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interference fringes. The reference flats are resting with their bottom surfaces in contact with the test flats, and they are illuminated by a monochromatic light source. The light waves reflected from both surfaces interfere, resulting in a pattern of bright and dark bands. The surface in the left photo is nearly flat, indicated by a pattern of straight parallel interference fringes at equal intervals. The surface in the right photo is uneven, resulting in a pattern of curved fringes. Each pair of adjacent fringes represents a difference in surface elevation of half a wavelength of the light used, so differences in elevation can be measured by counting the fringes. The flatness of the surfaces can be measured to millionths of an inch by this method. To determine whether the surface being tested is concave or convex with respect to the reference optical flat, any of several procedures may be adopted. One can observe how the fringes are displaced when one presses gently on the top flat. If one observes the fringes in white light, the sequence of colors becomes familiar with experience and aids in interpretation. Finally one may compare the appearance of the fringes as one moves ones head from a normal to an oblique viewing position. These sorts of maneuvers, while common in the optical shop, are not suitable in a formal testing environment. When the flats are ready for sale, they will typically be mounted in a Fizeau interferometer for formal testing and certification.
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Errors in determining the location of the fringe centers provide the inherent limit to precision of the classical analysis, and any intensity variations across the interferogram will also introduce error. There is a trade-off between precision and number of data points: closely spaced fringes provide many data points of low precision, while widely spaced fringes provide a low number of high precision data points. Since fringe center data is all that one uses in the classical analysis, all of the other information that might theoretically be obtained by detailed analysis of the intensity variations in an interferogram is thrown away. Finally, with static interferograms, additional information is needed to determine the polarity of the wavefront: In Fig. 13, one can see that the tested surface on the right deviates from flatness, but one cannot tell from this single image whether this deviation from flatness is concave or convex. Traditionally, this information would be obtained using non-automated means, such as by observing the direction that the fringes move when the reference surface is pushed.
1556:(OCT) is a medical imaging technique using low-coherence interferometry to provide tomographic visualization of internal tissue microstructures. As seen in Fig. 22, the core of a typical OCT system is a Michelson interferometer. One interferometer arm is focused onto the tissue sample and scans the sample in an X-Y longitudinal raster pattern. The other interferometer arm is bounced off a reference mirror. Reflected light from the tissue sample is combined with reflected light from the reference. Because of the low coherence of the light source, interferometric signal is observed only over a limited depth of sample. X-Y scanning therefore records one thin optical slice of the sample at a time. By performing multiple scans, moving the reference mirror between each scan, an entire three-dimensional image of the tissue can be reconstructed. Recent advances have striven to combine the nanometer phase retrieval of coherent interferometry with the ranging capability of low-coherence interferometry.
711:. A precisely figured reference flat is placed on top of the flat being tested, separated by narrow spacers. The reference flat is slightly beveled (only a fraction of a degree of beveling is necessary) to prevent the rear surface of the flat from producing interference fringes. Separating the test and reference flats allows the two flats to be tilted with respect to each other. By adjusting the tilt, which adds a controlled phase gradient to the fringe pattern, one can control the spacing and direction of the fringes, so that one may obtain an easily interpreted series of nearly parallel fringes rather than a complex swirl of contour lines. Separating the plates, however, necessitates that the illuminating light be collimated. Fig 6 shows a collimated beam of monochromatic light illuminating the two flats and a beam splitter allowing the fringes to be viewed on-axis.
1197:(CGHs) have begun to supplement null correctors in test setups for complex aspheric surfaces. Fig. 15 illustrates how this is done. Unlike the figure, actual CGHs have line spacing on the order of 1 to 10 ÎŒm. When laser light is passed through the CGH, the zero-order diffracted beam experiences no wavefront modification. The wavefront of the first-order diffracted beam, however, is modified to match the desired shape of the test surface. In the illustrated Fizeau interferometer test setup, the zero-order diffracted beam is directed towards the spherical reference surface, and the first-order diffracted beam is directed towards the test surface in such a way that the two reflected beams combine to form interference fringes. The same test setup can be used for the innermost mirrors as for the outermost, with only the CGH needing to be exchanged.
1150:. Michelson pointed out that constraints on geometry forced by limited coherence length required the use of a reference mirror of equal size to the test mirror, making the TwymanâGreen impractical for many purposes. Decades later, the advent of laser light sources answered Michelson's objections. (A TwymanâGreen interferometer using a laser light source and unequal path length is known as a Laser Unequal Path Interferometer, or LUPI.) Fig. 14 illustrates a TwymanâGreen interferometer set up to test a lens. Light from a monochromatic point source is expanded by a diverging lens (not shown), then is collimated into a parallel beam. A convex spherical mirror is positioned so that its center of curvature coincides with the focus of the lens being tested. The emergent beam is recorded by an imaging system for analysis.
1330:(PZT). Alternatively, precise phase shifts can be introduced by modulating the laser frequency. The captured images are processed by a computer to calculate the optical wavefront errors. The precision and reproducibility of PSI is far greater than possible in static interferogram analysis, with measurement repeatabilities of a hundredth of a wavelength being routine. Phase shifting technology has been adapted to a variety of interferometer types such as TwymanâGreen, MachâZehnder, laser Fizeau, and even common path configurations such as point diffraction and lateral shearing interferometers. More generally, phase shifting techniques can be adapted to almost any system that uses fringes for measurement, such as holographic and speckle interferometry.
727:, great care must be taken to equalize the optical paths or no fringes will be visible. As illustrated in Fig. 6, a compensating cell would be placed in the path of the reference beam to match the test cell. Note also the precise orientation of the beam splitters. The reflecting surfaces of the beam splitters would be oriented so that the test and reference beams pass through an equal amount of glass. In this orientation, the test and reference beams each experience two front-surface reflections, resulting in the same number of phase inversions. The result is that light traveling an equal optical path length in the test and reference beams produces a white light fringe of constructive interference.
