  We consider the problem of estimating the spatial separation between two
mutually incoherent point light sources using the super-resolution imaging
technique based on spatial mode demultiplexing with noisy detectors. We show
that in the presence of noise the resolution of the measurement is limited by
the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation
has a characteristic dependence of $\sim$SNR$^{-1/2}$. Several detection
techniques, including direct photon counting, as well as homodyne and
heterodyne detection are considered.
