Editing Light field (section)

==The 4D light field==
[[Image:Plenoptic-function-c.png|left|frame|Radiance along a ray remains constant if there are no blockers.]]

In a plenoptic function, if the region of interest contains a [[concave polygon|concave]] object (e.g., a cupped hand), then light leaving one point on the object may travel only a short distance before another point on the object blocks it. No practical device could measure the function in such a region.

However, for locations outside the object's [[convex hull]] (e.g., shrink-wrap), the plenoptic function can be measured by capturing multiple images. In this case the function contains redundant information, because the radiance along a ray remains constant throughout its length. The redundant information is exactly one dimension, leaving a four-dimensional function variously termed the photic field, the 4D light field<ref>Levoy 1996</ref> or lumigraph.<ref>Gortler 1996</ref> Formally, the field is defined as radiance along rays in empty space.

The set of rays in a light field can be parameterized in a variety of ways. The most common is the two-plane parameterization. While this parameterization cannot represent all rays, for example rays parallel to the two planes if the planes are parallel to each other, it relates closely to the [[analytic geometry]] of perspective imaging. A simple way to think about a two-plane light field is as a collection of perspective images of the ''st'' plane (and any objects that may lie astride or beyond it), each taken from an observer position on the ''uv'' plane. A light field parameterized this way is sometimes called a light slab.

[[Image:Light-field-parameterizations.png|left|frame| Some alternative parameterizations of the 4D light field, which represents the flow of light through an empty region of three-dimensional space. Left: points on a plane or curved surface and directions leaving each point. Center: pairs of points on the surface of a sphere. Right: pairs of points on two planes in general (meaning any) position.]]
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===Sound analog===
The analog of the 4D light field for sound is the sound field or wave field'','' as in [[wave field synthesis]], and the corresponding parametrization is the [[Kirchhoff–Helmholtz integral]], which states that, in the absence of obstacles, a sound field over time is given by the pressure on a plane. Thus this is two dimensions of information at any point in time, and over time, a 3D field.

This two-dimensionality, compared with the apparent four-dimensionality of light, is because light travels in rays (0D at a point in time, 1D over time), while by the [[Huygens–Fresnel principle]], a sound [[wave front]] can be modeled as spherical waves (2D at a point in time, 3D over time): light moves in a single direction (2D of information), while sound expands in every direction. However, light travelling in non-vacuous media may scatter in a similar fashion, and the irreversibility or information lost in the scattering is discernible in the apparent loss of a system dimension.