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[[Image:Splash-po.jpg|right|750px720px]]<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 a full-wave analysis solution becomes prohibitively expensive. Based on a high frequency asymptotic physical optics formulation, EM.Illumina it assumes that a source like a short dipole radiator or an incident plane wave induces source generates 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 Ray tracing from each source to the points on the scatterers to determine whether they fall into the are lit or shadow regions. But this can become shadowed is a time consuming task depending on the size of the computational problem. Besides GO-POTo avoid this difficulty, [[EM.Illumina also offers ]]'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.

{{Note|EM.Illumina is the high-frequency, asymptotic '''[[Physical Optics Module]]''' of '''[[EMImage:Info_icon.Cubepng|30px]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Illumina shares Click here to lean more about the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCADBasic Principles of Physical Optics | Theory of Physical Optics]]''' with all of [[EM.Cube]]'s other computational modules.}}

<table><tr><td> [[Image:Info_iconIllumina L2 Fig title.png|40px]] Click here to learn more about '''[[Getting_Started_with_EM.CUBE thumb| EMleft|420px|Analyzing scattering from a trihedral corner reflector using IPO solver.Cube Modeling Environment]]'''.</td>[[Image:Info_icon.png|40px]] Click here to learn more about the basic functionality of '''[[CubeCAD]]'''.</tr>=== Physical Optics as an Asymptotic Technique ===</table>

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== EM. 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 Illumina as 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 Module of the simulation engine of [[EM.Terrano]]. Cube ===

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[[EM. This concept Illumina]] is based on the fundamental equivalence theorem of electromagnetics and the Huygens principle. The electric surface currents are denoted by high-frequency, asymptotic '''J(r)Physical Optics Module''' and the magnetic surface currents are denoted by of '''M(r)[[EM.Cube]]''', where '''r''' is the position vectora comprehensive, integrated, modular electromagnetic modeling environment. [[EM. According to Illumina]] shares the Huygens principlevisual interface, 3D parametric CAD modeler, data visualization tools, the equivalent electric and magnetic surface currents are derived from the tangential components many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of magnetic and electric fields on a given surface, respectively[[EM. 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 consideredCube]]'s other computational modules.

[[Image:Info_iconEM.png|40pxIllumina]] Click here to lean more about the '''s simulator is seamlessly interfaced with [[Theory of Physical OpticsEM.Cube|EM.CUBE]]'''s other simulattion engines. This module is the ideal place to define Huygens sources. These are based on Huygens surface data that are generated using a full-wave simulator like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]].

[[Image:PO18(1).png|thumb|250px|=== Advantages & Limitations of EM.Illumina's Navigation Tree.]]=== Grouping Objects By Surface Type PO Solver ===

[[EM.Illumina organizes physical objects by their surface type. Any object in EM.Illumina is assumed to be made of one of the three surface types: # Perfect Electric Conductor (PEC)# Perfect Magnetic Conductor (PMC)# Generalized Impedance Surface EM.Illumina can only handle surface and solid CAD objects. Only the outer surface of [[Solid Objects|solid objects]] is considered in the PO simulation. No line or [[Curve Objects|curve objects]] are allowed in the project workspace; or else, they will be ignored during the PO simulation. You can define several PEC, PMC or impedance surface groups with different colors and impedance values. All the objects created and drawn under provides a group share the same color and other properties.  [[Image:Info_icon.png|40px]] Click here computationally efficient alternative to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Surface Group]]'''. Once a new surface node has been created on the navigation tree, it full-wave solutions for extremely large structures when full-wave analysis becomes the "Active" surface group of the project workspace, which is always listed in bold lettersprohibitively expensive. When you draw a new CAD object such as a Box or a SphereFor simple scatterer geometries, it is inserted under the currently active surface type. There is only one surface group that is active at any time. Any surface type can be made active by right clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu. It is recommended that you first create surface groups, and then draw new objects under the active surface group. However, if you start a new EM.Illumina project from scratch, and start drawing a new object without having previously defined any surface groups, a new default PEC surface group is created and added to the navigation tree to hold your new CAD object. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Material Groups]]'''. {{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 EM.Illumina.}} [[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Defining Materials in EM.Cube]]'''. == Discretizing the Physical Structure == [[File:PO4.png|thumb|360px|EM.Illumina's Mesh Settings dialogGO-PO solver is fairly adequate.]]EM.Illumina uses a triangular surface mesh to discretize But for complex geometries that involve multiple shadowing effects, the structure of your project workspaceIPO solver must be utilized. The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the entire structure. You IPO technique can control the cell size using the "Mesh Density" parameter. By defaulteffectively capture dominant, the mesh density is expressed in terms of the freenear-space wavelengthfield, multiple scattering effects from electrically large targets with concave surfaces. The default mesh density is 10 cells per wavelength. In the You have to remember that 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. Since EM.Illumina is a surface simulator, only the exterior surface of solid CAD objects is discretized, as the interior volume . This is not taken into account in a PO analysis. By contrast, surface CAD problem for PEC and PMC objects are assumed to be double-sided. In other words, the default PO mesh of a surface object consists of coinciding double cellswhich have zero internal fields, one representing the upper or positive side and even impedance surfaces, where you can satisfy the other representing the lower or negative boundary conditions on one side. This may lead to of 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''' and '''All Single-Sided Cells'''. This is useful when your project workspace contains well-organized and well-oriented surface CAD objects only. In PO analysis cannot handle the single-sided case, it is very important that all the normals to the cells point towards the sourcefields inside dielectric objects. OtherwiseAdditionally, 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|40px]] Click here to learn more about '''[[Mesh_Generation_Schemes_in_EM.Cube#Working_with_Mesh_Generator | Working with Mesh Generator ]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about EM.Illumina's '''[[Mesh_Generation_Schemes_in_EM.Cube#The_Triangular_Surface_Mesh_Generator | Triangular Surface Mesh Generator ]]'''most coupling effects between adjacent scatterers are ignored.

