Astigmatic tomography of orbital-angular-momentum superpositions

We use astigmatic transformations to characterize two-dimensional superpositions of orbital-angular-momentum states in laser beams. We propose two methods for doing this, both relying only on astigmatic transformations, viewed as rotations on the Poincaré sphere, followed by imaging. These methods can be used as a tomographic tool for communication protocols based on optical vortices