Radar cross section (${\sigma }_{\mathrm{back}}=4\pi (d\sigma /d\Omega {)}_{\mathrm{back}}$)

The monostatic radar cross section is $4\pi$ times the backward differential scattering cross-section. Equivalently, ${\sigma }_{\mathrm{back}}={\lim }_{r\to \infty }4\pi r^2{S}_{\mathrm{back}}/S_{\mathrm{inc}}$. It is a directional scattering measure with dimensions of area, not generally the geometric area or the total scattering cross-section. The definition may additionally specify the transmitted and received polarizations.

Retaining only the electric dipole induced in a small sphere gives $\mathbf{p}=4\pi {ϵ}_0{a}^3{\mathbf{E}}_{\mathrm{inc}}$. In the backward direction its differential scattering cross-section is $k^4{a}^6$, so the radar cross section is $4\pi k^4{a}^6$. This response model omits the sphere's induced magnetic dipole moment; it must be distinguished from perfect-conductor sphere dipole interference.