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[[Image:Splash-po.jpg|right|900px720px]]<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. {{Note|EM.Illumina is the high-frequency, asymptotic '''[[Physical Optics Module]]''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Illumina shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modules.}} [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE | EM.Cube Modeling Environment]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about the basic functionality of '''[[CubeCAD]]'''. === 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:Info_icon.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|280pxleft|The PEC dialog.]] </td><td> [[Image:PO20.png420px|thumb|280px|The PMC dialogAnalyzing scattering from a trihedral corner reflector using IPO solver.]] </td><td> [[Image:PO21.png|thumb|280px|The Impedance Surface dialog.]] </td>

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

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

[[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 ]]'s simulator is seamlessly interfaced with almost equal surface areas across the entire structure[[EM. You can control the cell size using the "Mesh Density" parameterCube|EM. By default, the mesh density CUBE]]'s other simulattion engines. This module is expressed in terms of the freeideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-space wavelengthwave simulator like [[EM. The default mesh density is 10 cells per wavelengthTempo]], [[EM. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project unitsPicasso]] or [[EM.Libera]].

[[File:PO4.png|thumb|300px|=== Advantages & Limitations of EM.Illumina's Mesh Settings dialog.]][[File:PO5.png|thumb|300px|The Tessellation Options dialog.]]The mesh generation process in EM.Illumina involves three steps:PO Solver ===

# Setting [[EM.Illumina]] provides a computationally efficient alternative to full-wave solutions for extremely large structures when full-wave analysis becomes prohibitively expensive. For simple scatterer geometries, [[EM.Illumina]]'s GO-PO solver is fairly adequate. But for complex geometries that involve multiple shadowing effects, the mesh propertiesIPO solver must be utilized.# Generating The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the meshboundary conditions on one side of a surface only.# Verifying PO analysis cannot handle the meshfields inside dielectric objects. Additionally, 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>

[[File:PO30.png|thumb|360px|<ul> <li> Physical Optics solution of metal scatterers and impedance surfaces</li> <li> Conventional Geometrical Optics - Physical Optics (GOPO) solver</li> <li> Novel iterative PO Module's Short Dipole Source dialog]]solver for fast simulation of multiple shadowing effects and multi-bounce reflections</li> <li> Calculation of near fields, far fields and scattering cross section (bistatic and monostatic RCS)</li> <li> Frequency and angular sweeps with data animation</li> <li> Parametric sweep with variable object properties or source parameters</li> <li> Multi-variable and multi-goal optimization of structure</li> <li> Remote simulation capability</li> <li>[[File:PO29.png|thumb|420px| Both Windows and Linux versions of PO Module's Plane Wave dialog]] simulation engine available</li>== Excitation Sources ==</ul>

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

A short Hertzian dipole is the simplest way of exciting a structure <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 [[EM.Illumina. A short dipole source acts like an infinitesimally small ideal current source. The total radiated power by your dipole source is calculated Cube]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and displayed in Watts in its property dialog.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>

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.Cube#Hertzian_Dipole_Sources | Hertzian Dipole Sources]]'''== Building the Physical Structure in EM.Illumina ==

=== Plane Wave Sources The Variety of Surface Types in EM.Illumina ===

Your [[EM.Illumina]] organizes physical structure objects by their surface type. Any object in [[EM.Illumina can be excited by an incident plane wave. In particular, a plane wave source ]] is needed assumed to compute the radar cross section be made of a target. A plane wave is defined by its propagation vector indicating the direction one of incidence and its polarization. EM.Illumina provides the following polarization optionsthree surface types: TMz, TEz, Custom Linear, LCPz and RCPz.

