  We analyze the fundamental resolution of incoherent optical point sources
from the perspective of a quantum detection problem: deciding whether the
optical field on the image plane is generated by one source or two weaker
sources with arbitrary separation. We investigate the detection performances of
two measurement methods recently proposed by us to enhance the estimation of
the separation. For the detection problem, we show that the method of binary
spatial-mode demultiplexing is quantum-optimal for all values of separations,
while the method of image-inversion interferometry is near-optimal for
sub-Rayleigh separations. Unlike the proposal by Helstrom, our schemes do not
require the separation to be given and can offer that information as a bonus in
the event of a successful detection. For comparison, we also demonstrate the
supremacy of our schemes over direct imaging for sub-Rayleigh separations.
These results demonstrate that simple linear optical measurements can offer
supremal performances for both detection and estimation.
