Parameter estimation techniques in sub-rayleigh imaging for incoherent point sources (2024)
This monograph explores advanced methodologies in quantum parameter estimation, with a particular focus on sub-Rayleigh imaging for incoherent point sources, building on the foundational work of Tsang, Nair, and Lu in "Quantum Theory of Superresolution for Two Incoherent Optical Point Sources" \cite{Tsang2016Quantum}. We thoroughly review and verify existing research, exploring the limitations of classical imaging techniques and highlighting strategies that rely on quantum optics principles to improve resolution and accuracy. Employing the Estimation Theory as a framework, we examine the efficiency of different measurements. Finally, the research results indicate that the use of spatial mode demultiplexing in the Hermite-Gauss basis functions substantially enhances the precision of estimating the separations in two point sources imaging systems. This work aims to contribute to the theoretical understanding of quantum parameter estimation.