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

TL;DR

This paper demonstrates a method to precisely locate a single point emitter within a known resonant environment using far-field measurements, overcoming the optical homogeneity requirement of traditional super-resolution microscopy.

Contribution

It introduces a computationally efficient approach that recovers emitter positions with high precision in resonant environments without solving PDEs.

Findings

Achieves localization precision two orders below the Rayleigh limit.

Does not require solving partial differential equations.

Suitable for large-scale emitter recovery.

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 \emph{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 \emph{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.