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[[Image:Splash-po.jpg|right|800px720px]]<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.

{{Note|[[EM.Illumina is the ]] 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 Module]]''' of '''[[EM.Cube]]'''physical optics formulation, it assumes that an incident source generates currents on a comprehensivemetallic structure, integrated, modular electromagnetic modeling environmentwhich in turn reradiate into the free space. EMA challenging step in establishing the PO currents is the determination of the lit and shadowed points on complex scatterer geometries.Illumina shares Ray tracing from each source to the visual interfacepoints on the scatterers to determine whether they are lit or shadowed is a time consuming task. To avoid this difficulty, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCAD]]''' with all of [[EM.CubeIllumina]]'s other computational modulessimulator uses a novel Iterative Physical Optics (IPO) formulation, which automatically accounts for multiple shadowing effects.The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets.}}

[[Image:Info_icon.png|40px30px]] Click here to learn lean more about the '''[[Getting_Started_with_EM.CUBE Basic Principles of Physical Optics | EM.Cube Modeling EnvironmentTheory of Physical Optics]]'''.

<table><tr><td> [[Image:Info_iconIllumina L2 Fig title.png|40pxthumb|left|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.]] Click here to learn more about the basic functionality of '''[[CubeCAD]]'''.</td></tr></table>

=== EM.Illumina as the Physical Optics as an Asymptotic Technique Module of EM.Cube ===

Asymptotic methods are usually valid at high frequencies as k₀ R = 2&pi; R/&lambda;₀ >> 1, where R [[EM.Illumina]] is the distance between the source and observation points, k₀ is the freehigh-space propagation constant and &lambda;₀is the free-space wavelengthfrequency, asymptotic '''Physical Optics Module''' of '''[[EM. Under such conditionsCube]]''', a comprehensive, integrated, modular electromagnetic fields and waves start to behave more like optical fields and wavesmodeling environment. Asymptotic methods are typically inspired by optical analysis[[EM. Two important examples of asymptotic methods are Illumina]] shares the Shoot-visual interface, 3D parametric CAD modeler, data visualization tools, and-Bounce-Rays (SBR) method many more utilities and Physical Optics (PO). The features collectively known as [[SBR MethodBuilding_Geometrical_Constructions_in_CubeCAD |SBR methodCubeCAD]] is a ray tracing method based on Geometrical Optics (GO) and forms the basis of the simulation engine with all of [[EM.TerranoCube]]'s other computational modules.

In the Physical Optics (PO) method, a scatterer surface [[EM.Illumina]]'s simulator is illuminated by an incident source, and it is modeled by equivalent electric and magnetic surface currentsseamlessly interfaced with [[EM.Cube|EM.CUBE]]'s other simulattion engines. This concept module is based on the fundamental equivalence theorem of electromagnetics. According ideal place to the define Huygens sources. These are based on Huygens principle, the equivalent electric and magnetic surface currents data that are derived from the tangential components of magnetic and electric fields on generated using a given closed surface, respectivelyfull-wave simulator like [[EM. A simple PO analysis involves only perfect electric conductorsTempo]], and only electric surface currents related to the tangential magnetic fields are considered. [[EM.Illumina assumes that a source like a short dipole radiator Picasso]] or an incident plane wave induces currents on the surface of the metallic structure[[EM. These induced currents, in turn, reradiate into the free space and produce the scattered fields. In the case of an impedance surface, both surface electric and magnetic currents are induced on the surface of the scattererLibera]].

A challenging step in establishing the PO currents is the determination of the lit and shadow 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 as the size of the computational problem grows. Besides GO-PO, EM.Illumina also offers a novel Iterative Physical Optics (IPO) solver, which dispenses with the GO part of GO-PO and automatically accounts for multiple shadowing effects using an iterative algorithm.  [[Image:Info_icon.png|40px]] Click here to lean learn more about the '''[[Theory of Physical OpticsGetting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.

