Power and sensitivity measured at the correlator output for one baseline

After the atmopheric calibration that converts the measurement scale from the correlator output (in counts) to the \ensuremath{T_\ensuremath{\mathrm{a}}^\star} scale, the output of the correlator for one correlation is a power equivalent temperature (in the Rayleigh-Jeans domain), which is sampled at a rate of $2\ensuremath{d\nu}$, where \ensuremath{d\nu} is the frequency bandwidth over which the power is measured. As explained in the previous section, the standard deviation of each power measurement is given by the system temperature power ( \ensuremath{T_\ensuremath{\mathrm{sys}}}). During the integration time ( \ensuremath{\Delta t_\ensuremath{\mathrm{}}}), $2\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}$ independent samples of the signal power are measured to ensure the Nyquist sampling of the signal in the bandwidth \ensuremath{d\nu}. The signal power is averaged over these independent samples. The uncertainty on the averaged signal power, named sensitivity ( \ensuremath{\sigma_\ensuremath{\mathrm{K}}}), is thus standard deviation of the average or

  $\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{K}}} = \frac{\ensuremath{T...
...}}{\sqrt{2\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}}.
$ (2)