Adaptive Super-Resolution Imaging Without Prior Knowledge Using a Programmable Spatial-Mode Sorter

Abstract: We consider an imaging system tasked with estimating the angular distance between two incoherently-emitting, identically bright, sub-Rayleigh-separated point sources, without any prior knowledge of the centroid or the constellation and with a fixed collected-photon budget. It was shown theoretically that splitting the optical recording time into two stages -- focal-plane direct imaging to obtain a pre-estimate of the centroid, and using that estimate to center a spatial-mode sorter followed by photon detection of the sorted modes -- can achieve lower mean squared error in estimating the separation~\cite{Grace:20}. In this paper, we demonstrate this in a proof-of-concept, using a programmable mode sorter we have built using multi-plane light conversion (MPLC) using a reflective spatial-light modulator (SLM) in an emulated experiment where we use a single coherent source to characterize the MPLC to electronically piece together the signature from two closely-separated quasi-monochromatic incoherent emitters. We show an improvement in estimator variance when compared to direct imaging, in good agreement with simulations.