Aggregate behavior of branch points--persistent pairs.

Light propagating through atmospheric turbulence acquires spatial and temporal phase variations. For strong enough turbulence conditions, interference from these phase variations within the optical wave can produce branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, our previous work has shown that these branch points can be used to estimate the number and velocities of atmospheric layers. Key to this previous demonstration was the property of branch point persistence. Branch points from a single turbulence layer persist in time and through additional layers. In this paper we extend persistence to include branch point pairs. We develop an algorithm for isolating persistent pairs and show that through experimental data that they exist through time and through additional turbulence.