  Photon losses are intrinsic for any translationally invariant optical imaging
system with a non-trivial Point Spread Function, and the relation between the
transmission factor and the coherence properties of an imaged object is
universal -- we demonstrate the rigorous proof of this statement, based on the
principles of quantum mechanics. The fundamental limit on the precision of
estimating separation between two partially coherent sources is then derived.
The careful study of the role of photon losses allows to resolve conflicting
claims present in previous works. We compute the Quantum Fisher Information for
the generic model of optical 4f imaging system, and use prior considerations to
validate the result for a general, translationally invariant imaging apparatus.
We prove that the spatial-mode demultiplexing (SPADE) measurement, optimal for
non-coherent sources, remains optimal for an arbitrary degree of coherence.
Moreover, we show that some approximations, omnipresent in theoretical works
about optical imaging, inevitably lead to unphysical, zero-transmission models,
resulting in misleading claims regarding fundamental resolution limits.
