Approaching all the configurations for the analytical ronchigram in relation to the caustic region for an arbitrary plano-convex lens

The aim of this work is twofold: first we present a general method to design a Ronchi grating, and second we compute its associated analytical ronchigram for a general plano-convex lens illuminated with a plane wave, for any configuration of the Ronchi grating and the detection planes. We remark that the analytical pattern depends directly on the caustic region magnitude; and moreover, the pattern features depend on the caustic projections and the virtual caustic projections. These general results are applied to three plano-convex lenses and a full analysis of the ronchigrams is presented for every possible configuration of the optical system. For the first time, the ronchigrams are computed for those configurations where the detection plane is placed inside the caustic region.