Super-resolution with Toraldo pupils: analysis with electromagnetic numerical simulations

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 developed with the aim of narrowing the central lobe of the illumination Point Spread Function (PSF). In Astronomy a few methods have been proposed to achieve reflector telescopes and antennas with resolution significantly better than the diffraction limit but, to our best knowledge, no working system is in operation. A possible practical approach consists of using the so-called "Toraldo Pupils" (TPs) or variable transmittance filters. These pupils were introduced by G. Toraldo di Francia in 1952,1 and consist of a series of discrete, concentric circular coronae providing specific optical transparency and dephasing in order to engineer the required PSF. The first successful laboratory test of TPs in the microwaves was achieved in 2003,2 and in the present work we build upon these initial measurements to perform electromagnetic (EM) numerical simulations of TPs, using a commercial full-wave software tool. These simulations were used to study various EM effects that can mask and/or affect the performance of the pupils and to analyze the near-field as well as the far-field response. Our EM analysis confirms that at 20 GHz the width of the central lobe in the far-field generated by a TP significantly decreases compared to a clear circular aperture with the same diameter.