Branch-point detection using a Shack–Hartmann wavefront sensor

In this paper, two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied; the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located towards the center of the SHWFS’s lenslet pupil, while the circulation of phase gradients approach works best when the branch point is located towards the edge of the SHWFS’s lenslet pupil. These behavior were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented within support researchers looking to study high scintillation optical-turbulence environments as well as will inform efforts looking to develop branch-point tolerant reconstruction algorithms.