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Fresnel Diffraction Integral
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. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, , of the optical arrangement. When F \gg 1 the diffracted wave is considered to be in the near field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written as \frac \ll 1, where \theta is the maximal angle described by \theta \approx a/L, and the same as in the definition of the Fresnel number. The m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arago Spot
Arago may refer to: People * Aragó, a family name of the kings of the Aragonese Crown * Étienne Arago (1802–1892), French journalist, theater director, and politician; brother of Juan, François, and Jacques * François Arago (1786–1853), French mathematician, physicist, astronomer, and politician; brother of Juan, Jacques, and Étienne * Jacques Arago (1790–1855), French writer, artist and explorer; brother of Juan, François, and Étienne * Josep Riera i Aragó (born 1954), Catalan artist * Marie Arago (1755–1845), French mother of the six Arago brothers Places Earth *Aragó, the name for Aragon in Catalan * Arago, Oregon, United States, an unincorporated community *Arago Township, Minnesota, United States *Cape Arago, Cape Arago State Park, Oregon, United States *Arago Glacier, Graham Land, Antarctica * Arago cave, Tautavel, France, a site where prehistoric remains of Tautavel Man were discovered *Arago hotspot, a geological hotspot near the Arago seamount in the sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase (waves)
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavefront
In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency (otherwise the phase is not well defined). Wavefronts usually move with time. For waves propagating in a unidimensional medium, the wavefronts are usually single points; they are curves in a two dimensional medium, and surfaces in a three-dimensional one. For a sinusoidal plane wave, the wavefronts are planes perpendicular to the direction of propagation, that move in that direction together with the wave. For a sinusoidal spherical wave, the wavefronts are spherical surfaces that expand with it. If the speed of propagation is different at different points of a wavefront, the shape and/or orientation of the wavefronts may change by refraction. In particular, lenses can change the shape of optical wavefronts from planar to spher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Aperture Fresnel Diffraction High Res
Circular may refer to: * The shape of a circle * ''Circular'' (album), a 2006 album by Spanish singer Vega * Circular letter (other) ** Flyer (pamphlet), a form of advertisement * Circular reasoning, a type of logical fallacy * Circular reference * Government circular, a written statement of government policy See also * Circular DNA (other) * Circular Line (other) Circle Line or circular line is an expression commonly used to describe a circle route in a public transport network or system. Circle Line or Circular line may also refer to: Railways Asia Bangladesh * Chittagong Circular Railway China ... * Circularity (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Wave Approximation
Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number **Lorentz scalar, a quantity in the theory of relativity which is invariant under a Lorentz transformation **Pseudoscalar, a quantity that behaves like a scalar, except that it changes sign under a parity inversion *Scalar (computing), any non-composite value *Scalar boson, in physics, a boson subatomic particle whose spin equals zero See also *dot product, also known as scalar product *dimensionless quantity, also known as scalar quantity *Inner product space *Scalar field *Scale (music) *Scaler (other) *''Pterophyllum scalare'' (Lichtenstein, 1823), a species of freshwater angelfish * Scala (other) Scala or SCALA may refer to: Automobiles * Renault Scala, multiple automobile models * Škoda Scala, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmholtz Equation
In mathematics, the eigenvalue problem for the Laplace operator is known as the Helmholtz equation. It corresponds to the linear partial differential equation \nabla^2 f = -k^2 f, where is the Laplace operator (or "Laplacian"), is the eigenvalue, and is the (eigen)function. When the equation is applied to waves, is known as the wave number. The Helmholtz equation has a variety of applications in physics, including the wave equation and the diffusion equation, and it has uses in other sciences. Motivation and uses The Helmholtz equation often arises in the study of physical problems involving partial differential equations (PDEs) in both space and time. The Helmholtz equation, which represents a time-independent form of the wave equation, results from applying the technique of separation of variables to reduce the complexity of the analysis. For example, consider the wave equation \left(\nabla^2-\frac\frac\right) u(\mathbf,t)=0. Separation of variables begins by assumi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Sommerfled-Fresnel-Fraunhofer
Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field: To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and in the arts. General usage Comparison is a natural activity, which even animals engage in when deci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (''ordinary frequency'') or radians per unit time (''angular frequency''). In multidimensional systems, the wavenumber is the magnitude of the ''wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the ''canonical momentum''. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
