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. 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 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 free space. A challenging step in establishing the PO simulationcurrents is the determination of the lit and shadowed points on complex scatterer geometries. No line 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, [[Curve Objects|curve objectsEM.Illumina]] are allowed in the project workspace; or else's simulator uses a novel Iterative Physical Optics (IPO) formulation, they will be ignored during the PO simulationwhich automatically accounts for multiple shadowing effects. You The IPO technique can define several PECeffectively capture dominant, 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 propertiesnear-field, multiple scattering effects from electrically large targets.

A new surface group can be defined by simply right clicking on one of the three '''PEC''', '''PMC''' or '''Impedance Surface''' items in [[Image:Info_icon.png|30px]] 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 ===

=== Generating &amp; Customizing PO Mesh === [[File:PO23EM.png|thumb|250px|[[PO ModuleIllumina]]'s Mesh Settings dialog]] The mesh generation process in [[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 provides a specified mesh density expressed in cells/&lambda;₀computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. The default mesh density is 20 cells/&lambda;₀. To view the PO mesh, click on the [[File:mesh_tool_tn.png]] button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Discretization &gt; Show Mesh''' or use the keyboard shortcut '''Ctrl+M'''. When the PO mesh is displayed in the project workspaceFor simple scatterer geometries, [[EM.CubeIllumina]]'s mesh view mode GO-PO solver is enabledfairly adequate. In this modeBut for complex geometries that involve multiple shadowing effects, you the IPO solver must be utilized. 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|300pxleft|Two ellipsoids 550px|Computed radiation pattern of different compositionsa short dipole radiator over a large metallic battleship.]] </td><td> [[Image:PO3.png|thumb|300px|Trinagular surface mesh of the two ellipsoids.]] </td>

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

'''As a general rule, <ul> <li> Short dipoles</li> <li> Import previously generated wire mesh solution as collection of short dipoles</li> <li> Plane wave excitation with linear and circular polarizations</li> <li> Multi-ray excitation capability (ray data imported from [[EM.CubeTerrano]]'s or external files)</li> <li> Huygens sources imported from 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 or other modules with arbitrary rotation and consistent mesh in the transition and junction areas between connected objects. In general, objects of the same 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.array configuration</li></ul>

Figure: Geometry and PO <ul> <li> Surface triangular mesh with control over tessellation parameters</li> <li> Local mesh editing of an overlapping sphere and ellipsoid.polymesh objects</li></ul>

=== Mesh Density &amp; Local Mesh Control Physical Optics Simulation ===

[[Image:PO31.png|thumb|400px|Locking the mesh density of a PEC group.]]<ul>[[Image:PO32.png|thumb|400px|Triangular surface mesh of two PEC box objects with the orange PEC group having a locked mesh <li> Physical Optics solution of higher density.]]metal scatterers and impedance surfaces</li>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 <li> Conventional Geometrical Optics -wave method of moments Physical Optics (MoMGOPO) solvers, you have to keep in mind that the triangular surface mesh cells in solver</li> <li> Novel iterative PO Modules act slightly differently. The complexsolver for fast simulation of multiple shadowing effects and multi-valuedbounce reflections</li> <li> Calculation of near fields, vectorial, electric far fields and magnetic surface currents, '''J''' scattering cross section (bistatic and '''M''' are assumed to be constant on the surface of each triangular cell. On plates monostatic RCS)</li> <li> Frequency and flat faces angular sweeps with data animation</li> <li> Parametric sweep with variable object properties 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 parameters</li> <li> Multi-variable and multi-goal optimization of curved objects like spheres or ellipsoids. structure</li> <li> Remote simulation capability</li> <li> Both Windows and Linux versions of PO simulation engine available</li></ul>

=== Hertzian Dipole Sources =Building the Physical Structure in EM.Illumina ==

[[File:PO30=== The Variety of Surface Types in EM.png|thumb|300px|PO Module's Short Dipole Source dialog]]Illumina ===

