Beating Rayleigh's Curse by Imaging Using Phase Information

TL;DR

This paper demonstrates that utilizing phase information in imaging systems allows surpassing Rayleigh's resolution limit, significantly improving the estimation of closely spaced sources and overcoming the traditional resolution barrier.

Contribution

The authors implement a phase-based imaging method that leverages quantum Fisher information to beat Rayleigh's curse, enhancing resolution beyond classical limits.

Findings

Phase information improves source separation estimates

The method overcomes Rayleigh's curse in practical imaging

Enhanced resolution with fewer photons

Abstract

Any imaging device such as a microscope or telescope has a resolution limit, a minimum separation it can resolve between two objects or sources; this limit is typically defined by "Rayleigh's criterion", although in recent years there have been a number of high-profile techniques demonstrating that Rayleigh's limit can be surpassed under particular sets of conditions. Quantum information and quantum metrology have given us new ways to approach measurement ; a new proposal inspired by these ideas has now re-examined the problem of trying to estimate the separation between two poorly resolved point sources. The "Fisher information" provides the inverse of the Cramer-Rao bound, the lowest variance achievable for an unbiased estimator. For a given imaging system and a fixed number of collected photons, Tsang, Nair and Lu observed that the Fisher information carried by the intensity of the light in the image-plane (the only information available to traditional techniques, including previous super-resolution approaches) falls to zero as the separation between the sources decreases; this is known as "Rayleigh's Curse." On the other hand, when they calculated the quantum Fisher information of the full electromagnetic field (including amplitude and phase information), they found it remains constant. In other words, there is infinitely more information available about the separation of the sources in the phase of the field than in the intensity alone. Here we implement a proof-of-principle system which makes use of the phase information, and demonstrate a greatly improved ability to estimate the distance between a pair of closely-separated sources, and immunity to Rayleigh's curse.