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 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 k₀ R = 2&pi; R/&lambda;₀ >> 1, where R is the distance between the source and observation points, k₀ 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]] provides a computationally efficient alternative for extremely large structures when a full-wave solution becomes prohibitively expensive. Any object Based on a high frequency asymptotic physical optics formulation, it assumes that an incident source generates currents on a metallic structure, which in EMturn reradiate into the free space.Illumina A challenging step in establishing the PO currents is assumed to be made of one the determination of the three surface types:lit and shadowed points on complex scatterer geometries. Ray tracing from each source to the points 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.

# 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 simulationImage:Info_icon. No line or [[Curve Objectspng|curve objects30px]] 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 Click here to lean more about the '''[[Basic Principles of Physical Structure''' section Optics | Theory 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 ImpedancePhysical Optics]]''' in Ohms.

<td> [[Image:PO19Illumina L2 Fig title.png|thumb|250pxleft|The PEC dialog.]] </td><td> [[Image:PO20.png420px|thumb|250px|The PMC dialogAnalyzing scattering from a trihedral corner reflector using IPO solver.]] </td><td> [[Image:PO21.png|thumb|250px|The Impedance Surface dialog.]] </td>

=== Creating New Objects &amp; Moving Them Around EM.Illumina as the Physical Optics Module of EM.Cube ===

[[Image:PO22(1).png|thumb|400px|Moving objects among different surface groups in EM.Illumina.]]The objects that you draw in is the high-frequency, asymptotic '''Physical Optics Module''' of '''[[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 ita comprehensive, integrated, modular electromagnetic modeling environment. The current active group is always listed in bold letters in the Navigation Tree[[EM. Any surface group can be made active by right clicking on its name in Illumina]] shares the Navigation Tree visual interface, 3D parametric CAD modeler, data visualization tools, and selecting the '''Activate''' item many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of the contextual menu. If you start a new [[PO ModuleEM.Cube]] 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's other computational modules.

You can move one or more selected objects to any material group[[EM. Right click on the highlighted selection and select Illumina]]'''Move To &gt; Physical Optics &gt;''' from the contextual menu. This opens another sub-menu s simulator is seamlessly interfaced with a list of all the available surface groups already defined in [[PO ModuleEM.Cube|EM.CUBE]]'s other simulattion engines. Select This module is the desired surface group, and all the selected objects will move ideal place to that groupdefine Huygens sources. 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 These are based on Huygens surface data that you hold the keyboard's '''Shift Key''' or '''Ctrl Key''' down while selecting are generated using a material group's name from the contextual menu. You can also move one or more objects from a PO surface group to full-wave simulator like [[EM.CubeTempo]]'s other modules, or vice versa. In that case, the sub-[[menusEM.Picasso]] of the '''Move To &gt;''' item of the contextual menu will indicate all the or [[EM.CubeLibera]] modules that have valid groups for transfer of the selected objects.

{{Note|In [[EMImage:Info_icon.Cubepng|40px]], you can import external CAD models (such as STEP, IGES, STL models, etc.) only Click here to learn more about '''[[CubeCAD]]Getting_Started_with_EM. From [[CubeCAD]], you can then move the imported objects to any other computational module including [[PO ModuleCube | EM.Cube Modeling Environment]]'''.}}

== Discretizing the Physical Structure = Advantages & Limitations of EM.Illumina's PO Solver ===

