  The fundamental limit on the precision of the separation estimation between
two partially coherent sources is derived. Photon losses, inevitably associated
with imperfect imaging, are properly taken into account. We begin our analysis
with a simple and common imaging model based on the 4f system. We then show
that our results are valid for any passive, linear, translationally invariant
optical imaging system. We obtain the expression for the Quantum Fisher
Information, which is consistent with the already computed classical Fisher
Information and latest experimental work. We also identify the source of
discrepancies in the results obtained earlier and show how to correctly
interpret them.
