Towards the Ronchi test for gravitational lenses: The gravitoronchigram

The aim of this work is to present a Ronchi test for a gravitational lens. To this end, we use the geometrical optics point of view of the Ronchi test and the definition of the exact lens equation without reference to a background space-time to introduce the analog of the ideal ronchigram, which we named the gravitoronchigram. We first present the ideal ronchigram for an axicon lens and then using the space-time perspective of the lensing phenomenon we obtain analytical equations of the ideal gravitoronchigram for the Schwarzschild lens in the thin lens approximation and in an exact way. Finally, because the caustic associated with the deflected light by the axicon and the Schwarzschild lenses is a line along the optical axis we conjecture the generation of a gravitoBessel beam by illuminating the Schwarzschild lens with a point light source analogous to that generated by an axicon lens. That is, a particular example of the so-called non-diffracting light fields.