Super-localisation of a point-like emitter in a resonant environment: correction of the mirage effect

Lorenzo Baldassari, Pierre Millien, Alice Lucie Vanel

Abstract: In this paper, we show that it is possible to overcome one of the fundamental limitations of super-resolution microscopy techniques: the necessity to be in an optically homogeneous environment. Using recent modal approximation results we show as a proof of concept that it is possible to recover the position of a single point-like emitter in a known resonant environment from far-field measurements with a precision two orders of magnitude below the classical Rayleigh limit. The procedure does not involve solving any partial differential equation, is computationally light (optimisation in $\R^d$ with $d$ of the order of $10$) and therefore suited for the recovery of a very large number of single emitters.