Past exam of the frontiers of Observational Astrophysics course of the University of Cambridge / 2012 / Paper 1 / 1 / a

The center-to-center extent is $18\mathrm{m}$ on each side and $18\sqrt{2}=25.46\mathrm{m}$ diagonally, while the shortest nonzero baseline is $6\mathrm{m}$. At $\lambda =0.02\mathrm{m}$, characteristic scales areThese describe the finest synthesized scale, a largest recoverable scale estimate, and the individual-dish field of view, respectively. Along an array side the longest baseline is only $18\mathrm{m}$, giving $3.82^{\prime }$ rather than the diagonal estimate. Projection, weighting and sidelobes determine an actual synthesized beam.

There is no sharp universal largest-scale cutoff: the commonly used $0.6\lambda /b_{\min }$ convention would give $6.88^{\prime }$. For an ideal uniformly illuminated circular dish, the primary-beam full width at half maximum is approximately $1.02\lambda /D=17.5^{\prime }$, while the first-null angular radius is $1.22\lambda /D=21.0^{\prime }$. These definitions should not be mixed. Uniform lattice spacing also produces grating sidelobes; the primary beam restricts the useful field but does not supply the missing zero-baseline flux.