[[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 IPO solver must be utilized. The IPO technique can effectively capture dominant, near-field, multiple scattering effects from electrically large targets with concave surfaces. You have to remember that Physical Optics is a surface simulator. This is not a problem for PEC and PMC objects, which have zero internal fields, or even impedance surfaces, where you can satisfy the boundary conditions on one side of a surface only. PO analysis cannot handle the fields inside dielectric objects. Additionally, most coupling effects between adjacent scatterers are ignored.

[[Image:PO18(1).png|thumb|250px|== EM.Illumina's Navigation Tree.]]=== Grouping Objects By Surface Type =Features at a Glance ==

# '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces | Perfect Electric Conductor <ul> <li> Metal (PEC) Surface]]'''solids and surfaces in free space</li># '''[[Defining_Materials_in_EM.Cube#Perfect_Magnetic_Conductors_.26_Slot_Traces | Perfect Magnetic Conductor ( <li> PMC) Surface]]'''and impedance surfaces in free space</li> <li> Import STL CAD files as native polymesh structures</li> <li> Huygens blocks imported from full-wave modules</li># '''[[Defining_Materials_in_EM.Cube#Impedance_Surfaces_.26_Conductive_Sheet_Traces | Generalized Impedance Surface]]'''</ul>

<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 [[Image:Info_iconEM.png|40pxTerrano]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Surface Group]]'''.or external files)</li> <li> Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li></ul>

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among <ul> <li> Surface Groups]]'''.triangular mesh with control over tessellation parameters</li> <li> Local mesh editing of polymesh objects</li></ul>

[[Image:Info_icon.png|40px]] Click here <ul> <li> Physical Optics solution of metal scatterers and impedance surfaces</li> <li> Conventional Geometrical Optics - Physical Optics (GOPO) solver</li> <li> Novel iterative PO solver for a general discussion 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> Both Windows and Linux versions of '''[[Defining Materials in EM.Cube]]'''.PO simulation engine available</li></ul>

== Discretizing the Physical Structure = Data Generation &amp; Visualization ===

[[File:PO4.png|thumb|360px|EM.Illumina's Mesh Settings dialog.]]<ul>EM.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric <li> Electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant current distributions on the surface of each triangular cell. On flat metallic or impedance surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. </li> <li>Since EM.Illumina is a Near field intensity plots (vectorial - amplitude &amp; phase)</li> <li> Huygens surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume is not taken into account data generation for use in a PO analysis. By contrast, surface CAD objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or positive side and the other representing the lower or negative side. This may lead to a very large number of cells. [[EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' Cube]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and '''All Single2-Sided Cells'''. This is useful when your project workspace contains well-organized D Cartesian and wellpolar graphs</li> <li> Bi-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, static and monostatic radar cross section: 3D visualization and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction 2D graphs</li> <li> Custom output parameters defined as mathematical expressions of the normal vectors globally at the surface of all the cells.standard outputs</li></ul>

[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator ]]'''== Building the Physical Structure in EM.Illumina ==

[[Image:Info_icon.png|40px]] Click here to learn more about === The Variety of Surface Types in EM.Illumina's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator ]]'''.===

<table><tr><td> [[Image:POShip1.png|thumb|600px|Geometry of a metallic battleship model with a short horizontal dipole radiator above itEM.Illumina]] </td></tr><tr><td> organizes physical objects by their surface type. Any object in [[Image:POShip2EM.png|thumb|600px|Trinagular surface mesh Illumina]] is assumed to be made of one of the metallic battleship model.]] </td></tr></table>three surface types:

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

EM.Illumina provides three types of sources for Click on each category to learn more details about it in the excitation [[Glossary of your physical optics simulation:EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

* '''[[#Hertzian Dipole Sources | Hertzian Dipole SourcesEM.Illumina]]'''* '''[[#Plane Wave Sources | Plane Wave Sources]]'''* '''[[Hybrid_Modeling_using_Multiple_Simulation_Engines#Working_with_Huygens_Sources | Huygens Sources]]''' can only handle surface and solid CAD objects. Only the outer surface of solid objects is considered in the PO simulation. No line or curve objects are allowed in the project workspace; or else, they will be ignored during the PO simulation.

A short Hertzian dipole is the simplest way of exciting a structure in EM[[Image:Info_icon.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 png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in its property dialogCubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.

