Оптикадағы векторлық функция

Vector function in optics
A light field, or lightfield, is a vector function that describes the amount of light flowing in every direction through every point in a space. 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. 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 term light field was coined by Andrey Gershun in a classic 1936 paper on the radiometric properties of light in three dimensional space. The term "radiance field" may also be used to refer to similar, or identical concepts. The term is used in modern research such as neural radiance fields

For 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 measure for the amount of light traveling along a ray is radiance, denoted by L and measured in W·sr−1·m−2, i. e., watts (W) per steradian (sr) per meter squared (m2). The steradian is a measure of solid angle, and meters squared are used 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. 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. 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. 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 3D space is called the vector irradiance field. 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.

Time, wavelength, and polarization angle can be treated as additional dimensions, yielding higher dimensional functions, accordingly.

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. 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 or lumigraph. 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.

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.

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, this collection typically spans some portion of a line, circle, plane, sphere, or other shape, although unstructured collections are possible. Devices for capturing light fields photographically may include a moving handheld camera or a robotically controlled camera, an arc of cameras (as in the bullet time effect used in The Matrix), a dense array of cameras, handheld cameras, microscopes, or other optical system. The number of images in a light field depends on the application. A light field capture of Michelangelo's statue of Night contains 24,000 1.3 megapixel images, which is considered large as of 2022. For light field rendering to completely capture an opaque object, images must be taken of at least the front and back. Less obviously, for an object that lies astride the st plane, finely spaced images must be taken on the uv plane (in the two plane parameterization shown above). 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. Also of interest are the effects of occlusion, lighting and reflection.

Gershun's reason for studying the light field was to derive (in closed form) illumination patterns that would be observed on surfaces due to light sources of various shapes positioned above these surface. The branch of optics devoted to illumination engineering is nonimaging optics. It extensively uses the concept of flow lines (Gershun's flux lines) and vector flux (Gershun's light vector). However, the light field (in this case the positions and directions defining the light rays) is commonly described in terms of phase space and Hamiltonian optics.

Extracting appropriate 2D slices from the 4D light field of a scene, enables novel views of the scene. Depending on the parameterization of the light field and slices, these views might be perspective, orthographic, crossed slit, general linear cameras, multi perspective, or another type of projection. Light field rendering is one form of image based rendering.

Integrating an appropriate 4D subset of the samples in a light field can approximate the view that would be captured by a camera having a finite (i. e., non pinhole) aperture. Such a view has a finite depth of field. Shearing or warping the light field before performing this integration can focus on different fronto parallel or oblique planes. Images captured by digital cameras that capture the light field 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.

Neural activity can be recorded optically by genetically encoding neurons with reversible fluorescent markers such as GCaMP that indicate the presence of calcium ions in real time. Since light field microscopy captures full volume information in a single frame, it is possible to monitor neural activity in individual neurons randomly distributed in a large volume at video framerate. Quantitative measurement of neural activity can be done despite optical aberrations in brain tissue and without reconstructing a volume image, and be used to monitor activity in thousands of neurons.

This is a method of 3D reconstruction from multiple images that creates a scene model comprising a generalized light field and a relightable matter field. The generalized light field represents light flowing in every direction through every point in the field. The relightable matter field represents the light interaction properties and emissivity of matter occupying every point in the field. Scene data structures can be implemented using Neural Networks, and Physics based structures, among others.

Image generation and predistortion of synthetic imagery for holographic stereograms is one of the earliest examples of computed light fields.

Glare arises due to multiple scattering of light inside the camera body and lens optics that reduces image contrast. While glare has been analyzed in 2D image space, it is useful to identify it as a 4D ray space phenomenon. Statistically analyzing the ray space inside a camera allows the classification and removal of glare artifacts. In ray space, glare behaves as high frequency noise and can be reduced by outlier rejection. Such analysis can be performed by capturing the light field inside the camera, but it results in the loss of spatial resolution. Uniform and non uniform ray sampling can be used to reduce glare without significantly compromising image resolution.

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