1368:(for high magnification objectives with limited working distance). The sample (or alternatively, the objective) is moved vertically over the full height range of the sample, and the position of maximum fringe contrast is found for each pixel. The chief benefit of coherence scanning interferometry is that systems can be designed that do not suffer from the 2 pi ambiguity of coherent interferometry, and as seen in Fig. 18, which scans a 180ÎŒm x 140ÎŒm x 10ÎŒm volume, it is well suited to profiling steps and rough surfaces. The axial resolution of the system is determined in part by the coherence length of the light source. Industrial applications include in-process
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technique of speckle pattern interferometry in 1970, and since then, speckle has been exploited in a variety of other applications. A photograph is made of the speckle pattern before deformation, and a second photograph is made of the speckle pattern after deformation. Digital subtraction of the two images results in a correlation fringe pattern, where the fringes represent lines of equal deformation. Short laser pulses in the nanosecond range can be used to capture very fast transient events. A phase problem exists: In the absence of other information, one cannot tell the difference between contour lines indicating a peak
876:. Michelson interferometers have the largest field of view for a specified wavelength, and are relatively simple in operation, since tuning is via mechanical rotation of waveplates rather than via high voltage control of piezoelectric crystals or lithium niobate optical modulators as used in a FabryâPĂ©rot system. Compared with Lyot filters, which use birefringent elements, Michelson interferometers have a relatively low temperature sensitivity. On the negative side, Michelson interferometers have a relatively restricted wavelength range and require use of prefilters which restrict transmittance.
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1289:, and the frequencies of the comb elements at the red end of the spectrum are doubled and heterodyned with the frequencies of the comb elements at the blue end of the spectrum, thus allowing the comb to serve as its own reference. In this manner, locking of the frequency comb output to an atomic standard can be performed in a single step. To measure an unknown frequency, the frequency comb output is dispersed into a spectrum. The unknown frequency is overlapped with the appropriate spectral segment of the comb and the frequency of the resultant heterodyne beats is measured.
227:(a partially reflecting mirror). Each of these beams travels a different route, called a path, and they are recombined before arriving at a detector. The path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths, then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the
899:(EIT) image of the Sun at 195 Ă
ngströms (19.5 nm), corresponding to a spectral line of multiply-ionized iron atoms. EIT used multilayer coated reflective mirrors that were coated with alternate layers of a light "spacer" element (such as silicon), and a heavy "scatterer" element (such as molybdenum). Approximately 100 layers of each type were placed on each mirror, with a thickness of around 10 nm each. The layer thicknesses were tightly controlled so that at the desired wavelength, reflected photons from each layer interfered constructively.
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390:. Between 1816 and 1818, Fresnel and Arago performed interference experiments at the Paris Observatory. During this time, Arago designed and built the first interferometer, using it to measure the refractive index of moist air relative to dry air, which posed a potential problem for astronomical observations of star positions. The success of Fresnel's wave theory of light was established in his prize-winning memoire of 1819 that predicted and measured diffraction patterns. The Arago interferometer was later employed in 1850 by
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light and high numerical apertures, and rather than looking at the phase of the fringes, as does PSI, looks for best position of maximum fringe contrast or some other feature of the overall fringe pattern. In its simplest form, CSI provides less precise measurements than PSI but can be used on rough surfaces. Some configurations of CSI, variously known as
Enhanced VSI (EVSI), high-resolution SWLI or Frequency Domain Analysis (FDA), use coherence effects in combination with interference phase to enhance precision.
1487:, exploited the low coherence length of white light. Initially, white light was split in two, with the reference beam "folded", bouncing back-and-forth six times between a mirror pair spaced precisely 1 m apart. Only if the test path was precisely 6 times the reference path would fringes be seen. Repeated applications of this procedure allowed precise measurement of distances up to 864 meters. Baselines thus established were used to calibrate geodetic distance measurement equipment, leading to a
783:, experimentalists struggled with continual fringe drift even though the interferometer might be set up in a basement. Since the fringes would occasionally disappear due to vibrations by passing horse traffic, distant thunderstorms and the like, it would be easy for an observer to "get lost" when the fringes returned to visibility. The advantages of white light, which produced a distinctive colored fringe pattern, far outweighed the difficulties of aligning the apparatus due to its low
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820:. Fig 7 illustrates a resonator experiment performed by MĂŒller et al. in 2003. Two optical resonators constructed from crystalline sapphire, controlling the frequencies of two lasers, were set at right angles within a helium cryostat. A frequency comparator measured the beat frequency of the combined outputs of the two resonators. As of 2009, the precision by which anisotropy of the speed of light can be excluded in resonator experiments is at the 10 level.
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from earthquakes, volcanoes and landslides, and also has uses in structural engineering, in particular for the monitoring of subsidence and structural stability. Fig 20 shows
Kilauea, an active volcano in Hawaii. Data acquired using the space shuttle Endeavour's X-band Synthetic Aperture Radar on April 13, 1994 and October 4, 1994 were used to generate interferometric fringes, which were overlaid on the X-SAR image of Kilauea.
