Ranjith Nair and Mankei Tsang of the National University of Singapore have proposed a framework for estimating the separation of two incoherent point sources of arbitrary closeness (including closer than the Rayleigh limit) and have designed a type of interferometer called SLIVER (super localization by image inversion interferometry) containing an image-inversion device that inverts the field in the transverse plane about the optical axis (with the axis passing through the centroid of the sources). The results, which are based on semiclassical photodetection theory, apply to sources of arbitrary strength and to imaging systems with two-dimensional, circularly symmetric point-spread functions.
In the SLIVER interferometer (which has a simple optical design using only bulk optics), two incoherent point sources separated by d produce a field entering the interferometer that is separated into symmetric (Es(ρ)) and antisymmetric (Ea(ρ)) components with respect to inversion about the centroid of the sources (the optical axis) via an image-inversion box that, in one example, splits the input field using a beamsplitter, spatially inverts the field from one output, then recombines the two beams at a second beamsplitter, forming a Mach-Zehnder interferometer. The two interferometer outputs are sent to photodetectors that simply gather photocounts (Ns and Nd). Statistical processing of the results provide an accurate estimate of d. Further theoretical studies of the device could lead to the construction of an actual SLIVER. Reference: R. Nair and M. Tsang, arXiv:1512.08304v1 [physics.optics] (Dec. 28, 2015).
