Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

We suggest tailoring of the illumination’s complex degree of coherence for imaging specific two- and three-point objects with resolution far exceeding the Rayleigh limit. We first derive a formula for the image intensity via the pseudo-mode decomposition and the fast Fourier transform valid for any partially coherent illumination (Schell-like, non-uniformly correlated, twisted) and then show how it can be used for numerical image manipulations. Further, for Schell-model sources, we show the impr