  Light-field microscopy represents a promising solution for microscopic
volumetric imaging, thanks to its capability to encode information on multiple
planes in a single acquisition. This is achieved through its peculiar
simultaneous capture of information on light spatial distribution and
propagation direction. However, state-of-the-art light-field microscopes suffer
from a detrimental loss of spatial resolution compared to standard microscopes.
We propose and experimentally demonstrate a light-field microscopy architecture
based on light intensity correlation, in which resolution is limited only by
diffraction. We demonstrate the effectiveness of our technique in refocusing
three-dimensional test targets and biological samples out of the focused plane.
We improve the depth of field by a factor 6 with respect to conventional
microscopy, at the same resolution, and obtain, from one acquired correlation
image, about $130,000$ images, all seen from different perspectives; such
multi-perspective images are employed to reconstruct over $40$ planes within a
$1 \,\mathrm{mm}^3$ sample with a diffraction-limited resolution voxel of $20
\times 20 \times 30\ \mu\mathrm{m}^3$.