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emitted from point A on the source is traced. As the ray passes through the paired flats, it is multiply reflected to produce multiple transmitted rays which are collected by the focusing lens and brought to point A' on the screen. The complete interference pattern takes the appearance of a set of concentric rings. The sharpness of the rings depends on the reflectivity of the flats. If the reflectivity is high, resulting in a high
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914:. In this application, the FabryâPĂ©rot cavity is used to store photons for almost a millisecond while they bounce up and down between the mirrors. This increases the time a gravitational wave can interact with the light, which results in a better sensitivity at low frequencies. Smaller cavities, usually called mode cleaners, are used for spatial filtering and frequency stabilization of the main laser. The
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1643:.) It has become an important method for visualizing cellular and histological structures in a wide range of biological and medical studies. There are several technologies being used for x-ray phase-contrast imaging, all utilizing different principles to convert phase variations in the x-rays emerging from an object into intensity variations. These include propagation-based phase contrast,
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40:. The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening in intensity) if they arrive out of phase, depending on the exact distances between the three mirrors.
449:). The phase difference between the two beams results in a change in the intensity of the light on the detector. The resulting intensity of the light after mixing of these two beams is measured, or the pattern of interference fringes is viewed or recorded. Most of the interferometers discussed in this article fall into this category.
1189:, will be of segmented design. Their primary mirrors will be built from hundreds of hexagonal mirror segments. Polishing and figuring these highly aspheric and non-rotationally symmetric mirror segments presents a major challenge. Traditional means of optical testing compares a surface against a spherical reference with the aid of a
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partially-coherent forward-scattered light propagation through the micro aberrations and heterogeneity of tissue structure provides opportunities to use phase-sensitive gating (optical coherence tomography) as well as phase-sensitive fluctuation spectroscopy to image subtle structural and dynamical properties.
1464:(ESPI), also known as TV holography, uses video detection and recording to produce an image of the object upon which is superimposed a fringe pattern which represents the displacement of the object between recordings. (see Fig. 21) The fringes are similar to those obtained in holographic interferometry.
1651:-based far-field interferometry, refraction-enhanced imaging, and x-ray interferometry. These methods provide higher contrast compared to normal absorption-contrast x-ray imaging, making it possible to see smaller details. A disadvantage is that these methods require more sophisticated equipment, such as
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images of a geographic feature are taken on separate days, and changes that have taken place between radar images taken on the separate days are recorded as fringes similar to those obtained in holographic interferometry. The technique can monitor centimeter- to millimeter-scale deformation resulting
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Interferometers are used in atmospheric physics for high-precision measurements of trace gases via remote sounding of the atmosphere. There are several examples of interferometers that utilize either absorption or emission features of trace gases. A typical use would be in continual monitoring of the
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generates interference fringes by combining direct light from a source (blue lines) and light from the source's reflected image (red lines) from a mirror held at grazing incidence. The result is an asymmetrical pattern of fringes. The band of equal path length, nearest the mirror, is dark rather than
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Optical interferometry, applied to biology and medicine, provides sensitive metrology capabilities for the measurement of biomolecules, subcellular components, cells and tissues. Many forms of label-free biosensors rely on interferometry because the direct interaction of electromagnetic fields with
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Double- and multi- exposure holography is one of three methods used to create holographic interferograms. A first exposure records the object in an unstressed state. Subsequent exposures on the same photographic plate are made while the object is subjected to some stress. The composite image depicts
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Holographic interferometry was discovered by accident as a result of mistakes committed during the making of holograms. Early lasers were relatively weak and photographic plates were insensitive, necessitating long exposures during which vibrations or minute shifts might occur in the optical system.
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One of the most common industrial applications of optical interferometry is as a versatile measurement tool for the high precision examination of surface topography. Popular interferometric measurement techniques include Phase
Shifting Interferometry (PSI), and Vertical Scanning Interferometry(VSI),
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The TwymanâGreen interferometer, invented by Twyman and Green in 1916, is a variant of the
Michelson interferometer widely used to test optical components. The basic characteristics distinguishing it from the Michelson configuration are the use of a monochromatic point light source and a collimator.
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Newton (test plate) interferometry is frequently used in the optical industry for testing the quality of surfaces as they are being shaped and figured. Fig. 13 shows photos of reference flats being used to check two test flats at different stages of completion, showing the different patterns of
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with the MIRC instrument. The brighter component is the primary star, or the mass donor. The fainter component is the thick disk surrounding the secondary star, or the mass gainer. The two components are separated by 1 milli-arcsecond. Tidal distortions of the mass donor and the mass gainer are
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overlap, the fringes near the axis will be straight, parallel, and equally spaced. If S is an extended source rather than a point source as illustrated, the fringes of Fig. 2a must be observed with a telescope set at infinity, while the fringes of Fig. 2b will be localized on the mirrors.
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would be used to produce a harmonic of the frequency of that step, which would be compared by heterodyne detection with the next step (the output of a microwave source, far infrared laser, infrared laser, or visible laser). Each measurement of a single spectral line required several years of effort
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difference between the two wavesâwaves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Waves which are not completely in phase nor completely out of phase will have an intermediate intensity pattern, which can be used
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Phase
Shifting Interferometry addresses several issues associated with the classical analysis of static interferograms. Classically, one measures the positions of the fringe centers. As seen in Fig. 13, fringe deviations from straightness and equal spacing provide a measure of the aberration.
