Approaching quantum-limited imaging resolution without prior knowledge of the object location.

Abstract

Passive imaging receivers that demultiplex an incoherent optical field into a set of orthogonal spatial modes prior to detection can surpass canonical diffraction limits on spatial resolution. However, these mode-sorting receivers exhibit sensitivity to contextual nuisance parameters (e.g., the centroid of a clustered or extended object), raising questions on their viability in realistic scenarios where prior information about the scene is limited. We propose a multistage detection strategy that segments the total recording time between different physical measurements to build up the required prior information for near quantum-optimal imaging performance at sub-Rayleigh length scales. We show, via Monte Carlo simulations, that an adaptive two-stage scheme that dynamically allocates recording time between a conventional direct detection measurement and a binary mode sorter outperforms idealized direct detection alone when no prior knowledge of the object centroid is available, achieving one to two orders of magnitude improvement in mean squared error for simple estimation tasks. Our scheme can be generalized for more sophisticated tasks involving multiple parameters and/or minimal prior information.