[[EM.Illumina uses ]] provides a triangular surface mesh computationally efficient alternative 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 freefull-space wavelengthwave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. The default mesh density is 10 cells per wavelength. AlternativelyFor simple scatterer geometries, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units.  === Generating &amp; Customizing PO Mesh === [[File:PO4.png|thumb|300px|EM.Illumina]]'s Mesh Settings dialog.]][[File:PO5.png|thumb|300px|The Tessellation Options dialog.]]The mesh generation process in [[GO-PO Module]] involves three steps: # Setting the mesh properties.# Generating the mesh.# Verifying the mesh. The objects of your physical structure are meshed based on a specified mesh density expressed in cells/&lambda;₀. The default mesh density solver is 20 cells/&lambda;₀fairly adequate. To view the PO meshBut for complex geometries that involve multiple shadowing effects, click on the [[File:mesh_tool_tnIPO solver must be utilized.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 The IPO technique can perform view operations like rotate vieweffectively capture dominant, pannear-field, zoom, etcmultiple scattering effects from electrically large targets with concave surfaces. However, you cannot select or move or edit objects. While the mesh view You have to remember that Physical Optics 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. &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 memorysurface simulator. This is not a useful feature because generating a PO mesh may take a long time depending on the complexity problem for PEC and size of PMC 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 of the Navigation Tree and selecting '''Regenerate''' from the contextual menu. To set the PO mesh propertieswhich have zero internal fields, 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 menueven impedance surfaces, or use the keyboard shortcut '''Ctrl+G'''. You where you can change satisfy the value boundary conditions on one side of '''Mesh Density''' to generate a triangular mesh with a higher or lower resolutionssurface only. [[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 analysis cannot handle 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 fields inside dielectric 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 cellsAdditionally, most coupling effects between adjacent scatterers are ignored.

<td> [[Image:PO2PO Ship Pattern.png|thumb|450pxleft|Two ellipsoids 550px|Computed radiation pattern of different compositionsa short dipole radiator over a large metallic battleship.]] </td><td> [[Image:PO3.png|thumb|450px|Trinagular surface mesh of the two ellipsoids.]] </td>

=== More On Triangular Surface Mesh =EM.Illumina Features at a Glance ==

'''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 <ul> <li> Metal (PEC) solids and consistent mesh surfaces in the transition free space</li> <li> PMC and junction areas between connected objects. In general, objects of the same impedance surfaces in free space</li> <li> Import STL CAD category can be &quot;unioned&quot;. For example, [[Surface Objects|surface objects]] 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.files as native polymesh structures</li> <li> Huygens blocks imported from full-wave modules</li></ul>

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 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. Generation ===

You can lock the <ul> <li> Surface triangular mesh density of any surface group to any desired value different than the global with control over tessellation parameters</li> <li> Local mesh density. To do so, open the property dialog editing of a surface group by right clicking on its name in the Navigation Tree and select '''Properties...''' from the contextual menu. At the bottom of the dialog, check the box labeled '''Lock Mesh'''. This will enable the '''Density '''box, where you can set a desired value. The default value is equal to the global mesh density.polymesh objects</li></ul>

=== Hertzian Dipole Sources Data Generation &amp; Visualization ===

<ul> <li> Electric and magnetic surface current distributions on metallic or impedance surfaces</li> <li> Near field intensity plots (vectorial - amplitude &amp; phase)</li> <li> Huygens surface data generation for use in PO or other [[File:PO30EM.png|thumb|300px|PO Module's Short Dipole Source dialogCube]]modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li> <li> Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

A short Hertzian dipole is == Building the simplest way of exciting a structure Physical Structure in EM.Illumina. A short dipole source acts like an infinitesimally small ideal current source. To define a short dipole source, follow these steps:==

* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' from the contextual menu. === The Short Dipole dialog opens up.* In the '''Source Location''' section Variety 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 (0,0,0). * * In the '''Source Properties''' section, you can specify the '''Amplitude''' Surface Types 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 dipoleEM. Illumina ===

The total radiated power [[EM.Illumina]] organizes physical objects by your dipole source is calculated and displayed their surface type. Any object in Watts in the dialog[[EM.Illumina]] is assumed to be made of one of the three surface types:

{| class="wikitable"|-! scope="col"| Icon! scope= Plane Wave "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|}

Click on each category to learn more details about it in the [[File:PO29Glossary of EM.png|thumb|300px|PO ModuleCube's Plane Wave dialogMaterials, Sources, Devices & Other Physical Object Types]]Your physical structure in EM.Illumina can be excited by an incident plane wave. In particular, a plane wave source is needed 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.Illumina provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz.