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Fig. 8 illustrates the operation of a
Fourier transform spectrometer, which is essentially a Michelson interferometer with one mirror movable. (A practical Fourier transform spectrometer would substitute corner cube reflectors for the flat mirrors of the conventional Michelson interferometer,
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of a collimating lens. A focusing lens produces what would be an inverted image of the source if the paired flats were not present, i.e., in the absence of the paired flats, all light emitted from point A passing through the optical system would be focused at point A'. In Fig. 6, only one ray
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is a more versatile instrument than the
Michelson interferometer. Each of the well separated light paths is traversed only once, and the fringes can be adjusted so that they are localized in any desired plane. Typically, the fringes would be adjusted to lie in the same plane as the test object, so
416:, to search for effects of the motion of the Earth on the speed of light. Michelson's null results performed in the basement of the Potsdam Observatory outside of Berlin (the horse traffic in the center of Berlin created too many vibrations), and his later more-accurate null results observed with
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Figure 3. Colored and monochromatic fringes in a
Michelson interferometer: (a) White light fringes where the two beams differ in the number of phase inversions; (b) White light fringes where the two beams have experienced the same number of phase inversions; (c) Fringe pattern using
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Real-time holography is a second method of creating holographic interferograms. A holograph of the unstressed object is created. This holograph is illuminated with a reference beam to generate a hologram image of the object directly superimposed over the original object itself while the object is
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to extend the range of capabilities for interference microscopy. These techniques are widely used in micro-electronic and micro-optic fabrication. PSI uses monochromatic light and provides very precise measurements; however it is only usable for surfaces that are very smooth. CSI often uses white
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Figure 16. Frequency comb of a mode-locked laser. The dashed lines represent an extrapolation of the mode frequencies towards the frequency of the carrierâenvelope offset (CEO). The vertical grey line represents an unknown optical frequency. The horizontal black lines indicate the two lowest beat
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nuclei. This allows interferometry depth measurements to be combined with density measurements. Various correlations have been found between the state of tissue health and the measurements of subcellular objects. For example, it has been found that as tissue changes from normal to cancerous, the
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was considered to be a severe drawback in using lasers to illuminate objects, particularly in holographic imaging because of the grainy image produced. It was later realized that speckle patterns could carry information about the object's surface deformations. Butters and
Leendertz developed the
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in his 1803 Bakerian
Lecture to the Royal Society of London. In preparation for the lecture, Young performed a double-aperture experiment that demonstrated interference fringes. His interpretation in terms of the interference of waves was rejected by most scientists at the time because of the
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markers. At a larger scale, cellular interferometry shares aspects with phase-contrast microscopy, but comprises a much larger class of phase-sensitive optical configurations that rely on optical interference among cellular constituents through refraction and diffraction. At the tissue scale,
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has had to overcome a number of technical issues not shared by radio telescope interferometry. The short wavelengths of light necessitate extreme precision and stability of construction. For example, spatial resolution of 1 milliarcsecond requires 0.5 ÎŒm stability in a 100 m baseline.
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Fig. 9 shows a doppler image of the solar corona made using a tunable Fabry-PĂ©rot interferometer to recover scans of the solar corona at a number of wavelengths near the FeXIV green line. The picture is a color-coded image of the doppler shift of the line, which may be associated with the
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Optical heterodyne detection is an essential technique used in high-accuracy measurements of the frequencies of optical sources, as well as in the stabilization of their frequencies. Until a relatively few years ago, lengthy frequency chains were needed to connect the microwave frequency of a
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is an imaging technique that photographically records the electron interference pattern of an object, which is then reconstructed to yield a greatly magnified image of the original object. This technique was developed to enable greater resolution in electron microscopy than is possible using
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illustrated in Fig 11, used arrays of telescopes arranged in a pattern on the ground. A limited number of baselines will result in insufficient coverage. This was alleviated by using the rotation of the Earth to rotate the array relative to the sky. Thus, a single baseline could measure
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Zhao, M.; Gies, D.; Monnier, J. D.; Thureau, N.; Pedretti, E.; Baron, F.; Merand, A.; Ten Brummelaar, T.; McAlister, H.; Ridgway, S. T.; Turner, N.; Sturmann, J.; Sturmann, L.; Farrington, C.; Goldfinger, P. J. (2008). "First Resolved Images of the Eclipsing and Interacting Binary ÎČ Lyrae".
779:, used monochromatic light only for initially setting up their equipment, always switching to white light for the actual measurements. The reason is that measurements were recorded visually. Monochromatic light would result in a uniform fringe pattern. Lacking modern means of
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corresponding to equal path length from the two slits, surrounded by a symmetrical pattern of colored fringes of diminishing intensity. In addition to continuous electromagnetic radiation, Young's experiment has been performed with individual photons, with electrons, and with
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in Cleveland, Ohio, contributed to the growing crisis of the luminiferous ether. Einstein stated that it was Fizeau's measurement of the speed of light in moving water using the Arago interferometer that inspired his theory of the relativistic addition of velocities.
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Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same
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Use of white light will result in a pattern of colored fringes (see Fig. 3). The central fringe representing equal path length may be light or dark depending on the number of phase inversions experienced by the two beams as they traverse the optical system. (See
1055:: Unlike macroscopic objects, when fermions are rotated by 360° about any axis, they do not return to their original state, but develop a minus sign in their wave function. In other words, a fermion needs to be rotated 720° before returning to its original state.
1372:, roughness measurement, 3D surface metrology in hard-to-reach spaces and in hostile environments, profilometry of surfaces with high aspect ratio features (grooves, channels, holes), and film thickness measurement (semi-conductor and optical industries, etc.).
1359:, interference is only achieved when the path length delays of the interferometer are matched within the coherence time of the light source. CSI monitors the fringe contrast rather than the phase of the fringes. Fig. 17 illustrates a CSI microscope using a
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the specimens, but staining procedures are time-consuming and kill the cells. As seen in Figs. 24 and 25, phase contrast and DIC microscopes allow unstained, living cells to be studied. DIC also has non-biological applications, for example in the
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W. J. Walecki et al. "Non-contact fast wafer metrology for ultra-thin patterned wafers mounted on grinding and dicing tapes" Electronics Manufacturing Technology Symposium, 2004. IEEE/CPMT/SEMI 29th International Volume, Issue, July 14â16, 2004 Page(s):
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Other uses of interferometers have been to study dispersion of materials, measurement of complex indices of refraction, and thermal properties. They are also used for three-dimensional motion mapping including mapping vibrational patterns of structures.
