  Astronomical imaging can be broadly classified into two types. The first type
is amplitude interferometry, which includes conventional optical telescopes and
Very Large Baseline Interferometry (VLBI). The second type is intensity
interferometry, which relies on Hanbury Brown and Twiss-type measurements. At
optical frequencies, where direct phase measurements are impossible, amplitude
interferometry has an effective numerical aperture that is limited by the
distance from which photons can coherently interfere. Intensity interferometry,
on the other hand, correlates only photon fluxes and can thus support much
larger numerical apertures, but suffers from a reduced signal due to the low
average photon number per mode in thermal light. It has hitherto not been clear
which method is superior under realistic conditions. Here, we give a
comparative analysis of the performance of amplitude and intensity
interferometry, and we relate this to the fundamental resolution limit that can
be achieved in any physical measurement. Using the benchmark problem of
determining the separation between two distant thermal point sources, e.g., two
adjacent stars, we give a short tutorial on optimal estimation theory and apply
it to stellar interferometry. We find that for very small angular separations
the large baseline achievable in intensity interferometry can more than
compensate for the reduced signal strength. We also explore options for
practical implementations of Very Large Baseline Intensity Interferometry
(VLBII).
