  The ray-based 4D light field representation cannot be directly used to
analyze diffractive or phase--sensitive optical elements. In this paper, we
exploit tools from wave optics and extend the light field representation via a
novel "light field transform". We introduce a key modification to the
ray--based model to support the transform. We insert a "virtual light source",
with potentially negative valued radiance for certain emitted rays. We create a
look-up table of light field transformers of canonical optical elements. The
two key conclusions are that (i) in free space, the 4D light field completely
represents wavefront propagation via rays with real (positive as well as
negative) valued radiance and (ii) at occluders, a light field composed of
light field transformers plus insertion of (ray--based) virtual light sources
represents resultant phase and amplitude of wavefronts. For free--space
propagation, we analyze different wavefronts and coherence possibilities. For
occluders, we show that the light field transform is simply based on a
convolution followed by a multiplication operation. This formulation brings
powerful concepts from wave optics to computer vision and graphics. We show
applications in cubic-phase plate imaging and holographic displays.