The direction [[EM.Illumina]] can only handle surface and solid CAD objects. Only the outer surface of incidence solid objects is defined through the &theta; and &phi; angles of the unit propagation vector considered in the spherical coordinate systemPO simulation. The values of these angles No line or curve objects are set in degrees allowed in the boxes labeled '''Theta''' and '''Phi'''. The default values are &thetaproject workspace; = 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 casesor else, 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 they will be satisfied: '''ê . ê''' = 1 and '''ê × k''' = 0 . This can be enforced using ignored during 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°)PO simulation.

* Right click on You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the '''Plane Waves''' item in objects created and drawn under a group share the '''Sources''' section of the Navigation Tree same color and select '''Insert New Sourceother properties...''' The Plane wave Dialog opens up.* In Once a new surface node has been created on the Field Definition section of the dialognavigation tree, you can enter it becomes the '''Amplitude''' "Active" surface group of the incident electric field project workspace, which is always listed in V/m and its '''Phase''' in degreesbold letters. The default field Amplitude When you draw a new CAD object such as a Box or a Sphere, it is 1 V/m with a zero Phase.* The direction of inserted under the Plane Wave currently active surface type. There is determined only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the incident '''Theta''' navigation tree and '''Phi''' angles in degrees. You can also set selecting the '''PolarizationActivate''' item of the plane wave contextual menu. It is recommended that you first create surface groups, and choose from then draw new objects under the five options described earlieractive surface group. * If the '''Custom Linear''' option is selectedHowever, if you also need to enter the Xstart a new EM.Illumina project from scratch, Yand start drawing a new object without having previously defined any surface groups, Z components of a new default PEC surface group is created and added to the '''E-Field Vector'''navigation tree to hold your new CAD object.

{{Note|In [[File:po_phys17EM.png|thumb|300px|PO Module's Huygens Source dialogCube]], 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.}}

At the end of a full-wave simulation in the <table><tr><td> [[File:PO MAN1.png|thumb|left|480px|EM.Cube]]Illumina's FDTD, MoM3D, Planar or Physical Optics Modules, you can generate Huygens surface datanavigation tree. According to Huygens' principle, if one knows the tangential electric and magnetic field components 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 a structure for recording the tangential components of electric and magnetic fields at the end of full-wave simulation of the structure. 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 to define a Huygens source, you need to have a Huygens data file of '''== EM.HUYIllumina''' 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.s Excitation Sources ==

To create a new Huygens source, follow these steps[[EM.Illumina]] provides three types of sources for the excitation of your physical optics simulation:

* Right click on the '''Huygens Sources''' item in the '''Sources''' section of the Navigation Tree and select '''Import Huygens {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source...''' from the contextual menu.Type* The standard ! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[WindowsFile:hertz_src_icon.png]] Open Dialog opens up| [[Glossary of EM. The file type is set to Cube'''.HUY''' 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 data.s Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]* Once imported| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, the Huygens stand-alone source appears in the Project Workspace as a wire|-frame box| style="width:30px;" | [[File:plane_wave_icon.png]]* You can open the property dialog | [[Glossary of a Huygens source by right clicking on its name in the Navigation Tree and selecting '''Properties..EM.Cube''' 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 Xs Materials, YSources, Z '''Center Coordinates''' and '''Rotation Angles''' of the Huygens box. You can also view the dimensions of the box.Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]* By default| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, the Huygens data are imported as a single Huygens stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon. You can create an arbitrary array png]]| [[Glossary of Huygens sources for your PO projectEM. To do soCube's Materials, in the Sources, Devices &quotOther Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;Create Array&quot" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px; section of the " | Imported from a 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.surface data file|}

Click on each category to learn more details about it in the [[File:PO34Glossary of EM.png|400pxCube's Materials, Sources, Devices & Other Physical Object Types]] [[File:PO35.png|400px]]

Figure: (Left) A rotated imported Huygens 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 (Right) An array displayed in Watts in 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 imported Huygens sources 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 excite a PEC boxnormally 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.

