Editing Light field (section)

==The plenoptic function==
[[Image:Plenoptic-function-a.png|right|frame|Radiance ''L'' along a ray can be thought of as the amount of light traveling along all possible straight lines through a tube whose size is determined by its solid angle and cross-sectional area.]]

For geometric [[optics]]—i.e., to [[Coherence (physics)|incoherent]] light and to objects larger than the wavelength of light—the fundamental carrier of light is a [[ray (optics)|ray]]. The measure for the amount of light traveling along a ray is [[radiance]], denoted by ''L'' and measured in {{nowrap|W·sr<sup>−1</sup>·m<sup>−2</sup>}}; i.e., [[watt]]s (W) per [[steradian]] (sr) per square meter (m<sup>2</sup>). The steradian is a measure of [[solid angle]], and meters squared are used as a measure of cross-sectional area, as shown at right.

[[Image:Plenoptic function b.svg|left|frame|Parameterizing a ray in [[three-dimensional space|3D]] space by position (''x'', ''y'', ''z'') and direction (''θ'', ''ϕ'').]]

The radiance along all such rays in a region of three-dimensional space illuminated by an unchanging arrangement of lights is called the plenoptic function.<ref>Adelson 1991</ref> The plenoptic illumination function is an idealized function used in [[computer vision]] and [[computer graphics]] to express the image of a scene from any possible viewing position at any viewing angle at any point in time. It is not used in practice computationally, but is conceptually useful in understanding other concepts in vision and graphics.<ref>Wong 2002</ref> Since rays in space can be parameterized by three coordinates, ''x'', ''y'', and ''z'' and two angles ''θ'' and ''ϕ'', as shown at left, it is a five-dimensional function, that is, a function over a five-dimensional [[manifold]] equivalent to the product of 3D [[Euclidean space]] and the [[2-sphere]].

[[Image:Gershun-light-field-fig17.png|right|thumb|175px|Summing the irradiance vectors '''D'''<sub>1</sub> and '''D'''<sub>2</sub> arising from two light sources I<sub>1</sub> and I<sub>2</sub> produces a resultant vector '''D''' having the magnitude and direction shown.<ref>Gershun, fig 17</ref>]]

The light field at each point in space can be treated as an infinite collection of vectors, one per direction impinging on the point, with lengths proportional to their radiances.

Integrating these vectors over any collection of lights, or over the entire sphere of directions, produces a single scalar value—the total irradiance at that point, and a resultant direction. The figure shows this calculation for the case of two light sources. In computer graphics, this vector-valued function of [[Three-dimensional space|3D space]] is called the vector irradiance field.<ref>Arvo, 1994</ref> The vector direction at each point in the field can be interpreted as the orientation of a flat surface placed at that point to most brightly illuminate it.

===Higher dimensionality===
Time, [[wavelength]], and [[Polarization (waves)|polarization]] angle can be treated as additional dimensions, yielding higher-dimensional functions, accordingly.