Phase retrieval of Laguerre-Gaussian beams through atmospheric turbulence by binary amplitude modulation.

Wavefront reconstruction of Laguerre-Gaussian (LG) beams presents a great challenge due to the singularities in their phase profiles. Interferometric methods are difficult to implement since they require a reference beam and they are very sensitive to mechanical perturbations. Deterministic methods such as those based on the phase-transport or intensity-transport equation are limited to the paraxial approximation. Furthermore, if such beams propagate in atmospheric turbulence, complex dynamic characteristics are added to the problem. We seek to find an implementation of a technique that is capable of dynamically recovering the singular phases of LG beams under such random conditions. In this work, we will demonstrate a phase-retrieval technique that allows the recovery of LG wavefronts in turbulence and will characterize its effectiveness under a range of atmospheric parameters and propagation length. This technique is based on binary amplitude modulation and is suitable for dynamic applications.