The direction of incidence is defined through the &theta{| class="wikitable"|-! scope="col"| Icon! scope="col"| Material Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed|-| style="width:30px; and &phi" | [[File:pec_group_icon.png]]| style="width:250px; angles " | [[Glossary of the unit propagation vector in the spherical coordinate systemEM. The values of these angles are set in degrees in the boxes labeled Cube'''Theta''' and '''Phi'''. The default values are s Materials, Sources, Devices &thetaOther Physical Object Types#Perfect Electric Conductor (PEC) |Perfect Electric Conductor (PEC) Surface]]| style="width:300px; " | Modeling perfect metal surfaces| style= 180° "width:250px;" | Solid and &phisurface objects|-| style="width:30px; " | [[File:pmc_group_icon.png]]| style= 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector"width:250px;" | [[Glossary of EM. In the TM_z and TE_z polarization casesCube's Materials, the 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 electric fields are parallel to the XY plane, respectivelysurface objects|-| style="width:30px;" | [[File:voxel_group_icon. The components png]]| style="width:250px;" | [[Glossary of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialogEM. In the more general case of custom linear polarizationCube's Materials, besides the incidence anglesSources, you have Devices & Other Physical Object Types#Impedance Surface |Impedance/Dielectric Surface]]| style="width:300px;" | Modeling impedance surfaces as an equivalent to enter the components surface of the unit electric '''Field Vector'''. However, two requirements must be satisfieddielectric objects | style="width: '''ê . ê''' = 1 250px;" | Solid and '''ê × k''' surface objects|-| style= 0 "width:30px;" | [[File:Virt_group_icon. This can be enforced using the '''Validate''' button at the bottom png]]| style="width:250px;" | [[Glossary of the dialogEM. If these conditions are not metCube's Materials, an error message pops up. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to the normal incidence only (Sources, Devices &thetaOther Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px; " | Used for representing non-physical items | style= 180°)."width:250px;" | All types of objects|}

* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source[[EM...''' The Plane wave Dialog opens up.* In the Field Definition section of the dialog, you Illumina]] can enter the '''Amplitude''' of the incident electric field in V/m only handle surface and its '''Phase''' in degreessolid CAD objects. The default field Amplitude is 1 V/m with a zero Phase.* The direction Only the outer surface of the Plane Wave solid objects is determined by the incident '''Theta''' and '''Phi''' angles considered in degrees. You can also set the '''Polarization''' of the plane wave and choose from the five options described earlierPO simulation. * If No line or curve objects are allowed in the '''Custom Linear''' option is selectedproject workspace; or else, you also need to enter the X, Y, Z components of they will be ignored during the '''E-Field Vector'''PO simulation.

=== Huygens Sources Organizing Geometric Objects by Surface Type ===

[[File:po_phys17You can define several PEC, PMC or impedance surface groups with different colors and impedance values.png|thumb|300px|PO ModuleAll 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 's Huygens Source dialog]]''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.

At the end of a full-wave simulation in the [[EMImage:Info_icon.Cubepng|30px]]'s FDTD, MoM3D, Planar or Physical Optics Modules, you can generate Huygens surface data. According Click here to Huygenslearn more about ''' 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 ModuleBuilding Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'s physical structure''.

{{Note|In order to define a Huygens source[[EM.Cube]], you need to have a Huygens data file of '''.HUY''' type. This file is generated can import external CAD models (such as an output data file at the end of an FDTDSTEP, MoM3DIGES, Planar or PO simulationSTL models, if you have defined a Huygens Surface observable in one of those projectsetc. When you define a Huygens source) only to CubeCAD. From CubeCAD, you indeed import an existing Huygens surface into can then move the project and set it as an excitation sourceimported objects to EM.Illumina.}}

To create a new Huygens source, follow these steps<table><tr><td> [[File:PO MAN1.png|thumb|left|480px|EM.Illumina's navigation tree.]] </td></tr></table>

* Right click on the == EM.Illumina'''Huygens s Excitation Sources''' item 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 of the dialog to import the data.* Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.* You can open the property dialog of a Huygens source by right clicking on its name in the Navigation Tree and selecting '''Properties...''' From this dialog you can change the color of the Huygens source box as well as its location and orientation. You can enter new values for the X, Y, Z '''Center Coordinates''' and '''Rotation Angles''' of the Huygens box. You can also view the dimensions of the box.* By default, the Huygens data are imported as a single Huygens source. You can create an arbitrary array of Huygens sources for your PO project. To do so, in the &quot;Create Array&quot; section of the Huygens source dialog, enter desired values for the '''Number of Elements''' and '''Element Spacing''' along the X, Y and Z directions. You will see an array of wire-frame box appear in the project workspace.==

[[File:PO34EM.png|400pxIllumina]] [[Fileprovides three types of sources for the excitation of your physical optics simulation:PO35.png|400px]]

Figure{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width: (Left) A rotated imported Huygens 30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, and (Right) An array 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 imported EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources defined to excite a PEC boximported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

=== Running A Basic PO Analysis =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 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:PO27.png|thumb|400px|== EM.Illumina's Simulation Run dialog.]]To open EM.Illumina's Simulation Run dialog, click the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu Data &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.Observables ==