A short dipole is the simplest way of exciting a structure in [[EM.CubeIllumina]]'s organizes physical objects by their surface type. Any object in [[PO ModuleEM.Illumina]]. A short dipole source acts like an infinitesimally small ideal current source. To define a short dipole source, follow these stepsis assumed to be made of one of the three surface types:

* Right click on the '''Short Dipoles''' item in the ''{| 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''' section of the Navigation Tree , 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 select '''Insert New Source...''' from the contextual menu. The Short Dipole dialog opens upsurface objects|-| style="width:30px;" | [[File:pmc_group_icon.png]]* In the '''Source Location''' section | style="width:250px;" | [[Glossary of the dialog, you can set the coordinate of the center of the short dipoleEM. By defaultCube's Materials, the source is placed at the origin of the world coordinate system at Sources, Devices & Other Physical Object Types#Perfect Magnetic Conductor (0,0,0PMC) |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. You can type in new coordinates or use the spin buttons to move the dipole aroundpng]]| style="width:250px;" | [[Glossary of EM.* In the Cube'''Source Properties''' sections Materials, you can specify the '''Amplitude''' in VoltsSources, the '''Phase''' in degrees as well Devices & Other Physical Object Types#Impedance Surface |Impedance/Dielectric Surface]]| style="width:300px;" | Modeling impedance surfaces as an equivalent to the '''Length''' surface of the dipole in project unitsdielectric objects | style="width:250px;" | Solid and surface objects|-| style="width:30px;" | [[File:Virt_group_icon.png]]* In the '''Direction Unit Vector''' section, you can specify the orientation | style="width:250px;" | [[Glossary of the short dipole by setting values for the components '''uX''EM.Cube's Materials, '''uY'''Sources, and '''uZ''' 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 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.objects|}

The solution of a problem in one of [[EM.CubeIllumina]]'s computational modules can serve as only handle surface and solid CAD objects. Only the excitation source for another problem in another computational module. An example outer surface of this solid objects is analyzing a wire antenna considered in the [[MoM3D Module]] and importing the wire current solution to [[PO Module]] to excite a large scatterersimulation. Remember that you cannot define wires No line or [[Curve Objects|curve objects]] are allowed in [[PO Module]]. Howeverthe project workspace; or else, 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 they will be ignored during the source of your PO projectsimulation.

When you simulate a wire structure in the [[MoM3D Module]], you can define a '''Current Distribution Observable''' in your project. This is used not only to visualize the current distribution in the project workspace, but also to save the current solution into an ASCII data file. This data file is called &quot;MoM.IDI&quot; === Organizing Geometric Objects by default and has a '''.IDI''' file extension. The current data are saved as line segments representing each of the wire cells together with the complex-valued, vectorial current at the center of each cell. You can import the current data from an existing '''.IDI''' file to [[PO Module]], To import a wire current solution, right click on '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Import Dipole Source...''' from the contextual menu. This opens up the standard [[Windows]] Open dialog with the file type set to '''.IDI'''. Browse your folders to find the right current data file. Once you find it, select it and click the '''Open''' button of the dialog. This will create as many short dipole sources on the [[PO Module]]'s Navigation Tree as the total number of mesh cells in the Wire MoM solution. From this point on, each of the imported dipoles behave like a regular short dipole source. You can open the property dialog of each individual source and modify its [[parameters]], if necessary.Surface Type ===

[[File:PO36You 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. Once a new surface node has been created on the navigation tree, it becomes the "Active" surface group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. There is 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 navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new EM.Illumina project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object.png|500px]]

Figure[[Image: Importing a Wire MoM current solution into the Info_icon.png|30px]] Click here to learn more about '''[[PO ModuleBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]. In this structure, 90 wire cell currents representing a helical antenna were imported and placed above a large sinusoidal PEC surface'''.

