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Abstract

This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this geometrical theory to our optical situation has enabled us to analytically reproduce the behaviours of various caustics. The interest lies mainly in the universal nature of these results since our treatment requires no prior knowledge of the optical configuration, but only a smart definition of the control space. This universal approach has finally made it possible to extract mathematical relationships between the aberration coefficients of any optical system, which were hidden by the complexity of optical trajectories but revealed by the set of catastrophes in the control space. These results provide a glimpse for future applications of caustics in the development of new corrected optical systems, especially for ions-based devices.