Resolution limits of spatial mode demultiplexing with noisy detection

TL;DR

This paper investigates the fundamental resolution limits of spatial mode demultiplexing in super-resolution imaging under noisy detection, revealing that noise imposes a SNR-dependent resolution bound.

Contribution

It provides a theoretical analysis of how noise affects the resolution limits in spatial mode demultiplexing, deriving a SNR-based resolution scaling law.

Findings

Resolution scales as SNR^{-1/2} in noisy conditions

Different detection techniques exhibit similar noise-limited resolution bounds

The study highlights the impact of detector noise on super-resolution imaging performance

Abstract

We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the presence of noise the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of $\sim$SNR$^{-1/2}$. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.