Moment-based superresolution: Formalism and applications

Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain ultimate resolution limit for estimation of separation between two incoherent point sources. However, methods that saturate these limits, require full measurement statistics, which can be challenging access. In work, we introduce a simple superresolution protocol estimate thermal sources relies only on average value single accessible observable. We show how optimal observables technique may constructed arbitrary sources, and study their sensitivities when one access spatially resolved intensity measurements (direct imaging) photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates quantum also investigate impact noise observables, sensitivity scaling with number detected photons smallest resolvable separation. low signals in image plane, demonstrate bound even presence noise.