Quantum-limited estimation of the axial separation of two incoherent point sources

TL;DR

This paper introduces a quantum-limited axial superresolution method using spatial mode demultiplexing with a radial mode sorter, achieving optimal measurement bounds without fluorophore activation or complex stabilization, applicable to fluorescence microscopy.

Contribution

The paper presents a novel axial superresolution scheme based on radial mode sorting that reaches the quantum Cramér-Rao bound, outperforming existing methods.

Findings

Achieves quantum-limited axial resolution

Demonstrates experimental validation of the scheme

Applicable to single point source localization

Abstract

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cram\'er-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require neither activation of fluorophores nor sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful to a variety of applications such as far-field fluorescence microscopy.