  We have designed a plenoptic sensor to retrieve phase and amplitude changes
resulting from a laser beam's propagation through atmospheric turbulence.
Compared with the commonly restricted domain of (-pi, pi) in phase
reconstruction by interferometers, the reconstructed phase obtained by the
plenoptic sensors can be continuous up to a multiple of 2pi. When compared with
conventional Shack-Hartmann sensors, ambiguities caused by interference or low
intensity, such as branch points and branch cuts, are less likely to happen and
can be adaptively avoided by our reconstruction algorithm. In the design of our
plenoptic sensor, we modified the fundamental structure of a light field camera
into a mini Keplerian telescope array by accurately cascading the back focal
plane of its object lens with a microlens array's front focal plane and
matching the numerical aperture of both components. Unlike light field cameras
designed for incoherent imaging purposes, our plenoptic sensor operates on the
complex amplitude of the incident beam and distributes it into a matrix of
images that are simpler and less subject to interference than a global image of
the beam. Then, with the proposed reconstruction algorithms, the plenoptic
sensor is able to reconstruct the wavefront and a phase screen at an
appropriate depth in the field that causes the equivalent distortion on the
beam. The reconstructed results can be used to guide adaptive optics systems in
directing beam propagation through atmospheric turbulence. In this paper we
will show the theoretical analysis and experimental results obtained with the
plenoptic sensor and its reconstruction algorithms.