=== Setting [[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The Numerical Parameters ===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 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:PO28.png|thumb|350px|EM.Illumina's Simulation Engine Settings dialog.]]Before you run a PO simulation, you can change some of currently provides 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'''following observables: '''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{| class="wikitable"|- or lower! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-order integration schemes for the calculation of field integrals| style="width:30px;" | [[File:currdistr_icon. png]]| style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube]]'s PO simulation engine uses triangular cells for the mesh of the physical Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface structures current distribution on PEC and rectangular cells for discretization of Huygens sources impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces| style="width:250px;" | None|-| style="width:30px;" | [[File:fieldsensor_icon. For integration of triangular cells, you have three optionspng]]| style="width: '''7150px;" | Near-Point QuadratureField Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube''', '''3s Simulation Observables & Graph Types#Near-Point Quadrature''' Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and '''Constant'''magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon. For integration png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of rectangular cellsEM.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, tooaxial ratio, you have three optionsside lobe levels, etc. | style="width: '''9250px;" | None|-Point Quadrature''', '''4| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Point Quadrature''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'''Constant'''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|}

[[Image:po_phys52.png|thumb|300px|EM.Illumina's Frequency Settings dialog.]]You can run [[EM.Cube]]'s PO simulation engine in Current distributions are visualized on the sweep modesurface of PO mesh cells, whereby a parameter like frequency, plane wave incident angles or a user defined variable is varied over a specified range at predetermined samplesand the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. The output A single current distribution node in the navigation tree holds the current distribution data are saved into data files for visualization 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 plottinghidden inside smooth and curved objects. [[EMTo be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh view mode.Cube]]'s [[PO Module]] currently offers three types of sweep:

To run a PO sweep, open the '''Simulation ''''''Run Dialog''' and select one of the above sweep types from the '''Simulation Mode''' dropdown list of this dialog[[EM. If Illumina]] allows you select either frequency or angular sweep, the '''Settings''' button located next to visualize the simulation mode dropdown list becomes enablednear fields at a predefined field sensor plane of arbitrary dimensions. 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 Calculation of frequency samples. The start near fields is a post-processing process and end frequency values are initially set based on the project's center frequency and bandwidth. During may take a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh considerable amount of time depending on the structure also changes at each frequency sampleresolution that you specify. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:

# Fix mesh at {{Note|Keep in mind that since Physical Optics is an asymptotic method, the highest frequency.# Fix mesh field sensors must be placed at adequate distances (at least one or few wavelengths) away from the center frequency.# Re-mesh at each frequencyscatterers to produce acceptable results.}}

You can run an angular sweep only if your project has a plane wave excitation<table><tr><td> </td><td> [[Image:PO43. In this case, you have to define png|thumb|360px|Electric field distribution on a sensor plane wave source with the default settingsabove a metallic sphere. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range]] </td><td> [[Image:PO44. The other angle remains fixed at the value that is specified in the '''Plane Wave Dialog'''. You have to select either '''Theta''' or '''Phi''' as the '''Sweep Angle''' in the Angle Settings Dialog. You also need to set the start and end angles as well as the number of angle samplespng|thumb|360px|Magnetic field distribution on a sensor plane above a metallic sphere.]] </td></tr></table>

In You need to define 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 far field observable if you want to plot the product radiation patterns of the number of samples for each variable. The user defined [[variables]] are defined using [[EM.Cube]]'s '''[[Variables]] Dialog'''your physical structure. For After a description of [[EM.Cube]] [[variables]]PO simulation is finished, please refer to three 3D radiation patterns plots are displayed in the &quot;Parametric Modeling, Sweep &amp; [[Optimization]]&quot; section of [[EMproject workspace and are overlaid on your physical structure.Cube]] Manual or see These are the &quot;Parametric Sweep&quot; sections Theta and Phi components of the FDTD or [[Planar Module]] manualsfar-zone electric fields as well as the total far field.

== Working {{Note| The 3D radiation pattern is always displayed at the origin of the spherical coordinate system, (0,0,0), with PO Simualtion Data ==respect to which the far radiation zone is defined. Oftentimes, this might not be the radiation center of your physical structure.}}

At the end <table><tr><td> [[Image:PO46.png|thumb|360px|3D radiation pattern of a Physical Optics simulation, EM.Illumina generates parabolic dish reflector excited by a number of output data files that contain all the computed simulation data. The primary output data in Physical Optics are the electric and magnetic surface current distributions on the surface of your structure. Once these quantities are known, EM.Illumina can compute near-field distributions as well as far-field quantities such as radiation patterns and radar cross section (RCS). EM.Illumina does not generate any output data on short dipole at its own unless you define observables for your simulation projectfocal point. ]] </td></tr></table>

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 cellsTo calculate RCS, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order first you have to view these currents, you must first define an RCS observable instead of a current distribution observable before running the PO simulationradiation pattern. To do this, right click on At the '''Current Distributions''' item in the '''Observables''' section end 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 the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the current distribution node far field section of the Navigation Treenavigation 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 Keep in mind that computing the legend box. The phase maps are plotted in radians between 3D mono-p and p. Note that sometimes the current distribution plots static RCS 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 modetake an enormous amount of computation time.

