New insights into the problem of shadowlike projection of a plane object illuminated by a spherical wavefront

The problem of diffraction from a plane object illuminated by a monochromatic point spherical wavefront is investigated using a Fourier-domain approach based on general diffraction theory. In particular, we focus on the so-called shadowlike projection phenomenon, i.e., when the diffraction patterns of the illuminated object are magnified or reduced images of the object. The analysis conducted here allows us to provide a general mathematical formulation of the shadowlike projection phenomenon, including a formal derivation of the known equations governing this phenomenon. More importantly, our analysis also offers a deeper insight into this phenomenon. As an example, it has been shown that under certain conditions, the spherical wavefront illumination can induce a space-to-angular spectrum conversion in the diffracted field. Here we report an experimental observation of this so-called angular Fraunhofer effect.