Propagation of an arbitrary vortex pair through an astigmatic optical system and determination of its net topological charge

We embed a pair of vortices with different topological charges in a Gaussian beam and study its evolution through an astigmatic optical system, a tilted lens. The propagation dynamics is explained by a closed-form analytical expression. Furthermore, we show that a careful examination of the intensity distribution at a predicted position past the lens can provide us with the net charge present in the beam. To the best of our knowledge, our method is the first non-interferometric technique to measure the net charge of an arbitrary vortex pair. Our theoretical results are well supported by experimental observations.