Sensitivity for a single-source, single-field observations

That's the simplest case. The point source sensitivity in this case is

$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{...
...n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}},$ (29)

where $\Delta t_\ensuremath{\mathrm{on}}$ is related to the total elapsed telescope time $\Delta t_\ensuremath{\mathrm{tel}}$ through

$\displaystyle \boxed{%
\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensure...
...m{track}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}} \right) },
}$ (30)

where $\eta_\ensuremath{\mathrm{freq}}$ is the fraction of $\Delta t_\ensuremath{\mathrm{obs}}$ spent at one tuning frequency. $\ensuremath{\eta_\ensuremath{\mathrm{freq}}}= 1.0$ in “standard” mode and $\ensuremath{\eta_\ensuremath{\mathrm{freq}}}\sim 0.5$ when cycling between two frequencies. The sum of $\ensuremath{\eta_\ensuremath{\mathrm{freq}}}$ needs to equal 1.0!