Interferometric radiometer equation (${\sigma }_S=\frac{\mathrm{SEFD}}{\sqrt{N(N-1)\Delta \nu t}}$)

For $N$ equal antennas, weak-source independent receiver noise, natural weighting and total on-source time $t$, the point-source rms in one polarization of waves is the displayed value. There are $N(N-1)/2$ independent cross-correlation baselines, each with real-component error $\mathrm{SEFD}/\sqrt{2\Delta \nu t}$. Combining $n_{\mathrm{pol}}$ independent polarization of waves estimates reduces the rms by $\sqrt{n_{\mathrm{pol}}}$. Correlation losses divide the sensitivity by an efficiency factor; weighting, flagging and an extended source change the effective sensitivity.^[ref]