Optimal observables and estimators for practical superresolution imaging

TL;DR

This paper develops practical observables and estimators that achieve the theoretical resolution limits for imaging two thermal point sources, accounting for real-world imperfections like noise and misalignment.

Contribution

It introduces a method to construct estimators that saturate the Cramér-Rao bound using optimally designed observables under practical conditions.

Findings

Estimators reach the Cramér-Rao bound in realistic scenarios

Optimized observables improve superresolution imaging performance

Method accounts for imperfections like noise and misalignment

Abstract

Recent works identified resolution limits for the distance between incoherent point sources. However, it remains unclear how to choose suitable observables and estimators to reach these limits in practical situations. Here, we show how estimators saturating the Cram\'er-Rao bound for the distance between two thermal point sources can be constructed using an optimally designed observable in the presence of practical imperfections, such as misalignment, crosstalk and detector noise.