Wave-front sensing and deformable-mirror control in strong scintillation

Recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is significant a continuous phase function does not in general exist, owing to the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares approaches to wave-front reconstruction and deformable-mirror control can have large errors. Branch-point reconstructors are known to provide superior performance to least-squares reconstructors, but they require that branch points be explicitly detected. Detecting branch points is a significant practical impediment owing to spatial sampling and measurement noise in real wave-front sensors. Branch points are associated with real zeros in an optical field, and hence information about the phase of the field is encoded in the amplitude of the wave. We present a new wave-front-sensor processing algorithm that exploits this observation in the wave-front-reconstruction and deformable-mirror-control process. This algorithm jointly processes three intensity measurements by using light from the beacon field to develop a set of deformable-mirror actuator commands that are maximally consistent with three intensity measurements: (1) the entire wave-front-sensor image, (2) a pupil intensity image, and (3) a conventional image. Owing to the nonlinear nature of the resulting algorithm, we have used a simulation to evaluate performance. We find that in a focused laser beam projection paradigm that uses a point-source beacon, the new algorithm provides significantly improved performance over that of conventional Hartmann sensor least-squares deformable-mirror control based on centroid processing of wave-front-sensor outputs. The performance of the new algorithm approaches, the performance of an idealized branch-point reconstructor that requires pointwise phase differences for operation.