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We use astigmatic transformations to characterize two-dimensionalsuperpositions of Orbital Angular Momentum (OAM) states in laser beams. Wepropose two methods for doing this, both relying only on astigmatictransformations, viewed as rotations on the Poincar\'e sphere, followed byimaging. These methods can be used as a tomographic tool for communicationprotocols based on optical vortices.

Astigmatic tomography of orbital angular momentum superpositions