Breaking Rayleigh's curse for multi-parameter objects using BLESS technique

Abstract

According to the Rayleigh criterion, it is impossible to resolve two statistically independent point sources separated by a distance below the width of the point spread function (PSF). Almost twenty years ago it was shown that the distance between two point sources can be statistically estimated with an accuracy better than the PSF width. However, the estimation error increases with decreasing distance. This effect was informally named Rayleigh's curse. Next, it was demonstrated that PSF shaping allows breaking the curse provided that all other source parameters except for the distance, are known a priori. In this work, we propose a new imaging technique based on the target Beam moduLation and the Examination of Shot Statistics (BLESS). Using the Fisher information approach, we show that the technique can break Rayleigh's curse even for unbalanced point sources with unknown centroid and intensity ratio.