Theory of Super‐Resolved Parameter Estimation for Concurrently Emitting Molecules

ABSTRACT

Minimal photon fluxes (MINFLUX) nanoscopy is among the most advanced superresolution techniques to date, yet its broader applicability remains limited by the reliance on single‐molecule localization. In this work, we extend the MINFLUX framework to resolve concurrently excited fluorescent molecules. Theoretical modeling of two fluorescent molecules in confocal imaging shows that hollow beam illumination, compared with conventional Gaussian beam illumination, substantially enhances the localization precision of both molecules, enabling high‐precision estimation of molecular separation below the diffraction limit. The effects of practical imperfections such as centroid misalignment and background are also taken into account, revealing the convergence condition for the resolution in the limit of infinitesimal separation. By iteratively adjusting the scanning pattern, the attainable resolution can be markedly improved, as validated in numerical simulations. Moreover, the framework can be further generalized to analyze the subdiffraction spatial parameters of arbitrary molecular ensembles, thereby significantly broadening the scope of MINFLUX applications.