Detection and characterization of an optical vortex by the branch point potential method: analytical and simulation results.

Singularities are discontinuities in optical wavefronts that can be produced by turbulence effects. Since the presence of singularities in a wavefront severely degrades the adaptive optics correction performance, their detection is very important. The gradient of the wavefront phase, as measured by the Shack-Hartmann wavefront sensor in the presence of singularities, can be considered as the sum of the rotational and irrotational parts. The rotational part of the phase gradient originating from the phase singularities can be considered as a potential based on Helmholtz-Hodge decomposition. The potential at the singularities positions appears as peaks and valleys of the potential depending on the positive or negative charges of singularities. In this article, the detection of phase singularities based on the branch point potential (BPP) method is investigated. The irrotational part of the gradient produces a background potential where singularities positions appear as local extremum of the potential. With our method, the irrotational part of the gradient is eliminated and the value of peaks and valleys is increased. In addition, in this method, the potential value characterizes the optical singularities. Here, analytical and simulation results for the detection of general forms of the singularity are presented. Our simulations show the performance of singularities detection in noisy conditions.