Quantum fluctuations in superresolving Fourier-microscopy

A new scheme, superresolving Fourier-microscopy is proposed, which detects the spatial Fourier spectrum of the image created by an additional Fourier lens. This procedure amounts in directly imaging on the observation plane the field coming through the pupil, and all the field transmitted by the pupil is again concentrated on a finite region of space. Using decomposition on the basis of the prolate spheroidal functions, object reconstruction is shown to be in principle possible. The gain in superresolution achieved in this scheme over the classical Rayleigh limit is investigated numerically.