On the relative intensity of Poisson’s spot

The Fresnel diffraction phenomenon referred to as Poisson’s spot or spot of Arago has, beside its
historical significance, become relevant in a number of fields. Among them are for example
fundamental tests of the super-position principle in the transition from quantum to classical physics
and the search for extra-solar planets using star shades. Poisson’s spot refers to the positive on-axis
wave interference in the shadow of any spherical or circular obstacle. While the spot’s intensity is equal
to the undisturbed field in the plane wave picture, its intensity in general depends on a number of
factors, namely the size and wavelength of the source, the size and surface corrugation of the
diffraction obstacle, and the distances between source, obstacle and detector. The intensity can be
calculated by solving the Fresnel–Kirchhoff diffraction integral numerically, which however tends to
be computationally expensive. We have therefore devised an analytical model for the on-axis intensity
of Poisson’s spot relative to the intensity of the undisturbed wave field and successfully validated it
both using a simple light diffraction setup and numerical methods. ... mehrThe model will be useful for
optimizing future Poisson-spot matter-wave diffraction experiments and determining under what
experimental conditions the spot can be observed.