Wigner distributions and how they relate to the light field

Abstract

In wave optics, the Wigner distribution and its Fourier dual, the ambiguity function, are important tools in optical system simulation and analysis. The light field fulfills a similar role in the computer graphics community. In this paper, we establish that the light field as it is used in computer graphics is equivalent to a smoothed Wigner distribution and that these are equivalent to the raw Wigner distribution under a geometric optics approximation. Using this insight, we then explore two recent contributions: Fourier slice photography in computer graphics and wavefront coding in optics, and we examine the similarity between explanations of them using Wigner distributions and explanations of them using light fields. Understanding this long-suspected equivalence may lead to additional insights and the productive exchange of ideas between the two fields.