[[Image:Info_icon.png{{Note|40px]] Click here to learn more about '''In [[Common_Excitation_Source_Types_in_EMEM.Cube#Hertzian_Dipole_Sources | Hertzian Dipole Sources]]''', you can import external CAD models (such as STEP, IGES, STL models, etc. === Plane Wave Sources === Your physical structure in EM) only to CubeCAD.Illumina can be excited by an incident plane wave. In particularFrom CubeCAD, 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 can then move the incidence angles are &theta; = 180° and &phi; = 0° corresponding imported objects to a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. EM.Illumina provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Common_Excitation_Source_Types_in_EM.Cube#Plane_Wave_Sources | Plane Wave Sources]]'''.}}

<td> [[File:PO30PO MAN1.png|thumb|360pxleft|EM.Illumina's Short Dipole Source dialog.]] </td><td> [[File:PO29.png|thumb|360px480px|EM.Illumina's Plane Wave dialognavigation tree.]] </td>

== Running PO Simulations EM.Illumina's Excitation Sources ==

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:PO27hertz_src_icon.png]]|thumb|400px|[[Glossary of EM.IlluminaCube's Simulation Run dialog.Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]To open EM.Illumina's Simulation Run dialog| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, click the '''Run''' stand-alone source|-| style="width:30px;" | [[File:run_iconplane_wave_icon.png]] button | [[Glossary of the '''Simulate ToolbarEM.Cube''' or select '''Menu s Materials, Sources, Devices &gtOther Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px; Simulate &gt" | Used for modeling scattering | style="width:300px; Run" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon...'''or use the keyboard shortcut '''Ctrl+R'''. To start the simulation click the '''Run''' button png]]| [[Glossary of this dialogEM. Once the PO simulation starts, a new dialog called Cube'''Output Window''' opens up that reports the various stages of PO simulations Materials, 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 timeSources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] generates modules | style="width:300px;" | Imported from a number of output Huygens surface 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.file|}

A short Hertzian dipole is the simplest way of exciting a structure in [[File:PO28.png|thumb|350px|EM.Illumina's Simulation Engine Settings dialog.]]Before you run a PO simulation, you can change some of the PO simulation engine settings. While 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 the [[PO ModuleEM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown listcan also be excited by an incident plane wave. In the Physical Optics Engine Settings Dialogparticular, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is you need a zero-order PO simulator that uses Geometrical Optics (GO) plane wave source to determine compute the lit and shadow cells in the structure's mesh. For the termination radar cross section of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''a target. The default Termination Criterion is based on convergence error, which has a default value direction of 0.1 and can be changed to any desired accuracy. The convergence error incidence is defined as by the L2 norm &theta; and &phi; angles of the normalized residual error unit propagation vector in the combined '''J/M''' current solution spherical coordinate system. The default values of the entire discretized structure from one iteration incidence angles are &theta; = 180° and &phi; = 0° corresponding to a normally incident plane wave propagating along the next-Z direction with a +X-polarized E-vector. Note Huygens sources are virtual equivalent sources that for this purpose, capture the radiated electric and magnetic currents are scaled by &eta;₀ fields from another structure that was previously analyzed in the residual error vectoranother [[EM.Cube]] computational module.

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[== EM.Cube]]Illumina's PO simulation engine uses triangular cells for the mesh of the physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three options: '''7-Point Quadrature''', '''3-Point Quadrature''' and '''Constant'''. For integration of rectangular cells, too, you have three options: '''9-Point Quadrature''', '''4-Point Quadrature''' and '''Constant'''.Simulation Data & Observables ==

=== [[EM.Illumina]] does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data in the Physical Optics method are the electric and magnetic surface current distributions on the surface of your structure. At the end of a PO Sweep Simulations ===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).

