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Luneburg lens

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A Luneburg lens (originally Lüneburg lens, often incorrectly spelled Luneberg lens) is a spherically symmetric gradient-index lens. [1]

43 relations: Angle of incidence (optics), Antenna feed, Beltrami identity, BLITS, Circular symmetry, Collimated light, Coma (optics), Constant of integration, Constant of motion, Differential equation, Electromagnetic radiation, Ellipse, Examples of differential equations, Feed horn, Fermat's principle, Focus (optics), Gradient, Gradient-index optics, Gravitational lens, Ground plane, Horn antenna, Image, Integral, James Clerk Maxwell, Lagrangian mechanics, Laser diode, Light, Microwave, Microwave antenna, Numerical methods for ordinary differential equations, Offset dish antenna, Optical axis, Parabolic antenna, Phase center, Polar coordinate system, Pythagorean theorem, Radar, Radio wave, Refractive index, Relative permittivity, Retroreflector, Rudolf Luneburg, The Quarterly Journal of Pure and Applied Mathematics.

Angle of incidence (optics)

In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

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Antenna feed

In telecommunications and electronics, an antenna feed refers to the components of an antenna which feed the radio waves to the rest of the antenna structure, or in receiving antennas collect the incoming radio waves, convert them to electric currents and transmit them to the receiver.

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Beltrami identity

The Beltrami identity, named after Eugenio Beltrami, is a simplified and less general version of the Euler–Lagrange equation in the calculus of variations.

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BLITS (Ball Lens In The Space) is a Russian satellite launched on September 17, 2009, as a secondary payload on a Soyuz-2.1b/Fregat, from the Baikonur Cosmodrome in Kazakhstan.

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Circular symmetry

In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.

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Collimated light

Collimated light is light whose rays are parallel, and therefore will spread minimally as it propagates.

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Coma (optics)

In optics (especially telescopes), the coma, or comatic aberration, in an optical system refers to aberration inherent to certain optical designs or due to imperfection in the lens or other components that results in off-axis point sources such as stars appearing distorted, appearing to have a tail (coma) like a comet.

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Constant of integration

In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.

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Constant of motion

In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Electromagnetic radiation

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space-time, carrying electromagnetic radiant energy.

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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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Examples of differential equations

Differential equations arise in many problems in physics, engineering, and other sciences.

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Feed horn

In parabolic antennas such as satellite dishes, a feed horn (or feedhorn) is a small horn antenna used to convey radio waves between the transmitter and/or receiver and the parabolic reflector.

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Fermat's principle

In optics, Fermat's principle or the principle of least time, named after French mathematician Pierre de Fermat, is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time.

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Focus (optics)

In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge.

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In mathematics, the gradient is a multi-variable generalization of the derivative.

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Gradient-index optics

Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradual variation of the refractive index of a material.

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Gravitational lens

A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer.

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Ground plane

In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground.

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Horn antenna

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam.

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An image (from imago) is an artifact that depicts visual perception, for example, a photo or a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person, thus providing a depiction of it.

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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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James Clerk Maxwell

James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.

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Lagrangian mechanics

Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.

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Laser diode

A laser diode, (LD), injection laser diode (ILD), or diode laser is a semiconductor device similar to a light-emitting diode in which the laser beam is created at the diode's junction.

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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum.

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Microwaves are a form of electromagnetic radiation with wavelengths ranging from one meter to one millimeter; with frequencies between and.

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Microwave antenna

A microwave antenna is a physical transmission device used to broadcast microwave transmissions between two or more locations.

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Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).

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Offset dish antenna

An offset dish antenna or off-axis dish antenna is a type of parabolic antenna.

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Optical axis

An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.

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Parabolic antenna

A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves.

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Phase center

In antenna design theory, the phase center is the point from which the electromagnetic radiation spreads spherically outward, with the phase of the signal being equal at any point on the sphere.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects.

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Radio wave

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light.

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Refractive index

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how light propagates through that medium.

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Relative permittivity

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the permittivity of vacuum.

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A retroreflector (sometimes called a retroflector or cataphote) is a device or surface that reflects light back to its source with a minimum of scattering.

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Rudolf Luneburg

Rudolf Karl Lüneburg (30 March 1903, Volkersheim (Bockenem) - 19 August 1949, Great Falls, Montana), after his emigration at first Lueneburg, later Luneburg, falsified Luneberg) was a professor of mathematics and optics at the Dartmouth College Eye Institute. He was born in Germany, received his doctorate at Göttingen, and emigrated to the United States in 1935. His work included an analysis of the geometry of visual space as expected from physiognomy and the assumption that the angle of vergence provides a constant measure of distance. From these premises he concluded that near field visual space is hyperbolic.

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The Quarterly Journal of Pure and Applied Mathematics

The Quarterly Journal of Pure and Applied Mathematics was a mathematics journal that first appeared as such in 1855, but as the continuation of The Cambridge Mathematical Journal that had been launched in 1836 and had run in four volumes before changing its title to The Cambridge and Dublin Mathematical Journal for a further nine volumes (these latter volumes carried dual numbering).

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Redirects here:

Dielectric lens, Lens Antenna, Luneberg lens, Maxwell fish-eye, Maxwell's fisheye.


[1] https://en.wikipedia.org/wiki/Luneburg_lens

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