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ISO. (2013). 25178-604:2013(E): Geometrical product specification (GPS) â Surface texture: Areal â Nominal characteristics of non-contact (coherence scanning interferometric microscopy) instruments (2013(E) ed.). Geneva: International Organization for
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Eventually, several independent groups of experimenters in the mid-60s realized that the fringes encoded important information about dimensional changes occurring in the subject, and began intentionally producing holographic double exposures. The main
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ring, and rotation of the system then causes a relative phase shift between those beams. In a RLG, the observed phase shift is proportional to the accumulated rotation, while in a FOG, the observed phase shift is proportional to the angular velocity.
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Wax, A.; Pyhtila, J. W.; Graf, R. N.; Nines, R.; Boone, C. W.; Dasari, R. R.; Feld, M. S.; Steele, V. E.; Stoner, G. D. (2005). "Prospective grading of neoplastic change in rat esophagus epithelium using angle-resolved low-coherence interferometry".
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but for simplicity, the illustration does not show this.) An interferogram is generated by making measurements of the signal at many discrete positions of the moving mirror. A Fourier transform converts the interferogram into an actual spectrum.
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in the objective; other forms of interferometer used with white light include the Michelson interferometer (for low magnification objectives, where the reference mirror in a Mirau objective would interrupt too much of the aperture) and the
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have provided a much simpler method of measuring optical frequencies. If a mode-locked laser is modulated to form a train of pulses, its spectrum is seen to consist of the carrier frequency surrounded by a closely spaced comb of optical
496:. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. The output signal will have an intensity proportional to the product of the amplitudes of the input signals.
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Pyhtila, J. W.; Chalut, K. J.; Boyer, J. D.; Keener, J.; d'Amico, T.; Gottfried, M.; Gress, F.; Wax, A. (2007). "In situ detection of nuclear atypia in Barrett's esophagus by using angle-resolved low-coherence interferometry".
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to vary their relative phase. A slight tilt of one of the beam splitters will result in a path difference and a change in the interference pattern. MachâZehnder interferometers are the basis of a wide variety of devices, from
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997:, the turbulence that causes stars to twinkle, introduces rapid, random phase changes in the incoming light, requiring data collection rates to be faster than the rate of turbulence. Despite these technical difficulties,
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to monitor small deformations in single wavelength implementations. In multi-wavelength implementations, it is used to perform dimensional metrology of large parts and assemblies and to detect larger surface defects.
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in wind tunnels, and for flow visualization studies in general. It is frequently used in the fields of aerodynamics, plasma physics and heat transfer to measure pressure, density, and temperature changes in gases.
286:. The characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. 2a, the optical elements are oriented so that
748:(i.e., high finesse), monochromatic light produces a set of narrow bright rings against a dark background. In Fig. 6, the low-finesse image corresponds to a reflectivity of 0.04 (i.e., unsilvered surfaces)
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Schmit, J. (1993). "Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension". In Brown, Gordon M.; Kwon, Osuk Y.; Kujawinska, Malgorzata; Reid, Graeme T. (eds.).
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White light fringes were chosen for the observations because they consist of a small group of fringes having a central, sharply defined black fringe which forms a permanent zero reference mark for all readings.
1130:, the technology that enables the use of multiple wavelengths of light through a single optical fiber, depends on filtering devices that are thin-film etalons. Single-mode lasers employ etalons to suppress all
1608:(DIC) microscopy are important tools in biology and medicine. Most animal cells and single-celled organisms have very little color, and their intracellular organelles are almost totally invisible under simple
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uses a transparent plate with two parallel reflecting surfaces.) As with the Fizeau interferometer, the flats are slightly beveled. In a typical system, illumination is provided by a diffuse source set at the
154:. In analytical science, interferometers are used to measure lengths and the shape of optical components with nanometer precision; they are the highest-precision length measuring instruments in existence. In
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consists of two or more separate telescopes that combine their signals, offering a resolution equivalent to that of a telescope of diameter equal to the largest separation between its individual elements.
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image sensor. As seen in Fig. 17, multiple interferograms (at least three) are analyzed with the reference optical surface shifted by a precise fraction of a wavelength between each exposure using a
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Eibenberger, Sandra; Gerlich, Stefan; Arndt, Markus; Mayor, Marcel; TĂŒxen, Jens (2013-08-14). "Matterâwave interference of particles selected from a molecular library with masses exceeding 10000 amu".
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is an extension of the heterodyne technique to higher (visible) frequencies. While optical heterodyne interferometry is usually done at a single point it is also possible to perform this widefield.
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Nieradko, Ć.; Gorecki, C.; JĂłZwik, M.; Sabac, A.; Hoffmann, R.; Bertz, A. (2006). "Fabrication and optical packaging of an integrated MachâZehnder interferometer on top of a movable micromirror".
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The third method, time-average holography, involves creating a holograph while the object is subjected to a periodic stress or vibration. This yields a visual image of the vibration pattern.
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being subjected to some stress. The object waves from this hologram image will interfere with new waves coming from the object. This technique allows real time monitoring of shape changes.
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Phase-contrast X-ray imaging (Fig. 26) refers to a variety of techniques that use phase information of a coherent x-ray beam to image soft tissues. (For an elementary discussion, see
567:. After being perturbed by interaction with the sample under test, the sample beam is recombined with the reference beam to create an interference pattern which can then be interpreted.
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In telecommunication networks, heterodyning is used to move frequencies of individual signals to different channels which may share a single physical transmission line. This is called
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Hornberger, Klaus; Gerlich, Stefan; Haslinger, Philipp; Nimmrichter, Stefan; Arndt, Markus (2012-02-08). "\textit{Colloquium} : Quantum interference of clusters and molecules".
