Resolution limits of spatial mode demultiplexing with noisy detection

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 (SPADE) 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 similar to SNR-1/2. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.