Radiometric equation

The radiometric equation (eq. 11) gives the thermal noise $\sigma$ as a function of observing bandwidth $\delta\nu$ , integration time $\delta t$ , for an array with $n$ antennas, where $A$ is the geometric surface of an antenna and $\eta_a$ is the aperture efficiency. It also depends on the correlator efficiency $\eta_q$ and the phase decorrelation factor $\eta_p$ .

For a baseline, we have the following noise equation:

$$\sigma= \frac{1}{\eta_q\eta_p}\frac{\sqrt{2}k}{\eta_a A}\frac{T_{sys}}{\sqrt{\delta\nu\delta t}}$$ (10)

The array point source sensitivity is given by:

$$\sigma= \frac{1}{\eta_q\eta_p}\frac{2k}{\eta_a A}\frac{T_{sys}}{\sqrt{n(n-1)\delta\nu\delta t}}$$ (11)