[[Image:Info_icon.png{{Note|40px]] Click here The 3D RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<td> [[Image:PO37PO48.png|thumb|300px420px|PO Module's Current Distribution dialog.]] </td><td> [[Image:PO38.png|thumb|500px|The current distribution plot RCS of a PEC sphere illuminated by an obliquely laterally incident plane wave.]] </td>

=== Near-Field Visualization =Discretizing the Physical Structure in EM.Illumina ==

[[EM.Cube]] allows you Illumina uses a triangular surface mesh to visualize discretize the near fields at a specific field sensor plane. Calculation structure of near fields 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 a postexpressed in terms of the free-processing process space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and may take a considerable amount of time depending magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the resolution that you specifysurface of each triangular cell. To define a new Field SensorOn flat surfaces, follow the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these stepscells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Illumina's Mesh Settings dialog.]]</td></tr></table>

* Right click on Since EM.Illumina is a surface simulator, only the '''Field Sensors''' item exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the '''Observables''' section default PO mesh of a surface object consists of coinciding double cells, one representing the Navigation Tree upper or positive side and select '''Insert New Observablethe other representing the lower or negative side.This may lead to a very large number of cells.EM.Illumina'''* The '''Label''' box allows s mesh generator has settings that allow you to change the sensor’s nametreat all mesh cells as double-sided or all single-sided. you You can also change do that in the color of the field sensor plane using Mesh Settings dialog by checking the boxes labeled '''ColorAll Double-Sided Cells''' button.* Set the and '''DirectionAll Single-Sided Cells''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' useful when your project workspace contains well-organized and '''Z''', with the last being the default optionwell-oriented surface CAD objects only.* By default [[EM.Cube]] creates a field sensor plane passing through In the origin of coordinates (0single-sided case,0,0) on it is very important that all the XY plane. You can change normals to the location of cells point towards the sensor plane to any point by typing source. Otherwise, your surfaces fall in new values for the Xshadow region, Y and Z no currents will be computed on them. By checking the box labeled '''Center CoordinatesReverse Normal''', you instruct EM. You can also change these coordinates using Illumina to reverse the spin buttons.* The initial size direction of the sensor plane is 100 × 100 project units. You can change normal vectors globally at the dimensions surface of all 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 timescells.

After closing the Field Sensor Dialog, a new field sensor item immediately appears under the [[Image:Info_icon.png|30px]] Click here to learn more about '''Observables''' section in the Navigation Tree[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. Once a PO simulation is finished, a total of 14 plots are added to every field sensor node in the Navigation TreeCube. These include the magnitude and phase of all three components of 27s_Mesh_Generators | Working with Mesh Generator]]'''E''' and '''H''' fields and the total electric and magnetic field values. Click on any of these items and a color-coded intensity plot of it will be visualized on the project workspace. A legend box appears in the upper right corner of the field plot, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between 0 and 1. The legend box contains the minimum field value corresponding to 0 of the color map, maximum field value corresponding to 1 of the color map, and the unit of the field quantity, which is V/m for E-field and A/m for H-field. The values of phase plots are always shown in Radians between -p and p.To display the fields properly, the structure is cut through the field sensor plane, and only part of it is shown. If the structure still blocks your view, you can simply hide or freeze it. You can change the view of the field plot with the available view operations such as rotate view, pan, zoom, etc.

{{Note|Keep in mind that since Physical Optics is an asymptotic method, the field sensors must be placed at adequate distances (at least one or few wavelengths) away from the scatterers to produce acceptable results.}} [[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#Visualizing_3D_Near-Field_Maps The_Triangular_Surface_Mesh_Generator | Visualizing 3D Near Field MapsEM.Illumina's Triangular Surface Mesh Generator ]]'''.

