2.2 FoV in terms of arc-seconds

Take $\theta \simeq \lambda/B$, where $\lambda$ is the wavelength associated with $\nu_0$ and $B$ is the longest baseline in the array. We then obtain, after converting from radians to arc-seconds, with $B$ in units of 1000km, $\lambda$ in cm, $t_{\rm int}$ in seconds, and all $BW$ in MHz:

$\displaystyle {\rm Bandwidth:} \quad FoV$ $\textstyle \lesssim$ $\displaystyle 49.\!''5 \frac{1}{B} \frac{N_\nu}{BW_{\rm SB}} \quad
{\rm or} \quad \lesssim 49.\!''5 \frac{1}{B} \frac{N_{\rm SB}N_\nu}{BW_{\rm tot}}$  
$\displaystyle {\rm Time:} \quad FoV$ $\textstyle \lesssim$ $\displaystyle 18.\!''56   \frac{\lambda}{B} \frac{1}{t_{\rm int}}$ (2)

Note that the bandwidth smearing is now independent of the observing frequency when expressing the field of view in arc-seconds.



campbell@jive.eu