Toraldo’s Composed Pupil: A Theoretical Analysis of the Near Field

Abstract

Over the years, there has been much speculation to understand whether (and how) it was possible to go below the diffraction limit. An advance in knowledge was achieved with the development of microwave techniques. In fact, more than fifty years after the publication of Toraldo’s article dealing with this topic, some experimental measurements in the range of microwaves confirmed the validity of his model. Since some measurements were performed in the region of near field, while Toraldo’s model refers to the far field, the need for a theoretical analysis in the framework of the Fresnel optics arose. The main goal of the present paper is to describe the problem of propagation in the near field (Fresnel optics) by using the same theoretical model already proposed by Toraldo. In order to test the validity of this new approach, the theoretical model has been compared with the FEKO simulation. The comparison of the theoretical model with the FEKO simulation in the far field for an open pupil (an open circular aperture) shows perfect agreement, as expected. We will demonstrate that there is also good agreement in the near field, although it is limited to the region around the main lobe, which is usually the region of main physical interest. Moving away from the main lobe, namely away from the optical axis, the agreement becomes less significant.