  Research and medicine rely on non-invasive optical techniques to image living
tissue with high resolution in space and time. But so far a single data
acquisition could not provide entirely diffraction-limited tomographic volumes
of rapidly moving or changing targets, which additionally becomes increasingly
difficult in the presence of aberrations, e.g., when imaging retina in vivo. We
show, that a simple interferometric setup based on parallelized optical
coherence tomography acquires volumetric data with 10 billion voxels per
second, exceeding previous imaging speeds by an order of magnitude. This allows
us to computationally obtain and correct defocus and aberrations resulting in
entirely diffraction-limited volumes. As demonstration, we imaged living human
retina with clearly visible nerve fiber layer, small capillary networks, and
photoreceptor cells, but the technique is also applicable to obtain
phase-sensitive volumes of other scattering structures at unprecedented
acquisition speeds.
