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.
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