Spatial analysis of discrete plenoptic sampling

Plenoptic cameras are intended to fully capture the light rays in a scene. Using this information, optical elements can be applied to a scene computationally rather than physically-allowing an infinite variety of pictures to be rendered after the fact from the same plenoptic data. Practical plenoptic cameras necessarily capture discrete samples of the plenoptic function, which together with the overall camera design, can constrain the variety and quality of rendered images. In this paper we specifically analyze the nature of the discrete data that plenoptic cameras capture, in a manner that unifies the traditional and focused plenoptic camera designs. We use the optical properties of plenoptic cameras to derive the geometry of discrete plenoptic function capture. Based on this geometry, we derive expressions for expected resolution from a captured plenoptic function. Our analysis allows us to define the "focused plenoptic condition," a necessary condition in the optical design that distinguishes the traditional plenoptic camera from the focused plenoptic camera.