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Temporal Coherence
Coherence expresses the potential for two waves to Wave interference, interfere. Two Monochromatic radiation, monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be ''partly coherent''. When interfering, two waves add together to create a wave of greater amplitude than either one (constructive Wave interference, interference) or subtract from each other to create a wave of minima which may be zero (destructive interference), depending on their relative phase (waves), phase. Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. Two waves with constant relative phase will be coherent. The amount of coherence can readily be measured by the interference visibility, which looks at the size of the interference fringes relative to the input waves (as the phase offset is varied); a precise mathematical definition of the de ...
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Wave Interference
In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves. Etymology The word ''interference'' is derived from the Latin words ''inter'' which means "between" and ''fere'' which means "hit or strike", and was used in the context of wave superposition by Thomas Young in 1801. Mechanisms The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to t ...
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Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ...
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Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m−1). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the '' ordinary frequency'', defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the ''angular frequency'', defined as the phase angle divided by time (in radians per second). 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 ...
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Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at different points in time. The analysis of autocorrelation is a mathematical tool for identifying repeating patterns or hidden periodicities within a signal obscured by noise. Autocorrelation is widely used in signal processing, time domain and time series analysis to understand the behavior of data over time. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Various time series models incorporate autocorrelation, such as unit root processes, trend-stationary processes, autoregressive processes, and moving average processes. Autocorrelation of stochastic processes In statistics, the autocorrelation of a real ...
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Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy. In probability and statistics, the term ''cross-correlations'' refers to the correlations between the entries of two random vectors \mathbf and \mathbf, while the ''correlations'' of a random vector \mathbf are the correlations between the entries of \mathbf itself, those forming the correlation mat ...
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Fourier Transforms
In mathematics, the Fourier transform (FT) is an integral transform that takes a function (mathematics), function as input then outputs another function that describes the extent to which various Frequency, frequencies are present in the original function. The output of the transform is a complex number, complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the Operation (mathematics), mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical Chord (music), chord into the sound intensity, intensities of its constituent Pitch (music), pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the #Uncertainty principle, uncerta ...
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Spectral Density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of any sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (PSD, or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The PSD then refers to the spectral energy distribution that would be ...
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Cross-spectral Density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of any sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (PSD, or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The PSD then refers to the spectral energy distribution that would be ...
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Radio Telescope
A radio telescope is a specialized antenna (radio), antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency portion of the electromagnetic spectrum, just as optical telescopes are used to make observations in the visible light, visible portion of the spectrum in traditional optical astronomy. Unlike optical telescopes, radio telescopes can be used in the daytime as well as at night. Since astronomical radio sources such as planets, stars, nebulas and galaxy, galaxies are very far away, the radio waves coming from them are extremely weak, so radio telescopes require very large antennas to collect enough radio energy to study them, and extremely sensitive receiving equipment. Radio telescopes are typically large Parabolic antenna, parabolic ("dish") antennas similar to those employed in tracking and communicating with satellites an ...
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Astronomical Optical Interferometer
In optical astronomy, interferometry is used to combine signals from two or more telescopes to obtain measurements with higher resolution than could be obtained with either telescopes individually. This technique is the basis for astronomical interferometer arrays, which can make measurements of very small astronomical objects if the telescopes are spread out over a wide area. If a large number of telescopes are used a picture can be produced which has resolution similar to a single telescope with the diameter of the combined spread of telescopes. These include radio telescope arrays such as VLA, VLBI, SMA, astronomical optical interferometer arrays such as COAST, NPOI and IOTA, resulting in the highest resolution optical images ever achieved in astronomy. The VLT Interferometer is expected to produce its first images using aperture synthesis soon, followed by other interferometers such as the CHARA array and the Magdalena Ridge Observatory Interferometer which may consis ...
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Optical Coherence Tomography
Optical coherence tomography (OCT) is a high-resolution imaging technique with most of its applications in medicine and biology. OCT uses coherent near-infrared light to obtain micrometer-level depth resolved images of biological tissue or other scattering media. It uses interferometry techniques to detect the amplitude and time-of-flight of reflected light. OCT uses transverse sample scanning of the light beam to obtain two- and three-dimensional images. Short-coherence-length light can be obtained using a superluminescent diode (SLD) with a broad spectral bandwidth or a broadly tunable laser with narrow linewidth. The first demonstration of OCT imaging (in vitro) was published by a team from MIT and Harvard Medical School in a 1991 article in the journal ''Science (journal), Science''. The article introduced the term "OCT" to credit its derivation from optical coherence-domain reflectometry, in which the axial resolution is based on temporal coherence. The first demonstrat ...
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Phased Array
In antenna (radio), antenna theory, a phased array usually means an electronically scanned array, a computer-controlled Antenna array, array of antennas which creates a radio beam, beam of radio waves that can be electronically steered to point in different directions without moving the antennas. In a phased array, the power from the transmitter is fed to the radiating elements through devices called ''phase shifters'', controlled by a computer system, which can alter the phase or signal delay electronically, thus steering the beam of radio waves to a different direction. Since the size of an antenna array must extend many wavelengths to achieve the high gain needed for narrow beamwidth, phased arrays are mainly practical at the high frequency end of the radio spectrum, in the ultrahigh frequency, UHF and microwave bands, in which the operating wavelengths are conveniently small. Phased arrays were originally invented for use in military radar systems, to detect fast moving pla ...
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