Branch point detection and correction using the branch point potential method Kevin Murphy, Ruth Mackey and Chris Dainty Applied Optics Group, Department of Physics, National University of Ireland, Galway, Galway, Ireland; 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. 1 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. Keywords: Branch points, adaptive optics, Shack Hartmann, wavefront reconstruction 1. INTRODUCTION Branch points occur in an optical wavefront when it is heavily distorted or the interference is such that zeros of intensity are seen at the plane of the receiver. At these nulls of intensity, the phase of the optical wavefront is undefined and it is at these positions that branch points are formed. Branch points occur in pairs (which are of opposite rotation or sign) and are connected by wave dislocations called branch cuts. Along these branch cuts the phase of the wavefront undergoes a 2π jump. The branch point is at the origin of the 2π discontinuity that causes these wave dislocations. Due to branch points the phase of the optical wavefront at the receiver is not continuous and this causes difficulties in adaptive optics (AO) systems in strong turbulence. Nye and Berry observed branch points as early as 1974 2 due to interference caused by certain types of scattering. A paper by Baranova et al. in 1983 3 highlighted some of the problems that branch points may cause AO systems, mainly because of the fact that it would be extremely difficult for a continuous plate deformable mirror to correct for them. Fried and Vaughn 4 explained and quantified the existence of branch points in the phase function. The authors explained that branch points (and their associated branch cuts) were unavoidable when the intensity of the light dropped to zero at the cross-section of the receiver. Their suggestion to take care of branch points was to first find the branch point locations, then form the branch cuts so that they are ‘tucked away’ into regions of low intensity and then to reconstruct the phase function around them by using a path dependent least-squares method which never crosses a branch cut. This method was deemed to be too slow and impractical due to difficulties in the pairing up of branch points to form branch cuts. The authors also used an intensity weighted least-squares multigrid method that does not rely on identifying branch points or positioning branch cuts. It should also be noted that the contour sum method for detecting branch points was outlined in this paper. Other papers have indicated that using a different branch point corrector, such as an exponential or multigrid reconstructor, would be better when reconstructing the phase function. 5, 6 (Send correspondence to Kevin Murphy) E-mail: murphyk@nuigalway.ie: Telephone: +353 (0)91492824