<table><tr><td> [[File:PO29PO MAN1.png|thumb|300pxleft|PO Module480px|EM.Illumina's Plane Wave dialognavigation tree.]]</td></tr></table>

Your physical structure 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]]Illumina's [[PO Module]] provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz.Excitation Sources ==

The direction of incidence is defined through the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system[[EM. The values Illumina]] provides three types of these angles are set in degrees in sources for the boxes labeled '''Theta''' and '''Phi'''. The default values are &theta; = 180° and &phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM_z and TE_z polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components excitation of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfiedyour physical optics simulation: '''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 {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of 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 follow these steps|-| 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|}

* 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]].

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

[[File:po_phys17== EM.png|thumb|300px|PO ModuleIllumina's Huygens Source dialog]]Simulation Data & Observables ==

At the end of a full-wave simulation in the [[EM.CubeIllumina]]'s FDTD, MoM3D, Planar 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 Modules, you can generate Huygens surface data. According to Huygens' principle, if one knows method are the tangential electric and magnetic field components surface current distributions on a closed surface, one can determine the total electric and magnetic fields everywhere inside and outside that closed surfaceof your structure. Huygens surfaces are defined around a structure for recording the tangential components of electric and magnetic fields at At the end of full-wave a PO simulation , [[EM.Illumina]] generates a number of output data files that contain all the structure. The tangential electric and magnetic fields are saved into ASCII computed simulation data files as magnetic and electric currents, respectively. These Once the current can be used as excitation for other structures. In other wordsdistributions are known, the electric and magnetic currents associated with a Huygens source radiate energy and provide the excitation for the [[PO ModuleEM.Illumina]]'s physical structurecan compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS).

In order to define a Huygens source, you need to have a Huygens data file of '''[[EM.HUY''' type. This file is generated as an output data file at Illumina]] currently provides 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.following observables:

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

* Right click Click on the '''Huygens Sources''' item each category to learn more details about it in the '''Sources''' section of the Navigation Tree and select '''Import Huygens Source...''' from the contextual menu.* The standard [[Windows]] Open Dialog opens up. The file type is set to '''.HUY''' by default. Browse your folders to find a Huygens surface data file with a '''.HUY''' file extension. Select the file and click the '''Open''' button Glossary of the dialog to import the dataEM.* Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.* You can open the property dialog of a Huygens source by right clicking on its name in the Navigation Tree and selecting Cube'''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 s Simulation Observables &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 workspaceGraph Types]].

[[File:PO34Current 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.png|400px]] [[File:PO35A 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|400px]]

Figure<table><tr><td> [[Image: (Left) A rotated imported Huygens source, and (Right) An array PO38.png|thumb|390px|The current distribution plot of imported Huygens sources defined to excite a PEC boxsphere illuminated by an obliquely incident plane wave.]] </td></tr></table>

To open <table><tr><td> </td><td> [[PO Module]]'s Simulation Run dialog, click the '''Run''' [[FileImage:run_iconPO43.png|thumb|360px|Electric field distribution on a sensor plane above a metallic sphere.]] 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, </td><td> [[EMImage:PO44.Cube]] generates a number of output data files that contain all the computed simulation data. These include current distributions, near field data, far png|thumb|360px|Magnetic field radiation pattern data as well bi-static or mono-static radar cross sections (RCS) if the structure is excited by distribution on a sensor plane wave sourceabove a metallic sphere.]] </td></tr></table>

[[File:PO27You need to define a far field observable if you want to plot the radiation patterns of your physical structure. After a PO simulation is finished, three 3D radiation patterns plots are displayed in the project workspace and are overlaid on your physical structure. These are the Theta and Phi components of the far-zone electric fields as well as the total far field.png]]

Figure 1: [[PO Module]]'s Simulation Run dialog{{Note| The 3D radiation pattern 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 radiation center of your physical structure.}}