<td> [[Image:PO42(4)POShip1.png|thumb|300px600px|PO Module's Field Sensor dialogGeometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td><td/tr> [[Image:PO43.png|thumb|400px|Near field plot of electric field on a sensor plane.]] </tdtr><td> [[Image:PO44POShip2.png|thumb|400px600px|Near field plot Trinagular surface mesh of magnetic field on a sensor planethe metallic battleship model.]] </td>

=== Computing Radiation Patterns =Running PO Simulations in EM.Illumina ==

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. The 3D plots can be viewed by clicking on their name in the navigation tree. They are displayed in [[=== EM.Cube]]Illumina's project workspace and are overlaid on the project's structure. Simulation Modes ===

Once you have set up your structure in [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about , have defined sources and observables and have examined the theory quality of the structure'''s mesh, you are ready to run a Physical Optics simulation. [[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field ComputationsEM.Illumina]]'''.offers five simulation modes:

{| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[Image#Running A Single-Frequency PO Analysis | Single-Frequency Analysis]]| style="width:Info_icon270px;" | 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.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube |40pxFrequency Sweep]] Click here to learn | 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 about '''project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Data_Visualization_and_ProcessingParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Visualizing_3D_Radiation_Patterns Performing_Optimization_in_EM.Cube | Visualizing 3D Radiation PatternsOptimization]]'''| 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|}

You can set the simulation mode from [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about '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. === Running A Single-Frequency PO Analysis === To open [[EM.Illumina]]'s Simulation Run dialog, click the '''Run'''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation GraphsFile:run_icon.png]]button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Run...'''or use the keyboard shortcut {{key|Ctrl+R}}. To start the simulation click the {{key|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.

<td> [[Image:PO45Illumina L1 Fig10A.png|thumb|300pxleft|480px|EM.Illumina's Radiation Pattern Simulation Run dialog.]] </td><td> [[Image:PO46.png|thumb|500px|3D radiation pattern of a parabolic dish reflector excited by a short dipole at its focal point.]] </td>

=== Computing Radar Cross Section Setting The Numerical Parameters ===

When the physical structure is excited by Before you run a plane wave sourcePO simulation, you can change some of the calculated far field data indeed represent the scattered fieldsPO simulation engine settings. While in the [[EM.CubeIllumina]] calculates 's '''Simulation Run Dialog''', click the radar cross section (RCS) of a target'''Settings''' button next to the '''Select Engine''' dropdown list. Three RCS quantities In the Physical Optics Engine Settings Dialog, there are computedtwo 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 &theta; lit and &phi; components shadow cells in the structure's mesh. For the termination of the radar cross section as well as the total radar cross sectionIPO solver, which there are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, [[EM.Cube]]'s [[PO Module]] calculates two types of RCS for each structureoptions: '''Bi-Static RCSConvergence Error''' and '''Mono-Static RCSMaximum Number of Iterations'''. In bi-static RCSThe default Termination Criterion is based on convergence error, the structure is illuminated by which has a plane wave at incidence angles &theta;_{default value of 0} .1 and &phi;<sub>0<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/sub>, and M''' current solution of the entire discretized structure from one iteration to the RCS is measured and plotted at all &theta; and &phi; anglesnext. In mono-static RCSNote that for this purpose, the structure is illuminated magnetic currents are scaled by a plane wave at incidence angles &thetaeta;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 recordedresidual error vector.

To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. Right click on You can also use higher- or lower-order integration schemes for the '''Far Fields''' item in the '''Observables''' section calculation of the Navigation Tree and select '''Insert New RCS.field integrals.[[EM.Cube]]''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change s PO simulation engine uses triangular cells for the name mesh of the far field or change the color physical surface structures and rectangular cells for discretization of the far field box using the '''Color''' buttonHuygens sources and surfaces. Select the type For integration of RCS from the two radio buttons labeled triangular cells, you have three options: '''Bi7-Static RCSPoint Quadrature''' and , '''Mono3-Static RCSPoint Quadrature'''. The former is the default choice. The resolution of RCS calculation is specified by and '''Angle IncrementConstant''' expressed in degrees. By default, the &theta; and &phi; angles are incremented by 5 degrees. At the end For integration of a PO simulationrectangular cells, besides calculating the RCS data over the entire (spherical) 3D spacetoo, a number of 2D RCS graphs are also generated. These are RCS cuts at certain planes, which include the you have three principal XY, YZ and ZX planes plus one additional constant f-cut. This latter cut is at f = 45° by default. You can assign another azimuth angle in degrees in the box labeled options: '''Non9-Principal Phi PlanePoint Quadrature'''. At the end of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the Navigation Tree. 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. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]4-Point Quadrature'''. [[Image:Info_icon.png|40px]] Click here to learn more about and '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]Constant'''.

<td> [[ImageFile:PO47PO28.png|thumb|300pxleft|480px|EM.Illumina's Radar Cross Section Simulation Engine Settings dialog.]] </td><td> [[Image:PO48.png|thumb|500px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>

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