If we restrict ourselves to geometric optics, i.e. to incoherent light and to objects larger than the wavelength of light, then the fundamental carrier of light is a ray. The measure for the amount of light traveling along a ray is radiance, denoted by L and measured in watts (W) per steradian (sr) per meter squared (m2). The steradian is a measure of solid angle, and meters squared are used here as a measure of cross-sectional area, as shown at right.
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 (Adelson 1991). 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 never actually used in practice, and is more useful in understanding other concepts in vision and graphics. Since rays in space can be parameterized by three coordinates, x, y, and z and two angles and , as shown at left, it is a five-dimensional function. (One can consider time, wavelength, and polarization angle as additional variables, yielding higher-dimensional functions.)
Like Adelson, Gershun defined the light field at each point in space as a 5D function. However, he treated it as an infinite collection of vectors, one per direction impinging on the point, with lengths proportional to their radiances. Equivalently, one can imagine an infinite collection of infinitesimal surfaces placed at that point, one per direction, with different values of irradiance assigned to each surface.
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 at right, reproduced from Gershun's paper, shows this calculation for the case of two light sources. In computer graphics, this vector-valued function of 3D space is called the vector irradiance field (Arvo, 1994). The vector direction at each point in the field can be interpreted as the orientation one would face a flat surface placed at that point to most brightly illuminate it.
In a plenoptic function, if the region of interest contains a concave object (think of a cupped hand), then light leaving one point on the object may travel only a short distance before being blocked by another point on the object. No practical device could measure the function in such a region.
However, if we restrict ourselves to locations outside the convex hull (think shrink-wrap) of the object, then we can measure the plenoptic function easily using a digital camera. Moreover, in this case the function contains redundant information, because the radiance along a ray remains constant from point to point along its length, as shown at left. In fact, the redundant information is exactly one dimension, leaving us with a four-dimensional function. Parry Moon dubbed this function the photic field (1981), while researchers in computer graphics call it the 4D light field (Levoy 1996) or Lumigraph (Gortler 1996). Formally, the 4D light 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, a few of which are shown below. Of these, the most common is the two-plane parameterization shown at right (below). While this parameterization cannot represent all rays, for example rays parallel to the two planes if the planes are parallel to each other, it has the advantage of relating closely to the analytic geometry of perspective imaging. Indeed, 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.
Light fields are a fundamental representation for light. As such, there are as many ways of creating light fields as there are computer programs capable of creating images or instruments capable of capturing them.
In computer graphics, light fields are typically produced either by rendering a 3D model or by photographing a real scene. In either case, to produce a light field views must be obtained for a large collection of viewpoints. Depending on the parameterization employed, this collection will typically span some portion of a line, circle, plane, sphere, or other shape, although unstructured collections of viewpoints are also possible (Buehler 2001).
Devices for capturing light fields photographically may include a moving handheld camera, a robotically controlled camera (Levoy, 2002) an arc of cameras (as in the bullet time effect used in The Matrix), a dense array of cameras (Kanade 1998; Yang 2002; Wilburn 2005), or a handheld camera (Ng 2005; Georgiev 2006), microscope (Levoy 2006), or other optical system in which an array of microlenses has been inserted in the optical path: see plenoptic camera. Some public domain archives of light field datasets are listed below.
How many images should be in a light field? The largest known light field (of Michelangelo's statue of Night) contains 24,000 1.3-megapixel images. At a deeper level, the answer depends on the application. For light field rendering (see the Application section below), if you want to walk completely around an opaque object, then of course you need to photograph its back side. Less obviously, if you want to walk close to the object, and the object lies astride the st plane, then you need images taken at finely spaced positions on the uv plane (in the two-plane parameterization shown above), which is now behind you, and these images need to have high spatial resolution.
The number and arrangement of images in a light field, and the resolution of each image, are together called the "sampling" of the 4D light field. Analyses of light field sampling have been undertaken by many researchers; a good starting point is Chai (2000). Also of interest is Durand (2005) for the effects of occlusion, Ramamoorthi (2006) for the effects of lighting and reflection, and Ng (2005) and Zwicker (2006) for applications to plenoptic cameras and 3D displays, respectively.
Computational imaging refers to any image formation method that involves a digital computer. Many of these methods operate at visible wavelengths, and many of those produce light fields. As a result, listing all applications of light fields would require surveying all uses of computational imaging - in art, science, engineering, and medicine. In computer graphics, some selected applications are:
Image generation and predistortion of synthetic imagery for holographic stereograms is one of the earliest examples of computed light fields, anticipating and later motivating the geometry used in Levoy and Hanrahan's work (Halle 1991, 1994).
US Patent Issued to Mitsubishi Electric Research Laboratories on Oct. 25 for "Method and System for Decoding and Displaying 3d Light Fields" (Massachusetts, California Inventors)
Oct 31, 2011; ALEXANDRIA, Va., Oct. 31 -- United States Patent no. 8,044,994, issued on Oct. 25, was assigned to Mitsubishi Electric Research...
US Patent Issued to Primesense on Nov. 1 for "Depth-Varying Light Fields for Three Dimensional Sensing" (Israeli Inventors)
Nov 05, 2011; ALEXANDRIA, Va., Nov. 5 -- United States Patent no. 8,050,461, issued on Nov. 1, was assigned to Primesense Ltd. (Tel-Aviv,...
US Patent Issued to Primesense on Feb. 12 for "Depth-Varying Light Fields for Three Dimensional Sensing" (Israeli Inventors)
Feb 13, 2013; ALEXANDRIA, Va., Feb. 13 -- United States Patent no. 8,374,397, issued on Feb. 12, was assigned to Primesense Ltd. (Tel Aviv,...