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Michelson (1918) criticized the TwymanâGreen configuration as being unsuitable for the testing of large optical components, since the light sources available at the time had limited
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The MachâZehnder interferometer's relatively large and freely accessible working space, and its flexibility in locating the fringes has made it the interferometer of choice for
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is a pair of partially silvered glass optical flats spaced several millimeters to centimeters apart with the silvered surfaces facing each other. (Alternatively, a FabryâPĂ©rot
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P. de Groot, J., "Interference Microscopy for Surface Structure Analysis", in Handbook of Optical Metrology, edited by T. Yoshizawa, chapt.31, pp. 791-828, (CRC Press, 2015).
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conventional imaging techniques. The resolution of conventional electron microscopy is not limited by electron wavelength, but by the large aberrations of electron lenses.
1219:. The distinction between RLGs and FOGs is that in a RLG, the entire ring is part of the laser while in a FOG, an external laser injects counter-propagating beams into an
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system can carry 500 television channels at the same time because each one is given a different frequency, so they don't interfere with one another. Continuous wave (CW)
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When used as a tunable narrow band filter, Michelson interferometers exhibit a number of advantages and disadvantages when compared with competing technologies such as
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Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E.; Peters, A. (2009). "Rotating optical cavity experiment testing Lorentz invariance at the 10-17 level".
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Oliver, W. D.; Yu, Y.; Lee, J. C.; Berggren, K. K.; Levitov, L. S.; Orlando, T. P. (2005). "MachâZehnder Interferometry in a Strongly Driven Superconducting Qubit".
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An amplitude splitting interferometer uses a partial reflector to divide the amplitude of the incident wave into separate beams which are separated and recombined.
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T.Young, âThe Bakerian Lecture:Experiments and Calculations Relative to Physical Optics,â Philosophical Transactions of the Royal Society of London 94 (1804): 1â16.
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Phase shifting interferometry overcomes these limitations by not relying on finding fringe centers, but rather by collecting intensity data from every point of the
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signal from the antenna is mixed with a signal from a local oscillator (LO) and converted by the heterodyne technique to a lower fixed frequency signal called the
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spatially coherent light) and, after allowing the two parts of the wavefront to travel through different paths, allows them to recombine. Fig. 5 illustrates
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Hitzenberger, C. K.; Sticker, M.; Leitgeb, R.; Fercher, A. F. (2001). "Differential phase measurements in low-coherence interferometry without 2pi ambiguity".
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Scherrer, P.H.; Bogart, R.S.; Bush, R.I.; Hoeksema, J.; Kosovichev, A.G.; Schou, J. (1995). "The Solar Oscillations Investigation â Michelson Doppler Imager".
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played a major role in the general acceptance of the wave theory of light. If white light is used in Young's experiment, the result is a white central band of
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633:. Other examples of wavefront splitting interferometer include the Fresnel biprism, the Billet Bi-Lens, diffraction-grating Michelson interferometer, and the
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developed the first single-beam interferometer (not requiring a splitting aperture as the Arago interferometer did) in 1856. In 1881, the American physicist
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Huang, D.; Swanson, E.A.; Lin, C.P.; Schuman, J.S.; Stinson, W.G.; Chang, W.; Hee, M.R.; Flotte, T.; Gregory, K.; Puliafito, C.A.; Fujimoto, J.G. (1991).
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Malbet, F.; Kern, P.; Schanen-Duport, I.; Berger, J.-P.; Rousselet-Perraut, K.; Benech, P. (1999). "Integrated optics for astronomical interferometry".
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technique is used for (1) shifting an input signal into a new frequency range as well as (2) amplifying a weak input signal (assuming use of an active
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changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different
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are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements,
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Davis, T J; Gao, D; Gureyev, T E; Stevenson, A W & Wilkins, S W (1995). "Phase-contrast imaging of weakly absorbing materials using hard X-rays".
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Heideman, R. G.; Kooyman, R. P. H.; Greve, J. (1993). "Performance of a highly sensitive optical waveguide MachâZehnder interferometer immunosensor".
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that fringes and test object can be photographed together. If it is decided to produce fringes in white light, then, since white light has a limited
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Fig. 6 illustrates the Fizeau, MachâZehnder, and FabryâPĂ©rot interferometers. Other examples of amplitude splitting interferometer include the
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MĂŒller, H.; Herrmann, S.; Braxmaier, C.; Schiller, S.; Peters, A. (2003). "Modern MichelsonâMorley experiment using cryogenic optical resonators".
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J. Lequeux, François Arago A 19th Century French Humanist and Pioneer in Astrophysics (Springer International Publishing: Imprint: Springer, 2015).
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measurements capable of detecting very weak light scattered in the atmosphere and monitoring wind speeds with high accuracy. It has application in
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2005:
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MachâZehnder interferometers are also used to study one of the most counterintuitive predictions of quantum mechanics, the phenomenon known as
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Michelson and Morley (1887) and other early experimentalists using interferometric techniques in an attempt to measure the properties of the
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FabryâPĂ©rot thin-film etalons are used in narrow bandpass filters capable of selecting a single spectral line for imaging; for example, the
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frequencies with a spacing equal to the pulse repetition frequency (Fig. 16). The pulse repetition frequency is locked to that of the
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Momose, A; Takeda, T; Itai, Y & Hirano, K (1996). "Phase-contrast X-ray computed tomography for observing biological soft tissues".
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1254:, in various high resolution spectroscopic techniques, and the self-heterodyne method can be used to measure the linewidth of a laser.
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Optical interferometric measurements require high sensitivity, low noise detectors that did not become available until the late 1990s.
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Wilkins, S W; Gureyev, T E; Gao, D; Pogany, A & Stevenson, A W (1996). "Phase-contrast imaging using polychromatic hard X-rays".
