Branch point agnostic full optical field reconstruction using Shack-Hartmann data

We present a solution to the problem of branch points in wavefront sensing by circumventing the problem altogether and reconstructing the full complex optical field instead of the phase. Traditional wavefront reconstruction algorithms are based on least-squares fitting of phase gradients and fail in the presence of strong scintillation due to the formation of branch point singularities in the phase. However, these points are simply zeros (and not singularities) of the optical field-thus, reconstruction of the full optical field is a well-posed problem. Using the intensity and gradient data of a Shack-Hartmann wavefront sensor, our method poses a linear least-squares problem for the full optical field rather than the phase, which can be solved efficiently using standard techniques. Crucially, the algorithm is efficient and readily implementable in real-time adaptive optics applications. Numerical results show the accuracy of our algorithm and its robustness to noise in nontrivial examples of highly scintillated fields with numerous branch points.