<td> [[Image:POShip1PO Ship Pattern.png|thumb|600pxleft|Geometry 550px|Computed radiation pattern of a metallic battleship model with a short horizontal dipole radiator above it.]] </td></tr><tr><td> [[Image:POShip2.png|thumb|600px|Trinagular surface mesh of the over a large metallic battleship model.]] </td>

[[File:PO30== EM.png|thumb|360px|PO Module's Short Dipole Source dialog]][[File:PO29.png|thumb|420px|PO Module's Plane Wave dialog]]Illumina Features at a Glance ==

== Excitation Sources = Structure Definition ===

<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 '''[[Common_Excitation_Source_Types_in_EM.Cube#Hertzian_Dipole_Sources | Hertzian Dipole Sources]]'''.or external files)</li> <li> Huygens sources imported from PO or other modules with arbitrary rotation and array configuration</li></ul>

=== Plane Wave Sources Mesh Generation ===

Your physical structure in EM.Illumina can be excited by an incident plane wave. In particular, a plane wave source is needed to compute the radar cross section <ul> <li> Surface triangular mesh with control over tessellation parameters</li> <li> Local mesh editing of a target. A plane wave is defined by its propagation vector indicating the direction of incidence and its polarization. EM.Illumina provides the following polarization options: TMz, TEz, Custom Linear, LCPz and RCPz.polymesh objects</li></ul>

The direction of incidence is defined through the &theta; and &phi; angles of the unit propagation vector in the spherical coordinate system. The values of these angles are set in degrees in the boxes labeled '''Theta''' and '''Phi'''. The default values are &theta; = 180° and &phi; = 0° representing a normally incident plane wave propagating along the -Z direction with a +X-polarized E-vector. In the TM_z and TE_z polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The components of the unit propagation vector and normalized E- and H-field vectors are displayed in the dialog. In the more general case of custom linear polarization, besides the incidence angles, you have to enter the components of the unit electric '''Field Vector'''. However, two requirements must be satisfied: '''ê . ê''' = 1 and '''ê × k''' Physical Optics Simulation == 0 . This can be enforced using the '''Validate''' button at the bottom of the dialog. If these conditions are not met, an error message pops up. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to the normal incidence only (&theta; = 180°).