4952:"2Ï ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer"
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de Groot, Peter; Deck, Leslie (1995). "Surface Profiling by Analysis of White-light Interferograms in the Spatial Frequency Domain".
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are tilted with respect to each other, the interference fringes will generally take the shape of conic sections (hyperbolas), but if
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Wojtek J. Walecki, Kevin Lai, Vitalij Souchkov, Phuc Van, SH Lau, Ann Koo Physica Status Solidi C Volume 2, Issue 3, Pages 984â989
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Gerlich, S.; Eibenberger, S.; Tomandl, M.; Nimmrichter, S.; Hornberger, K.; Fagan, P. J.; TĂŒxen, J.; Mayor, M.; Arndt, M. (2011).
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Chevalerias, R.; Latron, Y.; Veret, C. (1957). "Methods of Interferometry Applied to the Visualization of Flows in Wind Tunnels".
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816:. Recent repetitions of the MichelsonâMorley experiment perform heterodyne measurements of beat frequencies of crossed cryogenic
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is a class of interferometer in which the reference beam and sample beam travel along the same path. Fig. 4 illustrates the
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bright. In 1834, Humphrey Lloyd interpreted this effect as proof that the phase of a front-surface reflected beam is inverted.
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Plucinski, J.; Hypszer, R.; Wierzba, P.; Strakowski, M.; Jedrzejewska-Szczerska, M.; Maciejewski, M.; Kosmowski, B.B. (2008).
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contour lines indicating a trough. To resolve the issue of phase ambiguity, ESPI may be combined with phase shifting methods.
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How interference fringes are formed by an optical flat resting on a reflective surface. The gap between the surfaces and the
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The design and construction of a MachâZehnder interferometer for use with the GALCIT Transonic Wind Tunnel. Engineer's thesis
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system, a binary star system approximately 960 light-years (290 parsecs) away in the constellation Lyra, as observed by the
952:, mixing signals from a cluster of comparatively small telescopes rather than a single very expensive monolithic telescope.
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4891:"HDVSI â Introducing High Definition Vertical Scanning Interferometry for Nanotechnology Research from Veeco Instruments"
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Dimopoulos, S.; Graham, P.W.; Hogan, J.M.; Kasevich, M.A. (2008). "General Relativistic Effects in Atom Interferometry".
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Schmit, J.; Creath, K.; Wyant, J. C. (2007). "Surface Profilers, Multiple Wavelength, and White Light Intereferometry".
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Haack, G. R.; Förster, H.; BĂŒttiker, M. (2010). "Parity detection and entanglement with a MachâZehnder interferometer".
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Eisele, C.; Nevsky, A.; Schiller, S. (2009). "Laboratory Test of the Isotropy of Light Propagation at the 10-17 Level".
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article covers the disputes over priority of discovery that occurred during the issuance of the patent for this method.
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they are used to analyze light containing features of absorption or emission associated with a substance or mixture. An
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Figure 20. InSAR Image of Kilauea, Hawaii showing fringes caused by deformation of the terrain over a six-month period.
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Interference: The History of Optical Interferometry and the Scientists Who Tamed Light (Oxford University Press, 2023)
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Fundamental Physics â Heisenberg and Beyond: Werner Heisenberg Centennial Symposium "Developments in Modern Physics"
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are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to
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Miller, Dayton C. (1933). "The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth".
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In physics, one of the most important experiments of the late 19th century was the famous "failed experiment" of
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2890:"Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers"
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Michelson interferometers are used in tunable narrow band optical filters and as the core hardware component of
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262:. The fringes can be interpreted as the result of interference between light coming from the two virtual images
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1047:, to examine the effects of gravity acting on an elementary particle, and to demonstrate a strange behavior of
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Miao, Houxun; Panna, Alireza; Gomella, Andrew A.; Bennett, Eric E.; Znati, Sami; Chen, Lei; Wen, Han (2016).
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386:, unaware of Young's results, began working on a wave theory of light and interference and was introduced to
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The resultant holograms, which showed the holographic subject covered with fringes, were considered ruined.
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Butters, J. N.; Leendertz, J. A. (1971). "A double exposure technique for speckle pattern interferometry".
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5295:"Comparative Phase-Shifting Digital Speckle Pattern Interferometry Using Single Reference Beam Technique"
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Baldwin, J.E.; Haniff, C.A. (2002). "The application of interferometry to optical astronomical imaging".
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interferometers used a single baseline for measurement. Later astronomical interferometers, such as the
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5269:"Dynamic Electronic Speckle Pattern Interferometry in Application to Measure Out-Of-Plane Displacement"
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De Groot, P (2015). "Principles of interference microscopy for the measurement of surface topography".
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A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit (
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is one in which the reference beam and sample beam travel along divergent paths. Examples include the
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Atom interferometry techniques are reaching sufficient precision to allow laboratory-scale tests of
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detectors are basically heterodyne detection devices that compare transmitted and reflected beams.
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3005:. NASA/Goddard Space Flight Center Scientific Visualization Studio. 2 April 2008. Archived from
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Jones R & Wykes C, Holographic and Speckle Interferometry, 1989, Cambridge University Press
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Jönsson, C (1961). "Elektroneninterferenzen an mehreren kĂŒnstlich hergestellten Feinspalten".
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476:(LO). The nonlinear combination of the input signals creates two new signals, one at the sum f
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Typically (see Fig. 1, the well-known Michelson configuration) a single incoming beam of
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4827:"Optical wavefront measurement using a novel phase-shifting point-diffraction interferometer"
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1215:(FOGs) are interferometers used in navigation systems. They operate on the principle of the
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can be exploited to build interferometers. The first examples of matter interferometers were
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3888:"Infrared measurements in the Arctic using two Atmospheric Emitted Radiance Interferometers"
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column concentration of trace gases such as ozone and carbon monoxide above the instrument.
