Radar

Detection and inference about remote objects using transmitted radio waves and their returned electromagnetic radiation. A received signal depends on propagation, directional antenna gain, target scattering and receiver sensitivity.

For a far-field free-space link with one reciprocal antenna transmitting and receiving at range $D$, the outward intensity is $P_{T}G/(4\pi D^2)$. The backward scattered intensity at the receiver is this times ${\sigma }_{\mathrm{back}}/(4\pi D^2)$. Multiplying by the matched antenna effective area $G{\lambda }^2/(4\pi )$ gives the displayed received power. Attenuation, misalignment and polarization mismatch require additional factors. The threshold for a root mean square voltage $V_m$ across a real matched load $R$ is $V_m^2/R$.

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.