Moment-based superresolution: Formalism and applications

Giacomo Sorelli (1) , Manuel Gessner (2) , Mattia Walschaers (1) , Nicolas Treps (1)

1 LKB (Jussieu) - Laboratoire Kastler Brossel
2 LKB (Lhomond) - Laboratoire Kastler Brossel

Sensitivity limits are usually determined using the Cramér-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 Cramér-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 Cramér-Rao bound even in the presence of noise.

Domaines: Physique [physics]; Optique [physics.optics]

Giacomo Sorelli, Manuel Gessner, Mattia Walschaers, Nicolas Treps. Moment-based superresolution: Formalism and applications. Physical Review A, 2021, 104 (3), ⟨10.1103/PhysRevA.104.033515⟩. ⟨hal-03370419⟩