Quantum limited super-resolution of an unequal-brightness source pair in three dimensions

TL;DR

This paper analyzes quantum super-resolution of two incoherent sources with unequal brightness in three dimensions, revealing conditions under which quantum Fisher information remains unaffected by brightness asymmetry.

Contribution

It extends previous QFI analysis to unequal-brightness sources, showing how prior knowledge affects the estimation of separation parameters.

Findings

QFI remains independent of brightness asymmetry when the geometric center is known.

QFI depends on the separation vector when the brightness centroid is known.

Insights into superresolution imaging with extended incoherent sources.

Abstract

This paper extends our previous quantum Fisher information (QFI) based analysis of the problem of separating a pair of equal-brightness incoherent point sources in three dimensions to the case of a pair of sources that are unequally bright. When the pair's geometric center is perfectly known in advance, QFI with respect to the estimation of the three separation coordinates remains independent of the degree of brightness asymmetry. For the experimentally more relevant case of perfect prior knowledge of the pair's brightness centroid, however, such QFI becomes dependent on the pair separation vector in a way that is controlled by the degree of its brightness asymmetry. This study yields potentially useful insights into the analysis of a more general superresolution imaging problem involving extended incoherent sources with nontrivial brightness distributions.