2.3 FoV as a fraction of a single-dish beam

A single-dish beam will be $\simeq \lambda/D$. Instead of evaluating the fields of view resulting from the various types of smearing in arc-seconds as in the previous subsection, we can also form the ratios of the field of view to a single-dish beam. With $B$ in units of 1000km, $D$ in m, $\lambda$ in cm, $t_{\rm int}$ in seconds, and all $BW$ in MHz, we obtain:

$\displaystyle {\rm Bandwidth:} \quad \mathrm{Frac. s.d. beam}$ $\textstyle \lesssim$ $\displaystyle 0.024 \frac{D}{B} \frac{N_\nu}{BW_{\rm SB}\lambda} \quad {\rm or} \quad \lesssim 0.024 \frac{D}{B} \frac{N_{\rm SB} N_\nu}{BW_{\rm tot}\lambda}$  
$\displaystyle {\rm Time:} \quad \mathrm{Frac. s.d. beam}$ $\textstyle \lesssim$ $\displaystyle 0.009 \frac{D}{B} \frac{1}{t_{\rm int}}$ (3)