Surface dialoglink=EM.Libera]] </td></tr>

[[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''=== Creating New Objects &amp; Moving Them Around =Product Overview==

[[Image:PO22(1).png|thumb|400px|Moving objects among different surface groups in === EM.Illumina.]]The objects that you draw in [[EM.Cube]]'s project workspace always belong to the &quot;Active&quot; surface group. By default, the last object group that you created remains active until you change it. The current active group is always listed in bold letters in the Navigation Tree. Any surface group can be made active by right clicking on its name in the Navigation Tree and selecting the '''Activate''' item of the contextual menu. If you start a new [[PO Module]] project and draw any object without having previously defined a surface group, a default PEC group is automatically created and added to the Navigation Tree to hold your new object.  You can move one or more selected objects to any material group. Right click on the highlighted selection 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 in [[PO Module]]. Select the desired surface group, and all the selected objects will move to that group. The objects can be selected either in the project workspace, or their names can be selected 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 sub-[[menus]] of the '''Move To &gt;''' item of the contextual menu will indicate all the [[EM.Cube]] modules that have valid groups for transfer of the selected objects.  {{Note|In [[EM.Cube]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only to [[CubeCAD]]. From [[CubeCAD]], you can then move the imported objects to any other computational module including [[PO Module]].}} == Discretizing the Physical Structure == === Generating &amp; Customizing PO Mesh Nutshell ===

[[File:PO4.png|thumb|300px|EM.Illumina's Mesh Settings dialog.]]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 [[File:PO5.png|thumb|300px|The Tessellation Options dialogEM.Illumina]]The mesh generation process to compute the radar cross section (RCS) of large target structures like aircraft or vehicles or simulate the radiation of antennas in [[PO Module]] involves three steps:the presence of large platforms.

# Setting [[EM.Illumina]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in turn reradiate into the mesh propertiesfree space.# Generating A challenging step in establishing the meshPO currents is the determination of the lit and shadowed points on complex scatterer geometries.# Verifying Ray tracing from each source to the meshpoints on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, [[EM.Illumina]]'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.

The objects of your physical structure are meshed based on a specified mesh density expressed in cells/&lambda;₀. The default mesh density is 20 cells/&lambda;₀. To view the PO mesh, click on the [[FileImage:mesh_tool_tnInfo_icon.png|30px]] 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 Click here to the normal view or select mode, click this button one lean more time, or deselect '''Menu &gt; Simulate &gt; Discretization &gt; Show Mesh''' to remove its check mark or simply click about the '''Esc Key''' of the keyboard. &quot;Show Mesh&quot; generates a new mesh and displays it if there is none 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 [[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 '''3-D Mesh''' item Basic Principles of the Navigation Tree and selecting '''Regenerate''' from the contextual menu. To set the PO mesh properties, click on the [[File:mesh_settings.png]] button Physical Optics | Theory 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 ModulePhysical Optics]] 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 in more pointed triangular cells.

<td> [[Image:PO2Illumina L2 Fig title.png|thumb|450pxleft|Two ellipsoids of different compositions420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoids.]] </td>

=== More On Triangular Surface Mesh === The physical optics method assumes an unbounded, open-boundary computational domain, wherein the physical structure is placed against a free space background medium. As such, only finite-extent surfaces are discretized. [[EM.Cube]]'s [[PO Module]] uses a triangular surface mesh to discretize all Illumina as the surface and [[Solid Objects|solid objects]] in the project workspace. As mentioned earlier, [[Curve Objects|curve objects]] (or wires) are not allowed in [[PO Physical Optics Module]]. In the case of solids, only the surface of the object or its faces are discretized, 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 Objects|solid objects]]. In contrast, [[Surface Objects|surface objects]] 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. [[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 [[Surface Objects|surface objects]] only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, the [[Surface Objects|surface objects]] 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 [[EM.Cube]] to reverse the direction of the normal vectors at the surface of all the cells.===