[[Image:po_phys52.png|thumb|300px|EM.Illumina's Frequency Settings dialog.]]You can run EM.Illumina's PO simulation engine in currently provides the sweep mode, whereby a parameter like frequency, plane wave incident angles or a user defined variable is varied over a specified range at predetermined samples. The output data are saved into data files for visualization and plotting. EM.Illumina currently offers three types of sweepfollowing observables:

{| 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# Frequency SweepCurrent 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# Parametric SweepNear-Field Sensor |Near-Field Sensor]] | style="width:300px;" | Computing electric and magnetic field components on a specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]]| style="width:300px;" | Computing the radiation pattern and additional radiation characteristics such as directivity, axial ratio, side lobe levels, etc. | style="width:250px;" | None|-| style="width:30px;" | [[File:rcs_icon.png]]| style="width:150px;" | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] | style="width:300px;" | Computing the bistatic and monostatic RCS of a target| style="width:250px;" | Requires a plane wave source|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | Equivalent electric and magnetic surface current data| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface |Huygens Surface]]| style="width:300px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None|}

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. If you select either frequency or angular sweep, the '''Settings''' button located next Click on each category to learn more details about it in the simulation mode dropdown list becomes enabled. If you click this button, the Frequency Settings Dialog or Angle Settings Dialog opens up, respectively. In the frequency settings dialog, you can set the start and end frequencies as well as the number [[Glossary of frequency samplesEM. The start and end frequency values are initially set based on the projectCube's center frequency and bandwidthSimulation Observables & Graph Types]]. 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 Current distributions are visualized on the surface of PO mesh at cells, and the highest frequencymagnitude and phase of the electric and magnetic surface currents are plotted for all the objects.# Fix A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. Since the currents are plotted on the surface of the individual mesh at cells, some parts of the center frequencyplots may be blocked by and hidden inside smooth and curved objects.# Re-To be able to view those parts, you may have to freeze the obstructing objects or switch to the mesh at each frequencyview mode.

In a parametric sweep, one or more user defined <table><tr><td> [[variables]] are varied at the same time over their specified rangesImage:PO38. This creates png|thumb|390px|The current distribution plot of a parametric space with the total number of samples equal to the product of the number of samples for each variablePEC sphere illuminated by an obliquely incident plane wave. The user defined [[variables]] are defined using [[EM.Cube]]'s '''[[Variables]] Dialog'''.</td></tr></table>

EM.Illumina does not produce any output data on its own unless you define one or more observables for your simulation project. The primary output data {{Note|Keep in the mind that since Physical Optics is an asymptotic 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 sensors must be placed at adequate distances (RCSat least one or few wavelengths)away from the scatterers to produce acceptable results. EM.Illumina currently provides the following observables:}}

Current distributions are visualized on {{Note| The 3D radiation pattern is always displayed at the surface origin of the PO mesh cellsspherical coordinate system, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order (0,0,0), with respect to view these currents, you must first define a current distribution observable before running which the PO simulationfar radiation zone is defined. A single current distribution node in the navigation tree holds the current distribution data for all the objects in the project workspace. After a PO simulation is completedOftentimes, new plots are added under this might not be the current distribution node. Separate plots are produced for the magnitude and phase radiation center of each of the electric and magnetic surface current components (X, Y and Z) as well as the total current magnitudeyour physical structure. }}

The current distributions are plotted on the surface <table><tr><td> [[Image:PO46.png|thumb|360px|3D radiation pattern of the individual mesh cells. As a result, some parts of the plots may be blocked parabolic dish reflector excited 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 modea short dipole at its focal point.]] </td></tr></table>

When your physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about can calculate two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. It is clear that in the case of mono-static RCS, the PO 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 [Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps 0°, 360°], respectively, and the backscatter RCS is recorded. To calculate RCS, first you have to define an RCS observable instead of a radiation pattern. At the end of a PO simulation, the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount of computation time. {{Note| Visualizing The 3D Current Distribution Maps]]'''RCS plot is always displayed at the origin of the spherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<td> [[Image:PO37PO48.png|thumb|330px420px|PO Module's Current Distribution dialog.]] </td><td> [[Image:PO38.png|thumb|390px|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.Illumina uses a triangular surface mesh to discretize the structure of your project workspace. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You can control the cell size using the "Mesh Density" parameter. By default, the mesh density is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. In the Physical Optics method, the electric and magnetic surface currents, '''J''' and '''M''', are assumed to be constant on the surface of each triangular cell. On flat surfaces, the unit normal vectors to all the cells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. Therefore, a high resolution mesh may not be necessary on flat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. <table><tr><td> [[ImageFile:PO42(4)PO4.png|thumb|350pxleft|480px|EM.Illumina's Field Sensor Mesh Settings dialog.]] EM.Illumina 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. </td></tr></table>

