Quantifying classical and quantum bounds for resolving closely spaced, non-interacting, simultaneously emitting dipole sources in optical microscopy

TL;DR

This paper investigates the fundamental limits of resolving two closely spaced dipole emitters in optical microscopy, accounting for vectorial emission effects and proposing methods to approach quantum Fisher information bounds.

Contribution

It extends super-resolution estimation theory to vectorial dipole sources in high-NA microscopy, analyzing quantum and classical bounds with practical measurement schemes.

Findings

Quantum Fisher information remains finite at small separations.

Filtering in azimuthal-radial polarization basis can saturate quantum limits.

Vectorial emission complicates resolution analysis but can be mitigated.

Abstract

Recent theoretical and experimental work has shown that the quantum Fisher information associated with estimating the separation between two optical point sources remains finite at small separations, effectively opening new routes to super-resolution imaging of simultaneously emitting sources. Most studies to date, however, implicitly invoke the scalar approximation, which is not appropriate in the context of high-numerical-aperture microscopy. Utilizing parameter estimation theory, here we consider the estimation of separation between two closely spaced dipole emitters, a commonly employed model for single-molecule optical beacons. We consider two limiting cases: one in which the orientations of the emitters are fixed and equal, and another in which both dipoles freely sample all of orientation space over the course of the measurement. We quantify precision limits using quantum and classical variants of the Fisher information and Cram\'{e}r-Rao bound. In all cases, the vectorial nature of the emission complicates the analyses, but with appropriate filtering of the collected light in the azimuthal-radial polarization basis, a previously proposed scheme to saturate the quantum Fisher information via image inversion interferometry can be salvaged.