[[EM.Illumina]] is the high-frequency, asymptotic '''Physical Optics Module''' of '''As a general rule, [[EM.Cube]]'s PO mesh generator merges all the objects that belong to the same surface group using the Boolean Union operation.''' As a result, 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 generalcomprehensive, objects of the same CAD category can be &quot;unioned&quot;. For exampleintegrated, modular electromagnetic modeling environment. [[Surface Objects|surface objectsEM.Illumina]] can be merged togethershares the visual interface, 3D parametric CAD modeler, data visualization tools, and so can many more utilities and features collectively known as [[Solid ObjectsBuilding_Geometrical_Constructions_in_CubeCAD |solid objectsCubeCAD]]. 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 with all of PEC type and physically overlap[[EM.Cube]]'s other computational modules.

=== Advantages & Limitations of EM.Illumina applies the mesh density specified in the Mesh Settings dialog on a global scale to discretize all the objects in the project workspace. Although the mesh density is expressed in cells per free space wavelength similar to full-wave method of moments (MoM) solvers, you have to keep in mind that the triangular surface mesh cells in PO Modules act slightly differently. The complex-valued, vectorial, electric and magnetic surface currents, '''J''' and '''M''' are assumed to be constant on the surface of each triangular cell. On plates and flat faces or surfaces, the normal vectors to all the cells are identical. Incident plane waves or other types of relatively uniform source fields induce uniform s PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. However, a high mesh density is very important for accurate discretization of curved objects like spheres or ellipsoids. Solver ===

You can lock the mesh density of any surface group [[EM.Illumina]] provides a computationally efficient alternative to any desired value different than the global mesh densityfull-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. To do soFor simple scatterer geometries, open the property dialog of a surface group by right clicking on its name in the Navigation Tree and select '''Properties..[[EM.Illumina]]''' from the contextual menus GO-PO solver is fairly adequate. At the bottom of the dialogBut for complex geometries that involve multiple shadowing effects, check the box labeled '''Lock Mesh'''IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This will enable the '''Density '''boxis not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can set satisfy the boundary conditions on one side of a desired valuesurface only. The default value is equal to PO analysis cannot handle the global mesh densityfields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

<td> [[Image:PO6PO Ship Pattern.png|thumb|450pxleft|Two overlapping PEC spheres.]] </td><td> [[Image:PO7.png|thumb|450px550px|Trinagular surface mesh Computed radiation pattern of the two spheresa short dipole radiator over a large metallic battleship.]] </td>

== Excitation Sources EM.Illumina Features at a Glance ==

=== Hertzian Dipole Sources Structure Definition ===

* Right click on the '''<ul> <li> Short Dipoles''' item in the '''Sources''' section dipoles</li> <li> Import previously generated wire mesh solution as collection of the Navigation Tree short dipoles</li> <li> Plane wave excitation with linear and select '''Insert New Source...''' from the contextual menu. The Short Dipole dialog opens up.circular polarizations</li> <li>* In the '''Source Location''' section of the dialog, you can set the coordinate of the center of the short dipole. By default, the source is placed at the origin of the world coordinate system at Multi-ray excitation capability (0,0,0)ray data imported from [[EM. You can type in new coordinates Terrano]] or use the spin buttons to move the dipole around.external files)</li>* In the '''Source Properties''' section, you can specify the '''Amplitude''' in Volts, the '''Phase''' in degrees as well as the '''Length''' of the dipole in project units. <li>* In the '''Direction Unit Vector''' section, you can specify the orientation of the short dipole by setting values for the components '''uX''', '''uY''', Huygens sources imported from PO or other modules with arbitrary rotation and '''uZ''' of the dipole's unit vector. The default values correspond to a vertical (Z-directed) short dipole. The dialog normalizes the vector components upon closure even if your component values do not satisfy a unit magnitude.array configuration</li></ul>