{{Note|Keep in mind that since Physical Optics Since EM.Illumina is an asymptotic methoda surface simulator, only the field sensors must 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 placed at adequate distances (at least double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cells, one representing the upper or few wavelengths) away from positive side and the scatterers other representing the lower or negative side. This may lead to produce acceptable resultsa very large number of cells. EM.Illumina's mesh generator has settings that allow you to treat all mesh cells as double-sided or all single-sided. You can do that in the Mesh Settings dialog by checking the boxes labeled '''All Double-Sided Cells''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In the single-sided case, it is very important that all the normals to the cells point towards the source. Otherwise, your surfaces fall in the shadow region, and no currents will be computed on them. By checking the box labeled '''Reverse Normal''', you instruct EM.Illumina to reverse the direction of the normal vectors globally at the surface of all the cells.}}

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#The_Field_Sensor_Observable Working_with_EM.Cube.27s_Mesh_Generators | Defining a Field Sensor ObservableWorking with Mesh Generator]]'''.

[[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> </td><td> [[Image:PO43POShip1.png|thumb|360px600px|Electric field distribution on a sensor plane above Geometry of a metallic spherebattleship model with a short horizontal dipole radiator above it.]] </td></tr><tr><td> [[Image:PO44POShip2.png|thumb|360px600px|Magnetic field distribution on a sensor plane above a Trinagular surface mesh of the metallic spherebattleship model.]] </td>

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

Physical Optics is an open-boundary technique, and 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. 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 are displayed in the project workspace and are overlaid on your physical structure=== EM. Illumina's 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 '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''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''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or select '''Menu &gt; Simulate &gt; Run...'''or use the keyboard shortcut {{Notekey| The 3D radiation pattern is always displayed at Ctrl+R}}. To start the origin simulation click the {{key|Run}} button of this dialog. Once the spherical coordinate systemPO simulation starts, (0,0,0)a new dialog called '''Output Window''' opens up that reports the various stages of PO simulation, with respect to which displays the far radiation zone is definedrunning time and shows the percentage of completion for certain tasks during the PO simulation process. Oftentimes, A prompt announces the completion of the PO simulation. At this might not be 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 center of your physical pattern data as well bi-static or mono-static radar cross sections (RCS) if the structureis excited by a plane wave source.}}

<td> [[Image:PO45Illumina L1 Fig10A.png|thumb|360pxleft|480px|EM.Illumina's Radiation Pattern Simulation Run dialog.]] </td><td> [[Image:PO46.png|thumb|360px|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.Illumina 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.Illumina 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. At You can also use higher- or lower-order integration schemes for the end calculation of a field integrals. [[EM.Cube]]'s PO simulation, engine uses triangular cells for the thee RCS plots &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot are added under the far field section mesh of the navigation tree. Keep in mind that computing the 3D mono-static RCS may take an enormous amount physical surface structures and rectangular cells for discretization of computation timeHuygens sources and surfaces. [[ImageFor integration of triangular cells, you have three options:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D RCS]]7-Point Quadrature'''. [[Image:Info_icon.png|40px]] Click here to learn more about , '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS Graphs]]3-Point Quadrature''' and '''Constant'''. {{Note| The 3D RCS plot is always displayed at the origin For integration of the spherical coordinate systemrectangular cells, (0too,0you have three options: '''9-Point Quadrature''',0), with respect to which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure'''4-Point Quadrature''' and '''Constant'''.}}

<td> [[ImageFile:PO47PO28.png|thumb|300pxleft|480px|EM.Illumina's Radar Cross Section Simulation Engine Settings dialog.]] </td><td> [[Image:PO48.png|thumb|420px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>

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