Changes

=== Visualizing The the Far Fields -Field Radiation Patterns ===

Even though the planar EM.Pplanar MoM engine does not need a radiation box, you still have to define a "Far Field" observable for radiation pattern calculation. This is because far field calculations take time and you have to instruct [[EM.Cube]] to perform these calculations. To define a far field, right click the '''Far Fields''' item in the '''Observables''' section of the Navigation Tree and select '''Insert New Radiation Pattern...'''. The Radiation Pattern Dialog opens up. You may accept the default settings, or you can change the value of '''Angle Increment''', which is expressed in degrees. You can also choose to '''Normalize 2D Patterns'''. In that case, the maximum value of a 2D paten graph will have a value of 1; otherwise, the actual far field values in V/m will be used on the graph.

Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in θ direction, the far field component in φ direction and the "Total" far field. The 3D plots can be viewed in the project workspace by clicking on each item. The view of the 3D far field plot can be changed with the available view operations such as rotate view, pan, zoom, etc. If the structure blocks the view of the radiation pattern, you can simply hide or freeze the whole structure or parts of it. In a 3D radiation pattern plot, the fields are always normalized to the maximum value of the total far field for visualization purpose:

[[Image:<math>MORE.png|\mathbf{E_{ff,tot}}40px]] Click here to learn more about the theory of '''[[Data_Visualization_and_Processing#Far-Field_Observables | = \sqrt{ Far Field Computations]]'''. [[Image:MORE.png|E_{\theta}40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Radiation_Patterns |^2 + |E_{\phi}|^2 }</math>Visualizing 3D Radiation Patterns]]'''. <!--[[FileImage:PMOM89MORE.png|40px]]-->Click here to learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D Radiation Graphs]]'''.

When a planar structure is excited by a plane wave source, the calculated far field data indeed represent the scattered fields of that planar structure. [[EM.CubePicasso]] can also calculate the radar cross section (RCS) of a planar target: :<math> \sigma_{\theta} = 4\pi r^2 \dfrac{|E_{\theta}^{scat}|^2}{|E^{inc}|^2}, \quad \sigma_{\phi} = 4\pi r^2 \dfrac{|E_{\phi}^{scat}|^2}{|E^{inc}|^2}, \quad \sigma = \sigma_{\theta} + \sigma_{\phi} = 4\pi r^2 \dfrac{|E_{tot}^{scat}|^2}{|E^{inc}|^2} </math><!--[[File:PMOM123.png]]--> '''Note that in this case the RCS is defined for a finite-sized target in the presence of an infinite background structure.''' The scattered &theta; and &phi; components of the far-zone electric field are indeed what you see in the 3D far field visualization of radiation (scattering) patterns. Instead of radiation or scattering patterns, you can instruct [[EM.CubePicasso]] to plot 3D visualizations of &sigma;_&theta;, &sigma;_&phi; and the total RCS. To do so, you must define an RCS observable instead of a radiation pattern. Follow by following these steps:

At the end of a planar MoM simulation, in the far field section of the Navigation Tree, you will have the &theta; and &phi; components of RCS as well as the total radar cross section[[Image:MORE. You can view a png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_RCS | Visualizing 3D visualization of these quantities by clicking on their entries in the Navigation Tree. The RCS values are expressed in m²]]'''. The 3D plots are normalized  [[Image:MORE.png|40px]] Click here to the maximum learn more about '''[[Data_Visualization_and_Processing#2D_Radiation_and_RCS_Graphs | Plotting 2D RCS value, which is also displayed in the legend boxGraphs]]'''.