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# Fresnel diffraction

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. [1]

## Arago spot

In optics, the Arago spot, Poisson spot, or Fresnel bright spot, is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction.

## Atomic mirror

In physics, an atomic mirror is a device which reflects neutral atoms in the similar way as a conventional mirror reflects visible light.

## Augustin-Jean Fresnel

Augustin-Jean Fresnel (10 May 178814 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century.

## Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

## Diffraction

--> Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit.

## Euler spiral

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius).

## Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

## Francesco Maria Grimaldi

Francesco Maria Grimaldi (2 April 1618 – 28 December 1663) was an Italian Jesuit priest, mathematician and physicist who taught at the Jesuit college in Bologna.

## Fraunhofer diffraction

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.

## Fresnel Imager

--> A Fresnel imager is a proposed ultra-lightweight design for a space telescope that uses a Fresnel array as primary optics instead of a typical lens.

## Fresnel integral

Plots of ''S''(''x'') and ''C''(''x''). The maximum of ''C''(''x'') is about 0.977451424. If \frac\pi2t^2 were used instead of t^2, then the image would be scaled vertically and horizontally (see below). Fresnel integrals, S(x) and C(x), are two transcendental functions named after Augustin-Jean Fresnel that are used in optics, which are closely related to the error function (erf).

## Fresnel number

The Fresnel number (F), named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in scalar diffraction theory.

## Fresnel zone

A Fresnel zone, named for physicist Augustin-Jean Fresnel, is one of a series of concentric prolate ellipsoidal regions of space between and around a transmitting antenna and a receiving antenna system.

## Helmholtz equation

In mathematics & physics, the Helmholtz equation, named for Hermann von Helmholtz, is the partial differential equation where &nabla;2 is the Laplacian, k is the wavenumber, and A is the amplitude.

## Huygens–Fresnel principle

The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## Kirchhoff's diffraction formula

Kirchhoff's diffraction formula (also Fresnel–Kirchhoff diffraction formula) can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling.

## Linear canonical transformation

In Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms.

## Max Born

Max Born (11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics.

## McGraw-Hill Education

McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.

## Near and far field

The near field and far field are regions of the electromagnetic field (EM) around an object, such as a transmitting antenna, or the result of radiation scattering off an object.

## Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

## Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

## Physical Review Letters

Physical Review Letters (PRL), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society.

## Richard Cockburn Maclaurin

Richard Cockburn Maclaurin (June 5, 1870 &ndash; January 15, 1920) was a Scottish-born U.S. educator and mathematical physicist.

## Ridged mirror

In atomic physics, a ridged mirror (or ridged atomic mirror, or Fresnel diffraction mirror) is a kind of atomic mirror, designed for the specular reflection of neutral particles (atoms) coming at the grazing incidence angle, characterised in the following: in order to reduce the mean attraction of particles to the surface and increase the reflectivity, this surface has narrow ridges.

## Shear mapping

In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction.

## Specular reflection

Specular reflection, also known as regular reflection, is the mirror-like reflection of waves, such as light, from a surface.

## Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

## Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations.

## Wavefront

In physics, a wavefront is the locus of points characterized by propagation of positions of identical phase: propagation of a point in 1D, a curve in 2D or a surface in 3D.

## Wavenumber

In the physical sciences, the wavenumber (also wave number or repetency) is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.

## References

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