Theory Unifying Ray and Wavefront Lightfield Propagation

The ray-based representation cannot be directly used to analyze diffractive or phase-sensitive optical elements. 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 (i) in free space, the 4-D 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.