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Coherence Theory (optics)
In physics, coherence theory is the study of optical effects arising from partially coherent light and radio sources. Partially coherent sources are sources where the coherence time or coherence length are limited by bandwidth, by thermal noise, or by other effect. Many aspects of modern coherence theory are studied in quantum optics. The theory of partial coherence was awoken in the 1930s due to work by Pieter Hendrik van Cittert and Frits Zernike. Topics in coherence theory * * Mutual coherence function * * * * * * * See also * Nonclassical light * 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 oth ... References * Eugene Hecht and Alfred Zajac, ''Optics'', (1974) Addison-Wesley Publishing, Reading, Massachusetts . ''(Chapter 12 provides an ...
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Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ...
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Physical Optics
In physics, physical optics, or wave optics, is the branch of optics that studies Interference (wave propagation), interference, diffraction, Polarization (waves), polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory (optics), coherence theory. Principle ''Physical optics'' is also the name of an approximation commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray (optics), ray optics and not that it is an exact physical theory. This approximation consists of using ray optics to estimate the field on a surface and then integral, integrating that field ...
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Coherence (physics)
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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Coherence Time
For an electromagnetic wave, the coherence time is the time over which a propagating wave (especially a laser or maser beam) may be considered coherent, meaning that its phase is, on average, predictable. In long-distance transmission systems, the coherence time may be reduced by propagation factors such as dispersion, scattering, and diffraction. The coherence time, usually designated , is calculated by dividing the coherence length by the phase velocity of light in a medium; approximately given by \tau = \frac \approx \frac where is the central wavelength of the source, and is the spectral width of the source in units of frequency and wavelength respectively, and is the speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ... in vacuum. A single mode fiber ...
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Coherence Length
In physics, coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering. This article focuses on the coherence of classical electromagnetic fields. In quantum mechanics, there is a mathematically analogous concept of the quantum coherence length of a wave function. Formulas In radio-band systems, the coherence length is approximated by :L = \frac \approx \frac ~, where \, c \, is the speed of light in vacuum, \, n \, is the refractive index of the medium, and \, \mathrm f \, is the bandwidth of the source or \, \lambda \, is the signal wavelength and \, \Delta \lambda \, is the width of the range of wavelengths in ...
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Bandwidth (signal Processing)
Bandwidth is the difference between the upper and lower Frequency, frequencies in a continuous Frequency band, band of frequencies. It is typically measured in unit of measurement, unit of hertz (symbol Hz). It may refer more specifically to two subcategories: ''Passband bandwidth'' is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. ''Baseband bandwidth'' is equal to the upper cutoff frequency of a low-pass filter or baseband signal, which includes a zero frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel. A key characteristic of bandwidth is that any band of a given width can carry the same amount of information, regardless of where that band is located in the f ...
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Quantum Optics
Quantum optics is a branch of atomic, molecular, and optical physics and quantum chemistry that studies the behavior of photons (individual quanta of light). It includes the study of the particle-like properties of photons and their interaction with, for instance, atoms and molecules. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing. History Light propagating in a restricted volume of space has its energy and momentum quantized according to an integer number of particles known as photons. Quantum optics studies the nature and effects of light as quantized photons. The first major development leading to that understanding was the correct modeling of the blackbody radiation spectrum by Max Planck in 1899 under the hypothesis of light being emitted in discrete units of energy. The photoelectric effect was further evidence of thi ...
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Pieter Hendrik Van Cittert
Pieter Hendrik van Cittert (30 May 1889, Gouda – 8 October 1959, Utrecht) was a Dutch physicist and science historian. He was born in Gouda, Netherlands, to Benjamin Pieter van Cittert and Petronella Antonia Huber, and died on October 8, 1959, in Utrecht. His achievements include proving the van Cittert–Zernike theorem about the coherence of radiation and founding the University Museum in Utrecht. Career In 1912, Hendrik van Cittert joined the Physics Laboratory at the University of Utrecht. In 1918, he discovered thousands of historical scientific instruments from the eighteenth-century Physics Society in Utrecht. This collection was the starting point for the University Museum, which Hendrik van Cittert founded in 1928. He was promoted in 1919. In 1921, Hendrik van Cittert and Leonard Ornstein Leonard Salomon Ornstein (12 November 1880 in Nijmegen, the Netherlands – 20 May 1941 in Utrecht (city), Utrecht, the Netherlands) was a Dutch physicist. Biography Orn ...
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Frits Zernike
Frits Zernike (; 16 July 1888 – 10 March 1966) was a Dutch physicist who received the Nobel Prize in Physics in 1953 for his invention of the phase-contrast microscope. Early life and education Frederick "Frits" Zernike was born on 16 July 1888 in Amsterdam, Netherlands to Carl Friedrich August Zernike and Antje Dieperink. Both parents were teachers of mathematics, and he especially shared his father's passion for physics. In 1905 he enrolled at the University of Amsterdam, studying chemistry (his major), mathematics and physics. Academic career In 1912, he was awarded a prize for his work on opalescence in gases. In 1913, he became assistant to Jacobus Kapteyn at the astronomical laboratory of Groningen University. In 1914, Zernike and Leonard Ornstein were jointly responsible for the derivation of the Ornstein–Zernike equation in critical-point theory. In 1915, he became lector in theoretical mechanics and mathematical physics at the same university and in 1920 ...
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Van Cittert–Zernike Theorem
The van Cittert–Zernike theorem, named after physicists Pieter Hendrik van Cittert and Frits Zernike, is a formula in coherence theory that states that under certain conditions the Fourier transform of the intensity distribution function of a distant, incoherent source is equal to its complex visibility. This implies that the wavefront from an incoherent source will appear mostly coherent at large distances. Intuitively, this can be understood by considering the wavefronts created by two incoherent sources. If we measure the wavefront immediately in front of one of the sources, our measurement will be dominated by the nearby source. If we make the same measurement far from the sources, our measurement will no longer be dominated by a single source; both sources will contribute almost equally to the wavefront at large distances. This reasoning can be easily visualized by dropping two stones in the center of a calm pond. Near the center of the pond, the disturbance created ...
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Nonclassical Light
In optics, nonclassical light is light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ... that cannot be described using classical electromagnetism; its characteristics are described by the quantized electromagnetic field and quantum mechanics. The most common described forms of nonclassical light are the following: *Photon statistics of nonclassical Light is Photon Statistics, sub-PoissonianM. Fox, ''Quantum Optics: An Introduction'', Oxford University Press, New York, 2006 in the sense that the average number of photons in a photodetection of this kind of light shows a standard deviation that is less than the mean number of the photons. *Squeezed coherent state, Squeezed light exhibits reduced noise in one quadrature component. The most familiar kinds of squeezed light have either ...
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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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