  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.
