Towards superresolution surface metrology: Quantum estimation of angular and axial separations

TL;DR

This paper demonstrates that quantum metrology techniques enable superresolution localization of two incoherent point sources in three dimensions, surpassing classical limits and maintaining high precision even at sub-wavelength separations.

Contribution

It introduces a quantum measurement approach for simultaneous estimation of angular and axial separations, achieving the quantum Cramér-Rao bound without degradation in the sub-wavelength regime.

Findings

Achieves quantum-limited precision in estimating 3D separations.

Overcomes classical Rayleigh limit in superresolution imaging.

Applicable to surface metrology and 3D imaging.

Abstract

We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cram\'er-Rao bound. Such a precision is not degraded in the sub-wavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh's criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for the Gaussian instance. This analysis may have relevant applications in three-dimensional surface measurements.