Before you run When your physical structure is excited by a PO simulationplane wave source, you can change some of the PO simulation engine settingscalculated far field data indeed represent the scattered fields. While in the [[PO ModuleEM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are can calculate two options types of RCS for '''Solver Type'''each structure: '''IterativeBi-Static RCS''' and '''GOPOMono-Static RCS'''. The default option is Iterative. The GOPO solver is a zeroIn bi-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in static RCS, 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 illuminated by a default value of plane wave at incidence angles &theta;_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&phi;<sub>0</M''' current solution of sub>, and the entire discretized structure from one iteration to the nextRCS is measured and plotted at all &theta; and &phi; angles. Note that for this purposeIn mono-static RCS, the magnetic currents are scaled structure is illuminated by a plane wave at incidence angles &etatheta;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 residual error vectorcase 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.

You can also use higher- or lower-order integration schemes for To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the calculation end of field integrals. [[EM.Cube]]'s a PO simulation engine uses triangular cells for , the mesh thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the physical surface structures and rectangular cells for discretization of Huygens sources and surfacesnavigation tree. For integration of triangular cells, you have three options: '''7Keep in mind that computing the 3D mono-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration static RCS may take an enormous amount of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''computation time.

[[File:PO28{{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.png]]Oftentimes, this might not be the scattering center of your physical structure.}}

Figure 1: <table><tr><td> [[PO ModuleImage:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]]'s Simulation Engine Settings dialog.</td></tr></table>

=== PO Sweep Simulations =Discretizing the Physical Structure in EM.Illumina ==

EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can run [[EMcontrol the cell size using the "Mesh Density" parameter.Cube]]'s PO simulation engine By default, the mesh density is expressed in terms of the sweep modefree-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, whereby a parameter like frequencythe electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane wave incident angles waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a user defined variable is varied over high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a specified range at predetermined samples. The output data are saved into data files for visualization and plottinghigh mesh density. <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Cube]]Illumina's [[PO ModuleMesh Settings dialog.]] currently offers three types of sweep:</td></tr></table>

To run a PO sweep, open the '''Simulation ''''''Run Dialog''' and select one of the above sweep types from the '''Simulation Mode''' dropdown list of this dialog[[Image:Info_icon. If you select either frequency or angular sweep, the png|30px]] Click here to learn more about '''Settings''' button located next to the simulation mode dropdown list becomes enabled[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectivelyCube. In the frequency settings dialog, you can set the start and end frequencies as well as the number of frequency samples. The start and end frequency values are initially set based on the project27s_Mesh_Generators | Working with Mesh Generator]]''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 at the highest frequency[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation# Fix mesh at the center frequencyThe_Triangular_Surface_Mesh_Generator | EM.# Re-mesh at each frequencyIllumina's Triangular Surface Mesh Generator ]]'''.

You can run an angular sweep only if your project has a plane wave excitation<table><tr><td> [[Image:POShip1. In this case, you have to define png|thumb|600px|Geometry of a plane wave source metallic battleship model with the default settingsa short horizontal dipole radiator above it. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range]] </td></tr><tr><td> [[Image:POShip2. The other angle remains fixed at png|thumb|600px|Trinagular surface mesh of 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 samplesmetallic battleship model.]] </td></tr></table>

In a parametric sweep, one or more user defined [[variables]] are varied at the same time over their specified ranges. This creates a parametric space with the total number of samples equal to the product of the number of samples for each variable. The user defined [[variables]] are defined using [[== Running PO Simulations in EM.Cube]]'s '''[[Variables]] Dialog'''. For a description of [[EM.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.Illumina ==

[[File:po_phys52=== EM.png]] [[File:po_phys54.png]]Illumina's Simulation Modes ===

Figure 1: Once you have set up your structure in [[PO ModuleEM.Illumina]], have defined sources and observables and have examined the quality of the structure's Frequency Settings and Angle Settings dialogsmesh, you are ready to run a Physical Optics simulation.[[EM.Illumina]] offers five simulation modes:

{| class="wikitable"|-! scope= Working with "col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running A Single-Frequency PO Simualtion Data Analysis | Single-Frequency 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.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;" | Varies the operating frequency of the PO solver | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at a specified set of frequency samples| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the value(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.Cube#Performing_Optimization_in_EM.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 center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the value(s) of one or more project variables to generate a compact model| style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|}

[[File:PO37.png|thumb|300px|PO Module's Current Distribution dialog.]][[Image:PO38.png|thumb|500px|The current distribution plot of a PEC sphere illuminated by an obliquely incident plane wave.]]At the end of a PO simulation, [[EM.Cube]]'s PO engine generates a number of output data files that contain all the computed simulation data. The main output data are the electric and magnetic current distributions. You can easily examine the 3D color=== Running A Single-coded intensity plots of current distributions in the project workspace. Current distributions are visualized on the surface of the Frequency PO mesh cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order to view these currents, you must first define a current distribution observable before running the PO simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[PO Module]] you can define only one current distribution node in the Navigation Tree, which covers all the objects in the project workspace. After a PO simulation is completed, new plots are added under the current distribution node of the Navigation Tree. Separate plots are produced for the magnitude and phase of each of the electric and magnetic surface current components (X, Y and Z) as well as the total current magnitude. The magnitude maps are plotted on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -p and p. Note that sometimes the current distribution plots may hide inside smooth and curved objects, and you cannot see them. You may have to freeze such objects or switch to the mesh view mode.Analysis ===

<table><tr><td> [[Image:PO42(4)Illumina L1 Fig10A.png|thumb|300pxleft|PO Module480px|EM.Illumina's Field Sensor Simulation Run dialog]][[Image:PO43.png|thumb|400px|Near field plot of electric field on a sensor plane.]]</td>[[Image:PO44.png|thumb|400px|Near field plot of magnetic field on a sensor plane.]]</tr>[[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:</table>

* Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''* === Setting The '''Label''' box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the '''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 [[EM.Cube]] 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.Numerical Parameters ===

After closing Before you run a PO simulation, you can change some of the Field Sensor PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', a new field sensor item immediately appears under click the '''ObservablesSettings''' section in the Navigation Tree. Once a PO simulation is finished, a total of 14 plots are added button next to every field sensor node in the Navigation Tree'''Select Engine''' dropdown list. These include In the magnitude and phase of all three components of Physical Optics Engine Settings Dialog, there are two options for '''ESolver Type''' and : '''HIterative''' fields and the total electric and magnetic field values'''GOPO'''. Click on any of these items and The default option is Iterative. The GOPO solver is a colorzero-coded intensity plot of it will be visualized on order PO simulator that uses Geometrical Optics (GO) to determine the project workspace. A legend box appears lit and shadow cells in the upper right corner of the field plot, which can be dragged around using the left mouse buttonstructure's mesh. The values For the termination of the magnitude plots IPO solver, there are normalized between 0 two options: '''Convergence Error''' and 1'''Maximum Number of Iterations'''. The legend box contains the minimum field value corresponding to 0 of the color mapdefault Termination Criterion is based on convergence error, maximum field which has a default value corresponding to 1 of the color map, 0.1 and can be changed to any desired accuracy. The convergence error is defined as the unit L2 norm of the field quantity, which is Vnormalized residual error in the combined '''J/m for E-field and A/m for H-field. The values M''' current solution of phase plots are always shown in Radians between -p and p.To display the fields properly, the entire discretized structure is cut through from one iteration to the field sensor plane, and only part of it is shownnext. If the structure still blocks your viewNote that for this purpose, you can simply hide or freeze it. You can change the view of magnetic currents are scaled by &eta;₀ in the field plot with the available view operations such as rotate view, pan, zoom, etcresidual error vector.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, You can also use higher- or lower-order integration schemes for the calculation of field sensors must be placed at adequate distances (at least one or few wavelengths) away from integrals. [[EM.Cube]]'s PO simulation engine uses triangular cells for the scatterers to produce acceptable resultsmesh 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'''.}}

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

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

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

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

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