Single-photon sub-Rayleigh precision measurements of a pair of incoherent sources of unequal intensity

TL;DR

This paper demonstrates a quantum-inspired method for sub-Rayleigh resolution imaging of two incoherent sources with unequal brightness, achieving improved measurement precision over direct imaging through Hermite-Gaussian mode demultiplexing.

Contribution

It introduces a theoretical and experimental approach for estimating separation and relative intensity of unequal brightness sources using SPADE, surpassing classical limits.

Findings

Experimental errors match theoretical bounds

Achieved $ ext{SNR}$ improvement of $ ext{epsilon}^{-1/2}$ over direct imaging

Method effective for imaging faint secondary sources like exoplanets

Abstract

Interferometric methods have been recently investigated to achieve sub-Rayleigh imaging and precision measurements of faint incoherent sources up to the ultimate quantum limit. Here we consider single-photon imaging of two point-like emitters of unequal intensity. This is motivated by the fact that pairs of natural emitters will typically have unequal brightness, as for example binary star systems and exoplanets. We address the problems of estimating the transverse separation $d$ and the relative intensity $\epsilon$. Our theoretical analysis shows that the associated statistical errors are qualitatively different from the case of equal intensity. We employ multi-plane light conversion technology to experimentally implement Hermite-Gaussian (HG) spatial-mode demultiplexing (SPADE), and demonstrate sub-Rayleigh measurement of two emitters with Gaussian point-spread function. The experimental errors are comparable with the theoretical bounds. The latter are benchmarked against direct imaging, yielding a $\epsilon^{-1/2}$ improvement in the signal-to-noise ratio, which may be significant when the primary source is much brighter than the secondary one, as for example for imaging of exoplanets. However, achieving this improved scaling requires low noise in the implementation of SPADE, which is typically affected by crosstalk between HG modes.