Quantum-limited Localisation and Resolution in Three Dimensions

TL;DR

This paper investigates the fundamental quantum limits of three-dimensional optical imaging resolution, showing how quantum Fisher information bounds can optimize emitter localization and separation estimation.

Contribution

It derives the quantum Fisher information bounds for 3D emitter localization, revealing conditions for simultaneous precise estimation of multiple parameters in quantum-limited imaging.

Findings

Quantum Fisher information matrix is independent of emitter position.

Precise separation estimation requires known relative intensities and centroids.

Upper bounds established for resolution in far-field quantum imaging.

Abstract

As a method to extract information from optical system, imaging can be viewed as a parameter estimation problem. The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below by the multiparameter quantum Cramer-Rao bound (QCRB).Multiparameter QCRB gives an intrinsic bound in parameter estimation. We determine the ultimate potential of quantum-limited imaging for improving the resolution of a far-field, diffraction-limited within the paraxial approximation. We show that the quantum Fisher information matrix (QFIm) about one emitter's position is independent on the true value of it. We calculate the QFIm of two unequal-brightness emitters' relative positions and intensities, the results show that only when the relative intensity and centroids of two point sources including longitudinal and transverse direction are known exactly, the separation in different directions can be estimated simultaneously with finite precision. Our results give the upper bounds on certain far-field imaging technology and will find wide applications from microscopy to astrometry.