To define a plane wave <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 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 follow these steps:parameters</li> <li> Multi-variable and multi-goal optimization of structure</li> <li> Remote simulation capability</li> <li> Both Windows and Linux versions of PO simulation engine available</li></ul>

=== <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 Sources ===surface data generation for use in PO or other [[EM.Cube]] modules</li> <li> Far field radiation patterns: 3D pattern visualization and 2-D Cartesian and polar graphs</li> <li> Bi-static and monostatic radar cross section: 3D visualization and 2D graphs</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>

[[File:po_phys17== Building the Physical Structure in EM.png|thumb|300px|PO Module's Huygens Source dialog]]Illumina ==

At the end === The Variety of a full-wave simulation Surface Types in the [[EM.Cube]]'s FDTD, MoM3D, Planar or Physical Optics Modules, you can generate Huygens surface data. According to Huygens' principle, if one knows the tangential electric and magnetic field components on a closed surface, one can determine the total electric and magnetic fields everywhere inside and outside that closed surface. Huygens surfaces are defined around a structure for recording the tangential components of electric and magnetic fields at the end of full-wave simulation of the structure. The tangential electric and magnetic fields are saved into ASCII data files as magnetic and electric currents, respectively. These current can be used as excitation for other structures. In other words, the electric and magnetic currents associated with a Huygens source radiate energy and provide the excitation for the [[PO Module]]'s physical structure.Illumina ===

In order to define a Huygens source, you need to have a Huygens data file of '''[[EM.HUY''' Illumina]] organizes physical objects by their surface type. This file Any object in [[EM.Illumina]] is generated as an output data file at the end assumed to be made of an FDTD, MoM3D, Planar or PO simulation, if you have defined a Huygens Surface observable in one of those projects. When you define a Huygens source, you indeed import an existing Huygens the three surface into the project and set it as an excitation source.types:

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

* Right click Click on the '''Huygens Sources''' item each category to learn more details about it in the '''Sources''' section of the Navigation Tree and select '''Import Huygens Source...''' from the contextual menu.* The standard [[Windows]] Open Dialog opens up. The file type is set to '''.HUY''' by default. Browse your folders to find a Huygens surface data file with a '''.HUY''' file extension. Select the file and click the '''Open''' button Glossary of the dialog to import the dataEM.* Once imported, the Huygens source appears in the Project Workspace as a wire-frame box.* You can open the property dialog of a Huygens source by right clicking on its name in the Navigation Tree and selecting Cube'''Properties...''' From this dialog you can change the color of the Huygens source box as well as its location and orientation. You can enter new values for the Xs Materials, YSources, 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 Devices &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 workspaceOther Physical Object Types]].

[[File:PO34EM.png|400pxIllumina]] [[File:PO35can 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.png|400px]]

{{Note|In [[File:PO27.png|thumb|400px|EM.Illumina's Simulation Run dialog.Cube]]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 '''Ctrl+R'''. To start the simulation click the '''Run''' button of this dialog. Once the PO simulation startsyou can import external CAD models (such as STEP, a new dialog called '''Output Window''' opens up that reports the various stages of PO simulationIGES, STL models, displays the running time and shows the percentage of completion for certain tasks during the PO simulation processetc. A prompt announces the completion of the PO simulation) only to CubeCAD. At this timeFrom CubeCAD, [[you can then move the imported objects to 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 sourceIllumina.}}

[[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 in the [[PO Module]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by &eta;₀ in the residual error vector.Excitation Sources ==

You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.CubeIllumina]]'s PO simulation engine uses triangular cells provides three types of sources for the mesh excitation of the your physical surface structures and rectangular cells for discretization of Huygens sources and surfaces. For integration of triangular cells, you have three optionsoptics simulation: '''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'''.

{| class="wikitable"|-! scope="col"| Icon! scope= PO Sweep Simulations "col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:hertz_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source |Hertzian Short Dipole Source]]| style="width:300px;" | Almost omni-directional physical radiator| style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:plane_wave_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Plane Wave |Plane Wave Source]]| style="width:300px;" | Used for modeling scattering | style="width:300px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source |Huygens Source]]| style="width:300px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:300px;" | Imported from a Huygens surface data file|}

[[Image:po_phys52.png|thumb|300px|EM.Illumina's Frequency Settings dialog.]]You can run EM.Illumina's PO simulation engine Click on each category to learn more details about it in 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. [[Glossary of EM.Cube]]'s [[PO ModuleMaterials, Sources, Devices & Other Physical Object Types]] 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 you select either frequency or angular sweep, the '''Settings''' button located next to 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 of frequency samples. The start and end frequency values are initially set based on the projectIllumina's center frequency and bandwidth. During a frequency sweep, as the project's frequency changes, so does the wavelength. As a result, the mesh of the structure also changes at each frequency sample. The frequency settings dialog gives you three choices regarding the mesh of the project structure during a frequency sweep:Simulation Data & Observables ==

# Fix mesh at [[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 highest frequencyPhysical Optics method are the electric and magnetic surface current distributions on the surface of your structure.# Fix mesh at At the center frequencyend of a PO simulation, [[EM.# ReIllumina]] 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-mesh at each frequencyfield quantities such as radiation patterns and radar cross section (RCS).