=== Importing Short Dipoles From MoM3D Module Mesh Generation ===

The solution <ul> <li> Surface triangular mesh with control over tessellation parameters</li> <li> Local mesh editing of a problem in one of [[EM.Cube]]'s computational modules can serve as the excitation source for another problem in another computational module. An example of this is analyzing a wire antenna in the [[MoM3D Module]] and importing the wire current solution to [[PO Module]] to excite a large scatterer. Remember that you cannot define wires or [[Curve Objects|curve polymesh objects]] in [[PO Module]]. However, you can have short dipole sources that act like differential wire elements carrying fixed currents. Using this concept, you can realize a complex wire antenna or radiator array as the source of your PO project. </li></ul>

[[File:PO29== Building the Physical Structure in EM.png|thumb|300px|PO Module's Plane Wave dialog]]Illumina ==

Your physical structure === The Variety of Surface Types in [[PO Module]] can be excited by an incident plane wave. In particular, a plane wave source can be used to compute the radar cross section of a target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. [[EM.Cube]]'s [[PO Module]] provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz.Illumina ===

The direction of incidence is defined through the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system[[EM.Illumina]] organizes physical objects by their surface type. The values of these angles are set Any object in degrees in the boxes labeled '''Theta''' and '''Phi'''[[EM. 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 Illumina]] is assumed to the XY plane, respectively. The components be made of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case one 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 satisfiedthree surface types: '''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 is generated. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (&theta; = 180°).

To define a plane wave source follow these steps{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]| style="width:300px;" | Modeling perfect metal surfaces| style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (PMC) |Perfect Magnetic Conductor (PMC) Surface]]| style="width:300px;" | Modeling perfect magnetic surfaces| style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:voxel_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impedance Surface |Impedance/Dielectric Surface]]| style="width:300px;" | Modeling impedance surfaces as an equivalent to the surface of dielectric objects | style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:250px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:250px;" | All types of objects|}

* 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 up.* In the Field Definition section of the dialogs Materials, you can enter the '''Amplitude''' of the incident electric field in V/m and its '''Phase''' in degrees. The default field Amplitude is 1 V/m with a zero Phase.* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlier. When the '''Custom Linear''' option is selectedSources, you also need to enter the X, Y, Z components of the '''E-Field Vector'''Devices & Other Physical Object Types]].

At the end of a full-wave simulation in the [[EM.Cube]]'s FDTDYou can define several PEC, MoM3D, Planar PMC or Physical Optics Modules, you can generate Huygens impedance surface datagroups with different colors and impedance values. According to Huygens' principle, if one knows All the tangential electric objects created and magnetic field components on drawn under a closed surface, one can determine group share the total electric same color and magnetic fields everywhere inside and outside that closed surfaceother properties. Huygens surfaces are defined around Once a structure for recording new surface node has been created on the tangential components of electric and magnetic fields at navigation tree, it becomes the end of full-wave simulation "Active" surface group of the structureproject workspace, which is always listed in bold letters. The tangential electric and magnetic fields are saved into ASCII data files When you draw a new CAD object such as magnetic and electric currentsa Box or a Sphere, respectivelyit is inserted under the currently active surface type. These current There is only one surface group that is active at any time. Any surface type can be used as excitation for other structuresmade active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. In other wordsIt is recommended that you first create surface groups, and then draw new objects under the electric active surface group. However, if you start a new EM.Illumina project from scratch, and magnetic currents associated with start drawing a Huygens source radiate energy new object without having previously defined any surface groups, a new default PEC surface group is created and provide added to the excitation for the [[PO Module]]'s physical structurenavigation tree to hold your new CAD object.

In order [[Image:Info_icon.png|30px]] Click here to define a Huygens source, you need to have a Huygens data file of learn more about '''.HUY[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]''' type. This file is generated as an output data file at the end of an FDTD, MoM3D, Planar or PO simulation, if you have defined a Huygens Surface observable in one of those projects. When you define a Huygens source, you indeed import an existing Huygens surface into the project and set it as an excitation source.

