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Optical Autocorrelation
In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source of light, while the intensity autocorrelation and the interferometric autocorrelation are commonly used to ''estimate'' the duration of ultrashort pulses produced by modelocked lasers. The laser pulse duration cannot be easily measured by optoelectronic methods, since the response time of photodiodes and oscilloscopes are at best of the order of 200 femtoseconds, yet laser pulses can be made as short as a few femtoseconds. In the following examples, the autocorrelation signal is generated by the nonlinear process of second-harmonic generation (SHG). Other techniques based on two-photon absorption may also be used in autocorrelation measurements, as well as higher-order nonlinear optical processes such as third-harmonic generation, in which case the mathematical expressions of the signal will be slightly modified, but the bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinds Of Optical Autocorrelation
Kind or KIND may refer to: Concepts * Kindness, the human behaviour * Kind, a basic unit of categorization * Kind (type theory), a concept in logic and computer science * Natural kind, in philosophy * Created kind, often abbreviated to kinds, a creationist category of life forms * In kind, for non-monetary transactions Radio and television stations * KIND (AM), a radio station (1010 AM) licensed to Independence, Kansas, United States * KIND-FM, a radio station (94.9 FM) licensed to Elk City, Kansas, United States * KIND-LP, a low-power radio station (94.1 FM) licensed to serve List of radio stations in California, Oxnard, California, United States * KBIK, a radio station (102.9 FM) licensed to Independence, Kansas, United States that held the call sign KIND-FM from 1980 to 2010 Other uses * Kind (company), an American snack food manufacturer * Kids in Need of Defense, a children's rights organization co-founded by actress Angelina Jolie * Kind (album), ''Kind'' (album), a 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform Spectroscopy
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of ''spectroscopy'' including optical spectroscopy, infrared spectroscopy ( FTIR, FT-NIRS), nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer or Fourier-transform spectrograph. The term "Fourier-transform spectroscopy" reflects the fact that in all these techniques, a Fourier transform is required to turn the raw data into the actual spectrum, and in many of the cases in optics involving interferometers, is based on the Wiene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of Coherence
In quantum optics, correlation functions are used to characterize the statistical and coherence properties of an electromagnetic field. The degree of coherence is the normalized correlation of electric fields; in its simplest form, termed g^. It is useful for quantifying the coherence between two electric fields, as measured in a Michelson or other linear optical interferometer. The correlation between pairs of fields, g^, typically is used to find the statistical character of intensity fluctuations. First order correlation is actually the amplitude-amplitude correlation and the second order correlation is the intensity-intensity correlation. It is also used to differentiate between states of light that require a quantum mechanical description and those for which classical fields are sufficient. Analogous considerations apply to any Bose field in subatomic physics, in particular to mesons (cf. Bose–Einstein correlations). Degree of first-order coherence The normalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two 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 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-correlation of and , or and . For complex-valued fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocorrelator
A real time interferometric autocorrelator is an electronic tool used to examine the autocorrelation of, among other things, optical beam intensity and spectral components through examination of variable beam path differences. ''See Optical autocorrelation.'' Description In an interferometric autocorrelator, the input beam is split into a fixed path beam and a variable path beam using a standard beamsplitter. The fixed path beam travels a known and constant distance, whereas the variable path beam has its path length changed via rotating mirrors or other path changing mechanisms. At the end of the two paths, the beams are ideally parallel, but slightly separated, and using a correctly positioned lens, the two beams are crossed inside a second-harmonic generating (SHG) crystal. The autocorrelation term of the output is then passed into a photomultiplying tube (PMT) and measured. Details Considering the input beam as a single pulse with envelope E(t), the constant fixed path dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pupil Function
The pupil function or aperture function describes how a light wave is affected upon transmission through an optical imaging system such as a camera, microscope, or the human eye. More specifically, it is a complex function of the position in the pupil or aperture (often an iris) that indicates the relative change in amplitude and phase of the light wave. Sometimes this function is referred to as the ''generalized'' pupil function, in which case pupil function only indicates whether light is transmitted or not. Imperfections in the optics typically have a direct effect on the pupil function, it is therefore an important tool to study optical imaging systems and their performance. Relationship with other functions in optics The complex pupil function \mathrm(u,v) can be written in polar coordinates using two real functions: : \mathrm(u,v)= \mathrm(u,v)\cdot\mathrm(i\,\mathrm(u,v)), where \mathrm(u,v) is the phase change (in radians) introduced by the optics, or the surrounding mediu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Transfer Function
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations. Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: * hyperbolic sine "" (), * hyperbolic cosine "" (),''Collins Concise Dictionary'', p. 328 from which are derived: * hyperbolic tangent "" (), * hyperb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric " bell curve" shape. The parameter is the height of the curve's peak, is the position of the center of the peak, and (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value and variance . In this case, the Gaussian is of the form g(x) = \frac \exp\left( -\frac \frac \right). Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
