  Traditional optical imaging faces an unavoidable trade-off between resolution
and depth of field (DOF). To increase resolution, high numerical apertures (NA)
are needed, but the associated large angular uncertainty results in a limited
range of depths that can be put in sharp focus. Plenoptic imaging was
introduced a few years ago to remedy this trade off. To this aim, plenoptic
imaging reconstructs the path of light rays from the lens to the sensor.
However, the improvement offered by standard plenoptic imaging is practical and
not fundamental: the increased DOF leads to a proportional reduction of the
resolution well above the diffraction limit imposed by the lens NA. In this
paper, we demonstrate that correlation measurements enable pushing plenoptic
imaging to its fundamental limits of both resolution and DOF. Namely, we
demonstrate to maintain the imaging resolution at the diffraction limit while
increasing the depth of field by a factor of 7. Our results represent the
theoretical and experimental basis for the effective development of the
promising applications of plenoptic imaging.
