Branch point detection and correction using the branch point potential method

Abstract

Branch points have been shown to cause problems for adaptive optics (AO) systems which attempt to correct for atmospheric distortion over mid-to-long range horizontal paths. Where branch points (or singularities) occur, the phase of the optical wavefront is undefined and cannot be reconstructed by conventional wavefront reconstruction techniques. Branch points occur in pairs of opposite sign (or rotation) and are joined by wavefront dislocations called branch cuts, which have a 2π jump in phase across them. The aim of the project is to construct a branch point sensitive wavefront reconstructor using a Shack Hartmann wavefront sensor which can be used on a 3km line-of-sight (LOS) free space optical (FSO) communications system currently being tested within our group. The first step in our method is to detect the positions of singularities using the branch point potential method first proposed by LeBigot and Wild. The most common zonal reconstruction method used (the least squares reconstructor) is not sensitive to branch points and different methods are being investigated for this part of the project. Results for the detection of singularities using the branch point potential method in simulations are shown here. Some early results for the reconstruction of branch point affected wavefronts are also presented.