  Atmospheric turbulence causes fluctuations in the local refractive index of
air that accumulatively disturb a wave's phase and amplitude distribution as it
propagates. This impairs the effective range of laser weapons as well as the
performance of free space optical (FSO) communication systems. Adaptive optics
(AO) can be applied to effectively correct wavefront distortions in weak
turbulence situations. However, in strong or deep turbulence, where
scintillation and beam breakup are common phenomena, traditional wavefront
sensing techniques such as the use of Shack-Hartmann sensors lead to incorrect
results. Consequently, the performance of AO systems will be greatly
compromised. We propose a new approach that can determine the major phase
distortions in a beam instantaneously and guide an AO device to compensate for
the phase distortion in a few iterations. In our approach, we use a plenoptic
wavefront sensor to image the distorted beam into its 4D phase space. A fast
reconstruction algorithm based on graph theory is applied to recognize the
phase distortion of a laser beam and command the AO device to perform phase
compensation. As a result, we show in our experiments that an arbitrary phase
distortion with peak to peak value up to 22{\pi} can be corrected within a few
iteration steps. Scintillation and branch point problems are smartly avoided by
the plenoptic sensor and its fast reconstruction algorithm. In this article, we
will demonstrate the function of the plenoptic sensor, the fast reconstruction
algorithm as well as the beam correction improvements when our approach is
applied to an AO system.