== Running PO Simulations EM.Illumina's Simulation Data & Observables ==

=== Running A Basic [[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 Analysis ===simulation, [[EM.Illumina]] generates a number of output data files that contain all the computed simulation data. Once the current distributions are known, [[EM.Illumina]] can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

[[File:PO27.png|thumb|400px|EM.Illumina's Simulation Run dialog.]]To open [[PO Module]]'s Simulation Run dialog, click currently provides the '''Run''' [[Filefollowing observables: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.

{| class="wikitable"|-! scope="col"| Icon! scope= Setting The Numerical Parameters "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|-| 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|}

Click on each category to learn more details about it in the [[File:PO28.png|thumb|350px|Glossary of EM.IlluminaCube's Simulation Engine Settings dialog.Observables & Graph Types]]Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[PO Module]]'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''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default 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, the magnetic currents are scaled by &eta;₀ in the residual error vector.

You can also use higher- or lower-order integration schemes for Current distributions are visualized on the calculation surface of field integrals. [[EM.Cube]]'s PO simulation engine uses triangular mesh cells for , and the mesh magnitude and phase of the physical surface structures electric and rectangular cells magnetic surface currents are plotted for discretization of Huygens sources and surfacesall the objects. For integration 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 triangular the individual mesh cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' some parts of the plots may be blocked by and '''Constant'''hidden inside smooth and curved objects. For integration of rectangular cells, tooTo be able to view those parts, you may have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''to freeze the obstructing objects or switch to the mesh view mode.

[[Image:po_phys52.png|thumb|300px|EM.Illumina's Frequency Settings dialog.]]You can run [[EM.Cube]]'s PO simulation engine in allows you to visualize the sweep mode, whereby near fields at a parameter like frequency, predefined field sensor plane wave incident angles or a user defined variable of arbitrary dimensions. Calculation of near fields is varied over a specified range at predetermined samples. The output data are saved into data files for visualization post-processing process and plottingmay take a considerable amount of time depending on the resolution that you specify. [[EM.Cube]]'s [[PO Module]] currently offers three types of sweep:

To run <table><tr><td> </td><td> [[Image:PO43.png|thumb|360px|Electric field distribution on a PO sweep, open the '''Simulation ''''''Run Dialog''' and select one of the sensor plane above sweep types from the '''Simulation Mode''' dropdown list of this dialoga metallic sphere. If you select either frequency or angular sweep, the '''Settings''' button located next to the simulation mode dropdown list becomes enabled]] </td><td> [[Image:PO44. 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 png|thumb|360px|Magnetic field distribution on the project's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As sensor plane above a result, the mesh of the structure also changes at each frequency samplemetallic sphere. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:]] </td></tr></table>

# Fix mesh at You need to define a far field observable if you want to plot the highest frequencyradiation patterns of your physical structure.# Fix mesh at After a PO simulation is finished, three 3D radiation patterns plots are displayed in the center frequencyproject workspace and are overlaid on your physical structure.# ReThese are the Theta and Phi components of the far-mesh at each frequencyzone electric fields as well as the total far field.

You can 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 the default settings. During an angular sweep, either the incident theta angle or incident phi angle {{Note| The 3D radiation pattern is varied within the specified range. The other angle remains fixed always displayed at the value that is specified in origin of the '''Plane Wave Dialog'''. You have spherical coordinate system, (0,0,0), with respect to select either '''Theta''' or '''Phi''' as which the '''Sweep Angle''' in the Angle Settings Dialogfar radiation zone is defined. You also need to set Oftentimes, this might not be the start and end angles as well as the number radiation center of angle samplesyour physical structure.}}

In a parametric sweep, one or more user defined <table><tr><td> [[variables]] are varied at the same time over their specified rangesImage:PO46. This creates a parametric space with the total number png|thumb|360px|3D radiation pattern of samples equal to the product of the number of samples for each variable. The user defined [[variables]] are defined using [[EM.Cube]]'s '''[[Variables]] Dialog'''. For a description of [[EMparabolic dish reflector excited by a short dipole at its focal point.Cube]] [[variables]], please refer to the &quot;Parametric Modeling, Sweep &amp; [[Optimization]]&quot; section of [[EM.Cube]] Manual or see the &quot;Parametric Sweep&quot; sections of the FDTD or [[Planar Module]] manuals.</td></tr></table>

== Working with When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[EM.Illumina]] can calculate 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 Simualtion Data ==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.

