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. The most common is the two-plane parameterization. The set of rays in a light field can be parameterized in a variety of ways. Formally, the field is defined as radiance along rays in empty space. The redundant information is exactly one dimension, leaving a four-dimensional function variously termed the photic field, the 4D light field or lumigraph. ![]() In this case the function contains redundant information, because the radiance along a ray remains constant throughout its length. However, for locations outside the object's convex hull (e.g., shrink-wrap), the plenoptic function can be measured by capturing multiple images. No practical device could measure the function in such a region. In a plenoptic function, if the region of interest contains a 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. The 4D light field Radiance along a ray remains constant if there are no blockers. Time, wavelength, and polarization angle can be treated as additional dimensions, yielding higher-dimensional functions, accordingly. 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. In computer graphics, this vector-valued function of 3D space is called the vector irradiance field. The figure shows this calculation for the case of two light sources. 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 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. Summing the irradiance vectors D 1 and D 2 arising from two light sources I 1 and I 2 produces a resultant vector D having the magnitude and direction shown. ![]() 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. It is not used in practice computationally, but is conceptually useful in understanding other concepts in vision and graphics. 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. 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. Parameterizing a ray in 3D space by position ( x, y, z) and direction ( θ, ϕ). The steradian is a measure of solid angle, and meters squared are used as a measure of cross-sectional area, as shown at right. m −2, i.e., watts (W) per steradian (sr) per meter squared (m 2). ![]() The measure for the amount of light traveling along a ray is radiance, denoted by L and measured in W ![]() The plenoptic function 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.įor geometric optics-i.e., to incoherent light and to objects larger than the wavelength of light-the fundamental carrier of light is a ray. The term is used in modern research such as neural radiance fields. The term "radiance field" may also be used to refer to similar concepts. Modern approaches to light-field display explore co-designs of optical elements and compressive computation to achieve higher resolutions, increased contrast, wider fields of view, and other benefits. The phrase light field was coined by Andrey Gershun in a classic 1936 paper on the radiometric properties of light in three-dimensional space. Michael Faraday was the first to propose that light should be interpreted as a field, much like the magnetic fields on which he had been working. The space of all possible light rays is given by the five-dimensional plenoptic function, and the magnitude of each ray is given by its radiance. The light field is a vector function that describes the amount of light flowing in every direction through every point in space.
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