Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit

TL;DR

This paper establishes the fundamental quantum limit for resolving two thermal sources beyond the Rayleigh criterion, proposing practical measurement methods that approach this limit across various conditions and applications.

Contribution

It derives the quantum Cramér-Rao bound for thermal source separation and introduces feasible measurement schemes that achieve near-optimal resolution.

Findings

Quantum mechanics allows superresolution beyond Rayleigh limit.

Proposed measurement techniques approach the quantum limit.

Applicable across all wavelengths and source strengths.

Abstract

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cram\'er-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does notmandate any loss of precision in estimating even deep sub-Rayleigh separations. We propose two coherent measurement techniques, easily implementable using current linear-optics technology, that approach the quantum limit over an arbitrarily large range of separations. Our bound is valid for arbitrary source strengths, all regions of the electromagnetic spectrum, and for any imaging system with an inversion-symmetric point-spread function. The measurement schemes can be applied to microscopy, optical sensing, and astrometry at all wavelengths.