[[File:PO37.png|thumb|300px|PO Module's Current Distribution dialog.]][[Image:PO38.png|thumb|500px{{Note|The current distribution 3D RCS plot of a PEC sphere illuminated by an obliquely incident plane wave.]]At is always displayed at the end of a PO simulation, [[EM.Cube]]'s PO engine generates a number origin 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 cellsspherical coordinate system, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order to view these currents(0, you must first define a current distribution observable before running the PO simulation. To do this0, 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 dialog. A new current distribution node is added 0), with respect 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 workspacefar radiation zone is defined. After a PO simulation is completedOftentimes, new plots are added under this might not be the current distribution node scattering center 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 modeyour physical structure.}}

[[Image:PO42(4).png|thumb|300px|PO Module's Field Sensor dialog]][[Image:PO43.png|thumb|400px|Near field plot of electric field on a sensor plane.]][[Image:PO44.png|thumb|400px|Near field plot of magnetic field on a sensor plane.]][[== Discretizing the Physical Structure in 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:Illumina ==

* Right click on EM.Illumina uses a triangular surface mesh to discretize the '''Field Sensors''' item in the '''Observables''' section structure of the Navigation Tree and select '''Insert New Observableyour project workspace...'''* The '''Label''' box allows you mesh generating algorithm tries to change generate regularized triangular cells with almost equal surface areas across the sensor’s nameentire structure. you You can also change control the color of the field sensor plane cell size using the '''Color''' button"Mesh Density" parameter.* Set By default, the '''Direction''' mesh density is expressed in terms of the field sensorfree-space wavelength. This The default mesh density is specified by 10 cells per wavelength. In the normal vector of Physical Optics method, the sensor plane. The available options are '''X'''electric and magnetic surface currents, '''YJ''' and '''ZM''', with are assumed to be constant on the last being surface of each triangular cell. On flat surfaces, the default optionunit normal vectors to all the cells are identical.* By default [[EMIncident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells.Cube]] creates Therefore, a field sensor plane passing through the origin of coordinates (0,0,0) high resolution mesh may not be necessary on the XY planeflat surface or faces. You can change the location Accurate discretization of the sensor plane to any point by typing in new values for the Xcurved objects like spheres or ellipsoids, however, Y and Z '''Center Coordinates'''. You can also change these coordinates using the spin buttonsrequires a high mesh density. <table><tr><td> * The initial size of the sensor plane is 100 × 100 project units[[File:PO4. You can change the dimensions of the sensor plane to any desired sizepng|thumb|left|480px|EM. You can also set the Illumina'''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 timess Mesh Settings dialog.]]</td></tr></table>

After closing Since EM.Illumina is a surface simulator, only the Field Sensor Dialogexterior surface of solid CAD objects is discretized, a new field sensor item immediately appears under as the '''Observables''' section interior volume is not taken into account in the Navigation Tree. Once a PO simulation is finishedanalysis. By contrast, a total of 14 plots surface CAD objects are added assumed to every field sensor node in the Navigation Treebe double-sided. These include In other words, the magnitude default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and phase the other representing the lower or negative side. This may lead to a very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all three components of mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''EAll Double-Sided Cells''' and '''HAll Single-Sided Cells''' fields and the total electric and magnetic field values. Click on any of these items This is useful when your project workspace contains well-organized and a colorwell-coded intensity plot of it will be visualized on the project workspaceoriented surface CAD objects only. A legend box appears in In the upper right corner of the field plotsingle-sided case, 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 it is very important that all the minimum field value corresponding normals to 0 of the color map, maximum field value corresponding to 1 of cells point towards the color mapsource. Otherwise, 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 your surfaces fall in Radians between -p and p.To display the fields properly, the structure is cut through the field sensor planeshadow region, and only part of it is shownno currents will be computed on them. If By checking the structure still blocks your viewbox labeled '''Reverse Normal''', you can simply hide or freeze itinstruct EM. You can change Illumina to reverse the view direction of the field plot with normal vectors globally at the available view operations such as rotate view, pan, zoom, etcsurface of all the cells.