You can run an angular sweep only if your project has a plane wave excitation[[EM. In this case, you have to define a plane wave source with Illumina]] currently provides the default settings. During an angular sweep, either the incident theta angle or incident phi angle is varied within the specified range. The other angle remains fixed 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 samples.following observables:

In a parametric sweep, one or more user defined {| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[variablesFile:currdistr_icon.png]] are varied at the same time over their specified ranges. This creates a parametric space with the total number | style="width:150px;" | Current Distribution Maps| style="width:150px;" | [[Glossary of samples equal to the product of the number of samples for each variableEM. The user defined Cube's Simulation Observables & Graph Types#Current Distribution |Current Distribution]]| style="width:300px;" | Computing electric surface current distribution on PEC and impedance surfaces and magnetic surface current distribution on PMC and impedance surfaces| style="width:250px;" | None|-| style="width:30px;" | [[variablesFile:fieldsensor_icon.png]] are defined using | style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube]]'s '''[[VariablesSimulation Observables & Graph Types#Near-Field Sensor |Near-Field Sensor]] Dialog'''. For | style="width:300px;" | Computing electric and magnetic field components on a description of specified plane in the frequency domain| style="width:250px;" | None|-| style="width:30px;" | [[EMFile:farfield_icon.Cubepng]] | style="width:150px;" | Far-Field Radiation Characteristics| style="width:150px;" | [[variablesGlossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern |Far-Field Radiation Pattern]], please refer to the &quot| style="width:300px;Parametric Modeling" | Computing the radiation pattern and additional radiation characteristics such as directivity, Sweep &ampaxial ratio, side lobe levels, etc. | style="width:250px; " | None|-| style="width:30px;" | [[OptimizationFile:rcs_icon.png]]&quot| style="width:150px; section of " | Far-Field Scattering Characteristics| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Radar Cross Section (RCS) |Radar Cross Section (RCS)]] Manual or see | style="width:300px;" | Computing the &quotbistatic and monostatic RCS of a target| style="width:250px;Parametric Sweep&quot" | Requires a plane wave source|-| style="width:30px; sections of the FDTD or " | [[Planar ModuleFile:huyg_surf_icon.png]] manuals| 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|}

At Current distributions are visualized on the end surface of a Physical Optics simulationPO mesh cells, EM.Illumina generates a number and the magnitude and phase of output data files that contain all the computed simulation data. The primary output data in Physical Optics are the electric and magnetic surface currents are plotted for all the objects. A single current distributions 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 your structure. Once these quantities are knownthe individual mesh cells, EM.Illumina can compute near-field distributions as well as far-field quantities such as radiation patterns some parts of the plots may be blocked by and radar cross section (RCS)hidden inside smooth and curved objects. EM.Illumina does not generate any output data on its own unless To be able to view those parts, you define observables for your simulation projectmay have to freeze the obstructing objects or switch to the mesh view mode.

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 cells, and the magnitude and phase of the electric and magnetic surface currents are plotted for all the objects. In order to view these currents, you must first define a current distribution observable before running the PO simulation. To do this, right click on the '''Current Distributions''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''. The Current Distribution Dialog opens up. Accept the default settings and close the dialog. A new current distribution node is added to the Navigation Tree. Unlike the [[Planar Module]], in the [[PO ModuleEM.Illumina]] allows you can define only one current distribution node in to visualize the Navigation Tree, which covers all the objects in the project workspace. After near fields at a PO simulation is completed, new plots are added under the current distribution node predefined field sensor plane of the Navigation Treearbitrary dimensions. Separate plots are produced for the magnitude Calculation of near fields is a post-processing process and phase may take a considerable amount 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 time depending on a normalized scale with the minimum and maximum values displayed in the legend box. The phase maps are plotted in radians between -p and p. Note resolution that sometimes the current distribution plots may hide inside smooth and curved objects, and you cannot see them. You may have to freeze such objects or switch to the mesh view modespecify.