To create a new Huygens source{{Note|In [[EM.Cube]], follow these steps:you can import external CAD models (such as STEP, IGES, STL models, etc.) only to CubeCAD. From CubeCAD, you can then move the imported objects to EM.Illumina.}}

* 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 upFile:PO MAN1. The file type is set to '''png|thumb|left|480px|EM.HUYIllumina''' by default. Browse your folders to find a Huygens surface data file with a '''.HUY''' file extension. Select the file and click the '''Open''' button of the dialog to import the datas navigation tree.]] </td>* Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.</tr>* You can open the property dialog of a Huygens source by right clicking on 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 box.* 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.</table>

[[File:PO34== EM.png|400px]] [[File:PO35.png|400px]]Illumina's Excitation Sources ==

Figure: (Left) A rotated imported Huygens source, and (Right) An array [[EM.Illumina]] provides three types of imported Huygens sources defined to excite a PEC box.for the excitation of your physical optics simulation:

{| class="wikitable"|-! scope= Running PO Simulations "col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.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.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, Sources, 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|}

To open A short Hertzian dipole is the simplest way of exciting a structure in [[PO ModuleEM.Illumina]]'s Simulation Run . 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 its property dialog, click the '''Run''' . Your physical structure in [[File:run_iconEM.pngIllumina]] button 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 '''Simulate Toolbar''' or select '''Menu &gttheta; Simulate and &gtphi; Run...'''or use the keyboard shortcut '''Ctrl+R'''. To start the simulation click the '''Run''' button angles of this dialog. Once the PO simulation starts, a new dialog called '''Output Window''' opens up that reports unit propagation vector in the various stages spherical coordinate system. The default values of PO simulation, displays the running time incidence angles are &theta; = 180° and shows &phi; = 0° corresponding to a normally incident plane wave propagating along the percentage of completion for certain tasks during the PO simulation process-Z direction with a +X-polarized E-vector. A prompt announces Huygens sources are virtual equivalent sources that capture the completion of the PO simulation. At this time, radiated electric and magnetic fields from another structure that was previously analyzed in another [[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 sourcecomputational module.

[[File:PO27== EM.png]]Illumina's Simulation Data & Observables ==

Figure 1: [[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO Modulesimulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]]'s Simulation Run dialogcan compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[PO ModuleFile:currdistr_icon.png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type'''Observables & Graph Types#Current Distribution |Current Distribution]]| style="width: '''Iterative''' 300px;" | Computing electric surface current distribution on PEC and '''GOPO'''impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. The default option is Iterativepng]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM. The GOPO solver is a zeroCube's Simulation Observables & Graph Types#Near-order PO simulator that uses Geometrical Optics (GO) to determine the lit Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and shadow cells magnetic field components on a specified plane in the structurefrequency 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 mesh. For Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the termination of the IPO solverradiation pattern and additional radiation characteristics such as directivity, there are two optionsaxial 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'''Convergence Error''' s Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and '''Maximum Number monostatic RCS of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:huyg_surf_icon.1 png]]| style="width:150px;" | Equivalent electric 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''' magnetic surface current solution data| style="width:150px;" | [[Glossary of the entire discretized structure from one iteration to the nextEM. Note that for this purpose, the magnetic currents are scaled by Cube's Simulation Observables &etaGraph Types#Huygens Surface |Huygens Surface]]| style="width:300px;₀ " | Collecting tangential field data on a box to be used later as a Huygens source in the residual error vectorother [[EM.Cube]] modules| style="width:250px;" | None|}

You can also use higher- or lower-order integration schemes for Click on each category to learn more details about it in the calculation of field integrals. [[Glossary of EM.Cube's Simulation Observables & Graph Types]]'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 '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

[[File:PO28Current distributions are visualized on the surface of PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh cells, some parts of the plots may be blocked by and hidden inside smooth and curved objects. To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.png]]

