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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:

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

The array point source sensitivity is given by:

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



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