Moment-based superresolution: Formalism and applications

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

Automated summary

In this work, a simple superresolution protocol is introduced to estimate the separation between two thermal sources using the average value of a single accessible observable. The method is shown to saturate the Cramer-Rao bound even in the presence of noise.