Figure 1: <table><tr><td> [[PO ModuleImage:PO38.png|thumb|390px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]]'s Simulation Engine Settings dialog.</td></tr></table>

You can run [[EM.Cube]]'s PO simulation engine {{Note|Keep in mind that since Physical Optics is an asymptotic method, the sweep mode, whereby a parameter like frequency, plane wave incident angles field sensors must be placed at adequate distances (at least one or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data files for visualization and plotting. [[EMfew wavelengths) away from the scatterers to produce acceptable results.Cube]]'s [[PO Module]] currently offers three types of sweep:}}

To run You need to define a PO sweep, open far field observable if you want to plot the '''Simulation ''''''Run Dialog''' and select one radiation patterns of the above sweep types from the '''Simulation Mode''' dropdown list of this dialogyour physical structure. If you select either frequency or angular sweep, the '''Settings''' button located next to the After a PO simulation mode dropdown list becomes enabled. If you click this buttonis finished, three 3D radiation patterns plots are displayed in the Frequency Settings Dialog or Angle Settings Dialog opens up, respectivelyproject workspace and are overlaid on your physical structure. In These are the frequency settings dialog, you can set Theta and Phi components of the start and end frequencies far-zone electric fields as well as the number of frequency samplestotal far field. The start and end frequency values are initially set based on the project'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:

# Fix mesh {{Note| The 3D radiation pattern is always displayed at the highest frequencyorigin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined.# Fix mesh at Oftentimes, this might not be the radiation center frequency.# Re-mesh at each frequencyof your physical structure.}}

You can run an angular sweep only if your project has a plane wave excitation<table><tr><td> [[Image:PO46. In this case, you have to define png|thumb|360px|3D radiation pattern of a plane wave source with the default settings. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range. The other angle remains fixed parabolic dish reflector excited by a short dipole at the value that is specified in the '''Plane Wave Dialog'''. You have to select either '''Theta''' or '''Phi''' as the '''Sweep Angle''' in the Angle Settings Dialog. You also need to set the start and end angles as well as the number of angle samplesits focal point.]] </td></tr></table>

In When your physical structure is excited by a parametric sweepplane wave source, one or more user defined [[variables]] are varied at the same time over their specified ranges. This creates a parametric space with calculated far field data indeed represent the total number of samples equal to the product of the number of samples for each variablescattered fields. The user defined [[variables]] are defined using [[EM.CubeIllumina]]can calculate two types of RCS for each structure: 's ''Bi-Static RCS'[[Variables]] Dialog'' and '''Mono-Static RCS'''. For In bi-static RCS, the structure is illuminated by a description of [[EMplane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles.Cube]] [[variables]]In mono-static RCS, please refer to the structure is illuminated by a plane wave at incidence angles &quottheta;Parametric Modeling₀ and &phi;₀, Sweep and the RCS is measured and plotted at the echo angles 180°-&amptheta; [[Optimization]]₀; and &quotphi; section ₀. It is clear that in the case of [[EM.Cube]] Manual or see mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &quottheta;Parametric Sweepand &quotphi; sections of are varied over the FDTD or entire intervals [0°, 180°] and [Planar Module0°, 360°]] manuals, respectively, and the backscatter RCS is recorded.

[[File:po_phys52To calculate RCS, first you have to define an RCS observable instead of a radiation pattern.png]] [[File:po_phys54At 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.png]]

Figure 1: [[PO Module]]'s Frequency Settings and Angle Settings dialogs{{Note| The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined.Oftentimes, this might not be the scattering center of your physical structure.}}

=== Visualizing Current Distributions =Discretizing the Physical Structure in EM.Illumina ==

