Optimal observables for practical super-resolution imaging

Recently, it has been demonstrated that demultiplexing Hermite-Gauss (HG) modes represents the quantum-optimal measurement to estimate the distance between two incoherent sources. However, it remains unclear how to practically combine the information contained into several demultiplexing measurements to reach the ultimate resolution limits. In this contribution, we show how estimators saturating the Cramer-Rao bound for the distance between two thermal point sources can be constructed from an optimised linear combination of intensity measurements in a given number of HG modes, in presence of practical imperfection such as misalignment, crosstalk and detector noise. Moreover, we demonstrate that our strategy saturates the quantum Cramer-Rao bound, in the noiseless case, if sufficiently many modes are measured.