# Is radar cross section the same as scattering cross section?

There is a quantity known as scattering cross section which is given as a function of frequency. It means the ratio of the scattered power by the particle to the ratio of the incident power on the particle.

Is radar cross section the same thing as scattering cross section? Some electromagnetic solvers (like CST studio) give radar cross section and absorption cross section only, so I guess it should be the same as scattering cross section.

• yes, radar cross section = scattering cross section Commented Nov 22, 2014 at 19:24
• @user31748 But why radar cross section is given as a 3D farfield pattern, not a number (at each frequency)? (like antenna pattern) Commented Nov 22, 2014 at 19:56
• because scattering is direction dependent even in the case of a sphere. In radar this is called the "bi-static" cross section to distinguish it from the mono-static case. Mono-static: transmitter and receiver antenna are co-located, bi-static: transmitter and receiver antennas are at different locations. Commented Nov 22, 2014 at 21:36
• @user31748 Thank you! I think you could post these two comments as an answer, in order for me to accept it as answer. Commented Nov 23, 2014 at 5:22

From the CST Help:

The radar cross section (RCS) is a farfield parameter that determines the scattering properties of a specific radar target...

The RCS plot includes two integrated quantities which characterise the target:

### Total RCS:

The total radar cross section is defined as the ratio of the scattered power to the intensity of the incident plane wave.

### Total ACS:

The total absorption cross section is defined as the ratio of the absorbed power to the intensity of the incident plane wave.

That said, Total RCS is defined as the integral of scattered power divided by the intensity of the plane wave, that is, by definition, the scattering cross-section: $$\sigma_{\text{sca}} = \left(\frac{|E_0|^2}{2Z_0}\right)^{-1} P_{\text{sca}} = \left(\frac{|E_0|^2}{2Z_0}\right)^{-1} \frac{1}{2}\int\limits_{\text{around target}} \mathrm{Re}\left[\vec{E}_{\text{sca}} \times \vec{H}^{*}_{\text{sca}}\right]\cdot d\vec{s}$$ (here $$E_0$$ is the incident field, $$Z_0 \simeq 377~\Omega$$ is the free space impedance, $$E_{\text{sca}}$$ and $$H_{\text{sca}}$$ are the scattered fields).

Likewise, Total ACS is defined as the integral of all energy flux around the target, divided by the intensity: $$\sigma_{\text{abs}} = \left(\frac{|E_0|^2}{2Z_0}\right)^{-1} P_{\text{abs}} = \left(\frac{|E_0|^2}{2Z_0}\right)^{-1} \frac{1}{2}\int\limits_{\text{around target}} \mathrm{Re}\left[(\vec{E}_{0} + \vec{E}_{\text{sca}}) \times (\vec{H}^{*}_{0} + \vec{H}^{*}_{\text{sca}})\right]\cdot d\vec{s}$$ (Absorbed power is the power which entered the target, but did not leave it. For a non-absorbing target ingoing flux should be equal to outgoing flux, so the intergal would be equal to zero)

There’s a much easier answer: For a monostatic radar, take the differential cross-section for backscatter, $$d\sigma /d\Omega$$, and multiply by $$4\pi$$. In the special case of isotropic scattering, the RCS and total CS would be equal. (Spheres scatter isotropically in the ray-optic limit.)