[[File:PO37EM.png|thumb|300px|PO Module's Current Distribution dialog.]][[Image:PO38.png|thumb|500px|The current distribution plot of Illumina uses a PEC sphere illuminated by an obliquely incident plane wave.]]At triangular surface mesh to discretize the end structure of a PO simulation, [[EM.Cube]]'s PO engine generates a number of output data files that contain all the computed simulation datayour project workspace. The main output data are mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the electric and magnetic current distributionsentire structure. You can easily examine control the 3D color-coded intensity plots of current distributions in cell size using the project workspace"Mesh Density" parameter. Current distributions are visualized on By default, the surface mesh density is expressed in terms of the PO free-space wavelength. The default mesh density is 10 cellsper wavelength. In the Physical Optics method, 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 DistributionsJ''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...M'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added , are assumed to be constant on the Navigation Treesurface of each triangular cell. Unlike the [[Planar Module]]On flat surfaces, in the [[PO Module]] you can define only one current distribution node in the Navigation Tree, which covers unit normal vectors to all the objects in the project workspacecells are identical. After a Incident plane waves or other relatively uniform source fields induce uniform PO simulation is completed, new plots are added under the current distribution node of the Navigation Treecurrents on all these cells. Separate plots are produced for the magnitude and phase of each of the electric and magnetic surface current components (XTherefore, Y and Z) as well as the total current magnitude. The magnitude maps are plotted a high resolution mesh may not be necessary on a normalized scale with the minimum and maximum values displayed in the legend boxflat surface or faces. The phase maps are plotted in radians between -p and p. Note that sometimes the current distribution plots may hide inside smooth and Accurate discretization of curved objects, and you cannot see them. You may have to freeze such objects like spheres or switch to the ellipsoids, however, requires a high mesh view modedensity. <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]</td></tr></table>

[[Image:PO42(4)Info_icon.png|thumb|300px|PO Module's Field Sensor dialog30px]]Click here to learn more about '''[[Image:PO43Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.png|thumb|400px|Near field plot of electric field on a sensor planeCube.]][[Image:PO44.png27s_Mesh_Generators |thumb|400px|Near field plot of magnetic field on a sensor plane.Working with Mesh Generator]][[EM.Cube]] allows you to visualize the near fields at a specific field sensor plane. Calculation of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specify'''. To define a new Field Sensor, follow these steps:

* Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable[[Image:Info_icon...'''* The '''Label''' box allows you png|30px]] Click here to change the sensor’s name. you can also change the color of the field sensor plane using the learn more about '''Color''' button.* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default [[Preparing_Physical_Structures_for_Electromagnetic_Simulation#The_Triangular_Surface_Mesh_Generator | EM.CubeIllumina's Triangular Surface Mesh Generator ]] creates a field sensor plane passing through the origin of coordinates (0,0,0) 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 '''Center Coordinates'''. 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 '''Observables''' section in the Navigation Tree<table><tr><td> [[Image:POShip1. Once png|thumb|600px|Geometry of a PO simulation is finished, metallic battleship model with 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 '''E''' and '''H''' fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of short horizontal dipole radiator above 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]] </td></tr><tr><td> [[Image:POShip2. The values png|thumb|600px|Trinagular surface mesh of the magnitude plots are normalized between 0 and 1metallic battleship model. 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 Atd></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.tr></table>

{{Note|Keep == Running PO Simulations 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 resultsEM.}}Illumina ==

=== Visualizing 3D Radiation Patterns EM.Illumina's Simulation Modes ===

Once you have set up your structure in [[File:PO45EM.png|thumb|300px|PO ModuleIllumina]], have defined sources and observables and have examined the quality of the structure's Radiation Pattern dialogmesh, you are ready to run a Physical Optics simulation. [[EM.Illumina]]offers five simulation modes:

