Design of discrete and continuous super-resolving Toraldo pupils in the microwave range

The concept of super-resolution refers to various methods for improving the angular resolution of an optical imaging system beyond the classical diffraction limit. In optical microscopy, several techniques have been successfully developed with the aim of narrowing the central lobe of the illumination point spread function. In astronomy, however, no similar techniques can be used. A feasible method to design antennas and telescopes with angular resolution better than the diffraction limit consists of using variable transmittance pupils. In particular, discrete binary phase masks (0 or π) with finite phase-jump positions, known as Toraldo pupils (TPs), have the advantage of being easy to fabricate but offer relatively little flexibility in terms of achieving specific trade-offs between design parameters, such as the angular width of the main lobe and the intensity of sidelobes. In this paper, we show that a complex transmittance filter (equivalent to a continuous TP, i.e., consisting of infinitely narrow concentric rings) can achieve more easily the desired trade-off between design parameters. We also show how the super-resolution effect can be generated with both amplitude- and phase-only masks and confirm the expected performance with electromagnetic numerical simulations in the microwave range.