Sub-Rayleigh resolution of two incoherent sources by array homodyning

TL;DR

This paper demonstrates theoretically that array homodyne detection can estimate the distance between two incoherent sources below the Rayleigh diffraction limit by utilizing spatial coherence information, surpassing traditional intensity-based methods.

Contribution

It introduces a novel approach using array homodyne detection and Fisher information to achieve sub-Rayleigh resolution for incoherent sources.

Findings

Quadrature statistics enable sub-Rayleigh estimation.

Array homodyne detection provides spatial coherence data.

Proposed algorithm performs well in simulations.

Abstract

Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of the Fisher information that quadrature statistics measured by means of array homodyne detection enables estimation of the distance between two incoherent point sources well below the Rayleigh limit for sufficiently high signal-to-noise ratio. This capability is attributed to the availability of spatial coherence information between individual detector pixels acquired using the coherent detection technique. A simple analytical approximation for the precision attainable in the sub-Rayleigh region is presented. Furthermore, an estimation algorithm is proposed and applied to Monte Carlo simulated data.