Unlike the FDTD method, Physical Optics is an open{| class="wikitable"|-boundary technique. You do not need a far field box to perform near! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-to| style="width:120px;" | [[#Running A Single-farFrequency PO Analysis | Single-field transformationsFrequency Analysis]]| style="width:270px;" | Simulates the physical structure "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. Nonetheless, you still need to define a far field observable if you want to plot radiation patternsCube#Running_Frequency_Sweep_Simulations_in_EM. A far field can be defined by right clicking on Cube | Frequency Sweep]]| style="width:270px;" | Varies the '''Far Fields''' item in operating frequency of the '''Observables''' section PO solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of the Navigation Tree and selecting '''Insert New Radiation Pattern.frequency samples| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.''' from Cube | Parametric Sweep]]| style="width:270px;" | Varies the contextual menuvalue(s) of one or more project variables| 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. The Radiation Pattern dialog opens upCube#Performing_Optimization_in_EM. You can accept most Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the default settings in this dialogcenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The Output Settings section allows you to change Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the '''Angle Increment''' in the degrees, which sets the resolution value(s) of far field calculations. The default value is 5 degrees. After closing the radiation pattern dialog, one or more project variables to generate a far field entry immediately appears with its given name under compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the '''Far Fields''' item of the Navigation Tree.center frequency fc| style="width:80px;" | None|}

After a PO You can set the simulation mode from [[EM.Illumina]]'s "Simulation Run Dialog". A single-frequency analysis is finished, three radiation patterns plots are added to a single-run simulation. All the far field node other simulation modes in the Navigation Treeabove list are considered multi-run simulations. These If you run a simulation without having defined any observables, no data will be generated at the end of the simulation. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the far field component in &theta; directionend of a sweep simulation, you can graph the far field component simulation results in &phi; direction and EM.Grid or you can animate the total far field defines as:3D simulation data from the navigation tree.

:<math>|\mathbf{E_{ff,tot}}| = \sqrt{ |E_{\theta}|^2 + |E_{\phi}|^2 }</math><!== Running A Single--[[File:FDTD129.png]]-->Frequency PO Analysis ===

The 3D plots can be viewed by clicking on their name in the navigation tree. They are displayed in To open [[EM.CubeIllumina]]'s project workspace and are overlaid on Simulation Run dialog, click the project's structure''Run''' [[File:run_icon. The view png]] button of a 3D radiation pattern plots can be changed with the available view operations such as rotate view, pan, zoom, etc'''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Run. If ..'''or use the structure blocks keyboard shortcut {{key|Ctrl+R}}. To start the view simulation click the {{key|Run}} button of this dialog. Once the patternPO simulation starts, you can simply hide a new dialog called '''Output Window''' opens up that reports the whole structure or parts various stages of it. The fields are always normalized to PO simulation, displays the running time and shows the maximum percentage of completion for certain tasks during the total far fieldPO simulation process. A legend box appears in prompt announces the upper right corner completion of the 3D radiation plotPO simulation. At this time, which can be moved around by clicking and dragging with the left mouse button[[EM. The calculated Directivity Cube]] generates a number of output data files that contain all the radiating structure is displayed at the bottom of the legend boxcomputed simulation data. It is important to note that 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 PO structure is excited by an incident a plane wave, the radiation patterns indeed represent the far-zone scattered field datasource.

<table><tr><td> [[FileImage:PO46Illumina L1 Fig10A.png|500pxthumb|left|480px|EM.Illumina's Simulation Run dialog.]]</td></tr></table>

[[File:PO47.png|thumb|300px|PO Module's RCS dialog]] When You can also use higher- or lower-order integration schemes for the physical structure is excited by a plane wave source, the calculated far calculation of field data indeed represent the scattered fieldsintegrals. [[EM.Cube]] calculates 's PO simulation engine uses triangular cells for the radar cross section (RCS) mesh of a target, which is defined in the following mannerphysical 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 '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.

:<mathtable> \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} </mathtr><!--td> [[File:FDTD130PO28.png]]--> 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;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, [[|thumb|left|480px|EM.Cube]]Illumina's [[PO ModuleSimulation Engine Settings dialog.]] 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;<sub>0</subtd> and &phi;<sub>0</subtr>, 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;<sub>0</subtable> 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]]'''