Editing Radar cross section (section)

=== Optimization methods ===
Thin non-resonant or broad resonance coatings can be modeled with a [[Mikhail Leontovich|Leontovich]] [[Electromagnetic impedance|impedance]] [[boundary condition]] (see also [[Electrical impedance]]).  This is the ratio of the tangential electric field to the tangential magnetic field on the surface, and ignores fields propagating along the surface within the coating.  This is particularly convenient when using [[boundary element method]] calculations.  The surface impedance can be calculated and tested separately.
For an [[isotropic]] surface the ideal surface impedance is equal to the 377 [[Ohm (unit)|ohm]] [[impedance of free space]].
For non-isotropic ([[anisotropic]]) coatings, the optimal coating depends on the shape of the target and the radar direction, but duality, the symmetry of Maxwell's equations between the electric and magnetic fields,  tells one that optimal coatings have η<sub>0</sub> × η<sub>1</sub> = 377<sup>2</sup> Ω<sup>2</sup>, where η<sub>0</sub> and η<sub>1</sub> are perpendicular components of the anisotropic surface impedance, aligned with edges and/or the radar direction.

A perfect electric conductor has more back scatter from a leading edge for the linear polarization with the electric field parallel to the edge and more from a trailing edge with the electric field perpendicular to the edge, so the high surface impedance should be parallel to leading edges and perpendicular to trailing edges, for the greatest radar threat direction, with some sort of smooth transition between.

To calculate the radar cross-section of such a stealth body, one would typically do one-dimensional reflection calculations to calculate the surface impedance, then two dimensional [[numerical analysis|numerical calculations]] to calculate the diffraction coefficients of edges and small three dimensional calculations to calculate the diffraction coefficients of corners and points. The cross section can then be calculated, using the diffraction coefficients, with the physical theory of diffraction or other high frequency method, combined with [[physical optics]] to include the contributions from illuminated smooth surfaces and [[Fock space|Fock]] calculations to calculate [[creeping waves]] circling around any smooth shadowed parts.

Optimization is in the reverse order.  First one does high frequency calculations to optimize the shape and find the most important features, then small calculations to find the best surface impedances in the problem areas, then reflection calculations to design coatings. Large numerical calculations can run too slowly for numerical optimization or can distract workers from the physics, even when massive computing power is available.