[[Image:Info_icon.png{{Note|40px]] Click here 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 learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Current_Distribution_Maps | Visualizing 3D Current Distribution Maps]]'''produce acceptable results.}}

<td> </td><td> [[Image:PO37PO43.png|thumb|300px360px|PO Module's Current Distribution dialogElectric field distribution on a sensor plane above a metallic sphere.]] </td><td> [[Image:PO38PO44.png|thumb|500px360px|The current Magnetic field distribution plot of on a PEC sphere illuminated by an obliquely incident sensor plane waveabove a metallic sphere.]] </td>

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

[[EM.Cube]] allows you to visualize the near fields {{Note| The 3D radiation pattern is always displayed at a specific field sensor plane. Calculation the origin of near fields is a post-processing process and may take a considerable amount of time depending on the resolution that you specifyspherical coordinate system, (0,0,0), with respect to which the far radiation zone is defined. To define a new Field SensorOftentimes, follow these steps:this might not be the radiation center of your physical structure.}}

* Right click on the '''Field Sensors''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Observable...'''<table>* The '''Label''' box allows you to change the sensor’s name. you can also change the color of the field sensor plane using the '''Color''' button.<tr>* Set the '''Direction''' of the field sensor. This is specified by the normal vector of the sensor plane. The available options are '''X''', '''Y''' and '''Z''', with the last being the default option.* By default <td> [[EMImage:PO46.Cube]] creates png|thumb|360px|3D radiation pattern of a field sensor plane passing through the origin of coordinates (0,0,0) on the XY plane. You can change the location of the sensor plane to any parabolic dish reflector excited by a short dipole at its focal point by typing in new values for the X, Y and Z '''Center Coordinates'''. You can also change these coordinates using the spin buttons.]] </td>* The initial size of the sensor plane is 100 × 100 project units. You can change the dimensions of the sensor plane to any desired size. You can also set the '''Number of Samples''' along the different directions. These numbers determine the resolution of near field maps. Keep in mind that large numbers of samples may result in long computation times.</tr></table>

After closing the Field Sensor DialogWhen your physical structure is excited by a plane wave source, a new field sensor item immediately appears under the '''Observables''' section in the Navigation Tree. Once a PO simulation is finished, a total of 14 plots are added to every calculated far field sensor node in data indeed represent the Navigation Treescattered fields. These include the magnitude and phase of all three components [[EM.Illumina]] can calculate two types of RCS for each structure: '''EBi-Static RCS''' and '''HMono-Static RCS''' fields and the total electric and magnetic field values. Click on any of these items and a colorIn bi-coded intensity plot of it will be visualized on the project workspace. A legend box appears in the upper right corner of the field plotstatic RCS, which can be dragged around using the left mouse button. The values of the magnitude plots are normalized between structure is illuminated by a plane wave at incidence angles &theta;₀ and 1. The legend box contains the minimum field value corresponding to &phi;_{0 of the color map, maximum field value corresponding to 1 of the color map}, and the unit of the field quantity, which RCS is V/m for E-field measured and A/m for H-fieldplotted at all &theta; and &phi; angles. The values of phase plots are always shown in Radians between In mono-p and p.To display the fields properlystatic RCS, the structure is cut through the field sensor illuminated by a planewave at incidence angles &theta;₀ and &phi;₀, and only part of it the RCS is shownmeasured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. If It is clear that in the structure still blocks your viewcase of mono-static RCS, you can simply hide or freeze it. You can change the view PO simulation engine runs an internal angular sweep, whereby the values of the field plot with plane wave incidence angles &theta; and &phi; are varied over the available view operations such as rotate viewentire intervals [0°, pan180°] and [0°, zoom360°], etcrespectively, and the backscatter RCS is recorded.

{{Note|Keep in mind that since Physical Optics is To calculate RCS, first you have to define an asymptotic methodRCS 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 sensors must be placed at adequate distances (at least one or few wavelengths) away from section of the scatterers to produce acceptable resultsnavigation tree. Keep in mind that computing the 3D mono-static RCS may take 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_Near-Field_Maps | Visualizing 3D Near Field Maps]]'''which the far radiation zone is defined. Oftentimes, this might not be the scattering center of your physical structure.}}

<td> [[Image:PO42(4)PO48.png|thumb|300px420px|PO Module's Field Sensor dialog]] </td><td> [[Image:PO43.png|thumb|400px|Near field plot of electric field on a sensor plane.]] </td><td> [[Image:PO44.png|thumb|400px|Near field plot RCS of magnetic field on a sensor PEC sphere illuminated by an laterally incident planewave.]] </td>

