Sub-Rayleigh characterization of a binary source by spatially demultiplexed coherent detection

We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A general relation between the intensity distribution in the source plane and the covariance matrix for the complex field amplitudes measured in the image plane is derived. An algorithm to estimate parameters of a two-dimensional symmetric binary source is devised and verified using Monte Carlo simulations to provide super-resolving capability for high ratio of signal to detection noise (SNR). Specifically, the separation between two point sources can be meaningfully determined down to $\textrm{SNR}^{-1/2}$ in the units determined by the spatial spread of the transfer function of the imaging system. The presented algorithm is shown to make a nearly optimal use of the measured data in the sub-Rayleigh region.