Interferometric superlocalization of two incoherent optical point sources

TL;DR

This paper introduces SLIVER, an interferometric technique that achieves superlocalization of two incoherent optical sources with accuracy unaffected by their proximity, surpassing traditional resolution limits.

Contribution

The paper presents a novel interferometric method, SLIVER, that maintains high localization precision for closely spaced incoherent sources, supported by theoretical analysis and simulations.

Findings

SLIVER achieves superlocalization below the Rayleigh limit.

Performance is validated through Cramér-Rao bound analysis.

Robustness to misalignment is demonstrated.

Abstract

A novel interferometric method - SLIVER (Super Localization by Image inVERsion interferometry) - is proposed for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources are brought closer. The essential component of the interferometer is an image inversion device that inverts the field in the transverse plane about the optical axis, assumed to pass through the centroid of the sources. The performance of the device is analyzed using the Cram\'er-Rao bound applied to the statistics of spatially-unresolved photon counting using photon number-resolving and on-off detectors. The analysis is supported by Monte-Carlo simulations of the maximum likelihood estimator for the source separation, demonstrating the superlocalization effect for separations well below that set by the Rayleigh criterion. Simulations indicating the robustness of SLIVER to mismatch between the optical axis and the centroid are also presented. The results are valid for any imaging system with a circularly symmetric point-spread function.