=== Computing Radiation Patterns =Discretizing the Physical Structure in EM.Illumina ==

Unlike the FDTD method, Physical Optics is an open-boundary techniqueEM. You do not need Illumina uses a far field box triangular surface mesh 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 discretize the '''Far Fields''' item in the '''Observables''' section structure of the Navigation Tree and selecting '''Insert New Radiation Patternyour project workspace...''' from The mesh generating algorithm tries to generate regularized triangular cells with almost equal surface areas across the contextual menu. The Radiation Pattern dialog opens upentire structure. You can accept most of control the cell size using the "Mesh Density" parameter. By default settings in this dialog. The Output Settings section allows you to change , the '''Angle Increment''' mesh density is expressed in terms of the degrees, which sets the resolution of far field calculationsfree-space wavelength. The default value mesh density is 5 degrees10 cells per wavelength. After closing In the radiation pattern dialogPhysical Optics method, a far field entry immediately appears with its given name under the electric and magnetic surface currents, '''Far FieldsJ''' and '''M''' item of the Navigation Tree. After a PO simulation is finished, three radiation patterns plots are added assumed to be constant on the far field node in the Navigation Treesurface of each triangular cell. These are the far field component in &theta; directionOn flat surfaces, the far field component in &phi; direction and unit normal vectors to all the total far fieldcells are identical. Incident plane waves or other relatively uniform source fields induce uniform PO currents on all these cells. The 3D plots can Therefore, a high resolution mesh may not be viewed by clicking necessary on their name in the navigation treeflat surface or faces. Accurate discretization of curved objects like spheres or ellipsoids, however, requires a high mesh density. They are displayed in <table><tr><td> [[File:PO4.png|thumb|left|480px|EM.Cube]]Illumina's project workspace and are overlaid on the project's structureMesh Settings dialog. ]]</td></tr></table>

[[Image:Info_iconSince EM.png|40px]] Click here Illumina is a surface simulator, only the 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 learn more about be double-sided. In other words, the theory 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 ''[[Computing_the_Far_Fields_%26_Radiation_Characteristics| Far Field Computations]]'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#Visualizing_3D_Radiation_Patterns Working_with_EM.Cube.27s_Mesh_Generators | Visualizing 3D Radiation PatternsWorking with Mesh Generator]]'''.

[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Data_Visualization_and_ProcessingPreparing_Physical_Structures_for_Electromagnetic_Simulation#2D_Radiation_and_RCS_Graphs The_Triangular_Surface_Mesh_Generator | Plotting 2D Radiation GraphsEM.Illumina's Triangular Surface Mesh Generator ]]'''.

<td> [[Image:PO45POShip1.png|thumb|300px600px|EM.Illumina's Radiation Pattern dialogGeometry of a metallic battleship model with a short horizontal dipole radiator above it.]] </td></tr><tr><td> [[Image:PO46POShip2.png|thumb|500px600px|3D radiation pattern Trinagular surface mesh of a parabolic dish reflector excited by a short dipole at its focal pointthe metallic battleship model.]] </td>

=== Computing Radar Cross Section =Running PO Simulations in EM.Illumina ==

When the physical structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields. [[=== EM.Cube]] calculates the radar cross section (RCS) of a target. Three RCS quantities are computed: the &theta; and &phi; components of the radar cross section as well as the total radar cross section, which are dented by &sigma;_&theta;, &sigma;_&phi;, and &sigma;_tot. In addition, [[EM.Cube]]Illumina's [[PO Module]] calculates two types of RCS for each structure: '''Bi-Static RCS''' and '''Mono-Static RCS'''. In bi-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at all &theta; and &phi; angles. In mono-static RCS, the structure is illuminated by a plane wave at incidence angles &theta;₀ and &phi;₀, and the RCS is measured and plotted at the echo angles 180°-&theta;₀; and &phi;₀. It is clear that in the case of mono-static RCS, the PO simulation engine runs an internal angular sweep, whereby the values of the plane wave incidence angles &theta; and &phi; are varied over the entire intervals [0°, 180°] and [0°, 360°], respectively, and the backscatter RCS is recorded.Simulation Modes ===

