The aggregate behavior of branch points: the creation and evolution of branch points

Abstract

It has long been known that branch points cause degradation in adaptive optic performance. Here, we begin a study on the aggregate nature of branch points, specifically beginning the process to relate branch points measured in the pupil to the upstream turbulence that created them. As such, we study not only the wave as measured in the telescope's pupil, but also the wave in the intervening region between the turbulence layer and the pupil with this paper's focus on the intervening region. We show that for optical waves propagating in atmospheric turbulence upstream of the pupil, branch points are created infinitesimally close together in pairs of opposite polarity. Branch points are shown to be enduring features of the propagating wave and their branch cuts are shown to evolve smoothly in time. It is postulated that atmospherically created branch point pairs separate as they propagate, and that they carry both the velocity of, and distance to, the turbulence layer that created them. Subsequent papers will demonstrate this to be true.