  We solve the general problem of determining, through imaging, the
three-dimensional positions of $N$ weak incoherent point-like emitters in an
arbitrary spatial configuration. We show that a structured measurement strategy
in which a linear interferometer feeds into an array of photo-detectors is
always optimal for this estimation problem, in the sense that it saturates the
quantum Cram\'er-Rao bound. We provide a method for the explicit construction
of the optimal interferometer. Further explicit results for the quantum Fisher
information and the optimal interferometer design that attains it are obtained
for the case of one and two incoherent emitters in the paraxial regime. This
work provides insights into the phenomenon of super-resolution through
incoherent imaging that has attracted much attention recently. Our results will
find a wide range of applications over a broad spectrum of frequencies, from
fluorescence microscopy to stellar interferometry.