To calculate RCS, first Once you have to define an RCS observable instead of a radiation patternset up your structure in [[EM. Right click on the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree Illumina]], have defined sources and select '''Insert New RCS...''' to open the Radar Cross Section Dialog. Use the '''Label''' box to change observables and have examined the name quality of the far field or change the color of the far field box using the structure'''Color''' button. Select the type of RCS from the two radio buttons labeled '''Bi-Static RCS''' and '''Mono-Static RCS'''. The former is the default choice. The resolution of RCS calculation is specified by '''Angle Increment''' expressed in degrees. By defaults mesh, the &theta; and &phi; angles you are incremented by 5 degrees. At the end of ready to run a PO Physical Optics simulation, besides calculating the RCS data over the entire (spherical) 3D space, a number of 2D RCS graphs are also generated. These are RCS cuts at certain planes, which include the 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 '''Non-Principal Phi Plane'''[[EM.Illumina]] offers five simulation modes:

At the end {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of a Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running A Single-Frequency PO simulation, Analysis | Single-Frequency Analysis]]| style="width:270px;" | Simulates the thee RCS plots &sigmaphysical structure "As Is"| style="width:80px;_{&theta" | Single run| style="width:250px;}, &sigma" | Runs at the center frequency fc| style="width:80px;_{&phi" | None|-| style="width:120px;}, and &sigma" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:270px;_tot are added under " | Varies the far field section operating frequency of the Navigation TreePO 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. These plots are very similar to the three 3D radiation pattern plotsCube#Running_Parametric_Sweep_Simulations_in_EM. You can view them by clicking on their names in Cube | Parametric Sweep]]| style="width:270px;" | Varies the navigation treevalue(s) of one or more project variables| style="width:80px;" | Multiple runs| style="width:250px;" | Runs at the center frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. The RCS values are expressed in m²Cube#Performing_Optimization_in_EM. For visualization purposes, Cube | Optimization]]| style="width:270px;" | Optimizes the 3D plots are normalized value(s) of one or more project variables to achieve a design goal | style="width:80px;" | Multiple runs | style="width:250px;" | Runs at the maximum RCS value, which is also displayed in the legend boxcenter frequency fc| style="width:80px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. Keep in mind that computing Cube#Generating_Surrogate_Models | HDMR Sweep]]| style="width:270px;" | Varies the 3D mono-static RCS may take an enormous amount value(s) of computation time.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#Visualizing_3D_RCS | Visualizing 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 RCS]]'''simulation data from the navigation tree.

=== Running A Single-Frequency PO Analysis === To open [[Image:Info_iconEM.png|40pxIllumina]] Click here to learn more about 's Simulation Run dialog, click the '''Run'''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS 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:PO47Illumina L1 Fig10A.png|thumb|300pxleft|480px|EM.Illumina's Radar Cross Section Simulation Run dialog.]] </td><td> [[Image:PO48.png|thumb|500px|RCS of a PEC sphere illuminated by an laterally incident plane wave.]] </td>

<p>=== Setting The Numerical Parameters === Before you run a PO simulation, you can change some of the PO simulation engine settings. While in the [[EM.Illumina]]'s '''Simulation Run Dialog''', click the '''Settings''' button next to the '''Select Engine''' dropdown list. In the Physical Optics Engine Settings Dialog, there are two options for '''Solver Type''': '''Iterative''' and '''GOPO'''. The default option is Iterative. The GOPO solver is a zero-order PO simulator that uses Geometrical Optics (GO) to determine the lit and shadow cells in the structure's mesh. For the termination of the IPO solver, there are two options: '''Convergence Error''' and '''Maximum Number of Iterations'''. The default Termination Criterion is based on convergence error, which has a default value of 0.1 and can be changed to any desired accuracy. The convergence error is defined as the L2 norm of the normalized residual error in the combined '''J/M''' current solution of the entire discretized structure from one iteration to the next. Note that for this purpose, the magnetic currents are scaled by &nbspeta;<sub>0</psub>in the residual error vector. You can also use higher- or lower-order integration schemes for the calculation of field integrals. [[EM.Cube]]'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'''. <table><tr><td> [[File:PO28.png|thumb|left|480px|EM.Illumina's Simulation Engine Settings dialog.]]</td></tr></table> <br /> <hr> [[Image:Top_icon.png|48px30px]] '''[[EM.Illumina#An_EM.Illumina_Primer Product_Overview | Back to the Top of the Page]]''' [[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Illumina_Documentation | EM.Illumina Tutorial Gateway]]'''

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