{{Note[[Image:Info_icon.png|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 30px]] Click here to produce acceptable resultslearn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.}}

<table><tr><td> [[FileImage:PO45POShip1.png|thumb|300px600px|PO Module's Radiation Pattern dialogGeometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td></tr><tr><td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the metallic battleship model.]]</td></tr></table>

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 == Running PO Simulations 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 TreeEM.Illumina ==

After a PO simulation is finished, three radiation patterns plots are added to the far field node in the Navigation Tree=== EM. These are the far field component in &theta; direction, the far field component in &phi; direction and the total far field defines as:Illumina's Simulation Modes ===

:<math>|\mathbf{E_{ffOnce you have set up your structure in [[EM.Illumina]],tot}}| = \sqrt{ |E_{\theta}|^2 + |E_{\phi}|^2 }</math><!--have defined sources and observables and have examined the quality of the structure's mesh, you are ready to run a Physical Optics simulation. [[File:FDTD129EM.pngIllumina]]-->offers five simulation modes:

The 3D plots can be viewed by clicking on their name in the navigation tree. They are displayed in {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[EM.Cube#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]'s project workspace and are overlaid on | style="width:270px;" | Simulates the project's physical structure. The view of a 3D radiation pattern plots can be changed with "As Is"| style="width:80px;" | Single run| style="width:250px;" | Runs at the available view operations such as rotate view, pan, zoom, etccenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. If Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the structure blocks the view operating frequency of the pattern, you can simply hide the whole structure or parts PO solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of itfrequency samples| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The fields are always normalized to Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the maximum value(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the total far fieldcenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. A legend box appears in Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the upper right corner value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the 3D radiation plot, which can be moved around by clicking and dragging with the left mouse buttoncenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The calculated Directivity of Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the radiating structure is displayed at the bottom value(s) of the legend box. It is important one or more project variables to note that if generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the PO structure is excited by an incident plane wave, the radiation patterns indeed represent the far-zone scattered field data.center frequency fc| style="width:80px;" | None|}

You can set the simulation mode from [[File:PO46EM.png|500pxIllumina]]'s "Simulation Run Dialog". A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. 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 end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation tree.

<table><tr><td> [[FileImage:PO47Illumina L1 Fig10A.png|thumb|300pxleft|PO Module480px|EM.Illumina's RCS Simulation Run dialog.]]</td></tr></table>

:<math> \sigma_{\theta} = 4\pi r^2 \dfrac{ \big| \mathbf{E}_{\theta}^{scat} \big| ^2} {\big| \mathbf{E}^{inc} \big|^2}Before you run a PO simulation, \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} </math><!--you can change some of the PO simulation engine settings. While in the [[File:FDTD130EM.pngIllumina]]'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''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero--order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default 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, the magnetic currents are scaled by &eta;₀ in the residual error vector.

Three RCS quantities are computed: You can also use higher- or lower-order integration schemes for the &theta; and &phi; components calculation of the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_totfield integrals. In addition, [[EM.Cube]]'s [[PO Module]] calculates two types simulation engine uses triangular cells for the mesh of RCS the physical surface structures and rectangular cells for each structurediscretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''Bi7-Static RCSPoint Quadrature''' and , '''Mono3-Static RCSPoint Quadrature''' and '''Constant'''. In biFor integration of rectangular cells, too, you have three options: '''9-static RCSPoint Quadrature''', the structure is illuminated by a plane wave at incidence angles &theta;₀ '''4-Point Quadrature''' and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles'''Constant'''. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta; <subtable>0</subtr> and &phi;<subtd>0[[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]</subtd>, and the RCS is measured and plotted at the echo angles 180°-&theta;<sub>0</subtr>; and &phi;<sub>0</subtable>. 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]]'''