  This paper explores possibilities for new uses of the Radon transform for
imaging and analysis of lightfields. We show that the previously reported
Dimansionality Gap can be derived from an ultrahyperbolic PDE, first proposed
by F. John, which is satisfied by lightfields. Based on inverse John transform
we demonstrate rigorous Focal Stack rendering and viewing from arbitrary
angles. Based on Asgeirsson's theorems for the ultrahyperbolic PDE we derive
new kernels for processing lightfields. Our kernels provide alternative methods
for depth computation and other image processing in lightfields.