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An astronomical interferometer achieves high-resolution observations using the technique of
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787:. This was an early example of the use of white light to resolve the "2 pi ambiguity".
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Interferometers and interferometric techniques may be categorized by a variety of criteria:
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5338:"Traceability, stability and use of the Kyviskes calibration baselineâthe first 10 years"
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4217:"Measurement of aspheric mirror segments using Fizeau interferometry with CGH correction"
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Mantravadi, M. V.; Malacara, D. (2007). "Newton, Fizeau, and Haidinger Interferometers".
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Figure 15. Optical testing with a Fizeau interferometer and a computer generated hologram
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information in multiple orientations by taking repeated measurements, a technique called
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to measure the speed of light in air relative to water, and it was used again in 1851 by
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are now in operation offering resolutions down to the fractional milliarcsecond range.
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2138:"Fully symmetric dispersionless stable transmission-grating Michelson interferometer"
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The most important and widely used application of the heterodyne technique is in the
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4470:"Efficient nonlinear algorithm for envelope detection in white light interferometry"
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1627:(a/LCI) uses scattered light to measure the sizes of subcellular objects, including
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Lehmann, M; Lichte, H (December 2002). "Tutorial on off-axis electron holography".
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dominance of Isaac Newton's corpuscular theory of light proposed a century before.
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2949:"Additional Notes Concerning the Selection of a Multiple-Etalon System for ATST"
2029:"Widefield heterodyne interferometry using a custom CMOS modulated light camera"
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Proceedings of the National Academy of Sciences of the United States of America
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2324:"Heisenberg's Uncertainty and Matter Wave Interferometry with Large Molecules"
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sources can also be made to interfere under some circumstances. The resulting
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4441:. Interferometry: Techniques and Analysis. Vol. 1755. pp. 202â201.
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Modern Technologies in Space- and Ground-based Telescopes and Instrumentation
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Figure 24. Spyrogira cell (detached from algal filament) under phase contrast
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to measure the effect of Fresnel drag on the speed of light in moving water.
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3155:"Entanglement and visibility at the output of a MachâZehnder interferometer"
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5701:"Differential x-ray phase contrast imaging using a shearing interferometer"
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3129:"Flow visualization techniques in wind tunnels â optical methods (Part II)"
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local molecular polarizability eliminates the need for fluorescent tags or
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Figure 19. TwymanâGreen interferometer set up as a white light scanner
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5785:"A universal moiré effect and application in X-ray phase-contrast imaging"
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4918:"Optical low-coherence interferometry for selected technical applications"
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Figure 21. ESPI fringes showing a vibration mode of a clamped square plate
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were demonstrated, later followed by interferometers employing molecules.
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measured by these instruments. (This method has been superseded by GPS.)
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Interferometry is used in radio astronomy, with timing offsets of D sin Ξ
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Schreiber, H.; Bruning, J. H. (2007). "Phase Shifting Interferometry".
4728:"Phase-Shifting Interferometry for Determining Optical Surface Quality"
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445:, the interference occurs between two beams at the same wavelength (or
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to determine their relative phase difference. Most interferometers use
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Kolesnichenko, Pavel; Wittenbecher, Lukas; Zigmantas, Donatas (2020).
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in the construction of a custom frequency chain. Currently, optical
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in Berlin, invented the interferometer that is named after him, the
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As seen in Fig. 2a and 2b, the observer has a direct view of mirror
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coronal plasma velocity towards or away from the satellite camera.
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which extracts the audio signal, which is sent to the loudspeaker.
519:(IF). This IF is amplified and filtered, before being applied to a
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Mallick, S.; Malacara, D. (2007). "Common-Path Interferometers".
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Figure 26. High resolution phase-contrast x-ray image of a spider
2572:"On the Relative Motion of the Earth and the Luminiferous Ether"
1313:
Figure 17. Phase shifting and Coherence scanning interferometers
903:
3028:
2405:"Guideline for Use of Fizeau Interferometer in Optical Testing"
1005:
shows a movie assembled from aperture synthesis images of the
203:
combine, the resulting intensity pattern is determined by the
2287:
Jönsson, C (1974). "Electron diffraction at multiple slits".
968:. Baselines thousands of kilometers long were achieved using
142:, which are then combined again to produce interference; two
61:
and is an important investigative technique in the fields of
5347:. Vilnius Gediminas Technical University. pp. 1274â1280
4826:
4283:""Sagnac effect" A century of Earth-rotated interferometers"
175:
Figure 2. Formation of fringes in a Michelson interferometer
5345:
Environmental Engineering, The 7th International Conference
3050:
Castelvecchi, Davide; Witze, Alexandra (11 February 2016).
2027:
Patel, R.; Achamfuo-Yeboah, S.; Light R.; Clark M. (2011).
1835:
Patel, R.; Achamfuo-Yeboah, S.; Light R.; Clark M. (2014).
1406:
the difference between the stressed and unstressed states.
592:. Other examples of common path interferometer include the
245:
seen through the beam splitter, and sees a reflected image
5699:
David, C; Nohammer, B; Solak, H H & Ziegler E (2002).
3029:"LIGO-Laser Interferometer Gravitational-Wave Observatory"
3003:"Halloween 2003 Solar Storms: SOHO/EIT Ultraviolet, 195 Ă"
1379:
set up for white light scanning of a macroscopic object.
484:
of the two frequencies, and the other at the difference f
5533:"Nomarski Differential Interference-Contrast Microscopy"
3886:
Mariani, Z.; Strong, K.; Wolff, M.; et al. (2012).
1343:
visualized by Scanning White Light Interferometry (SWLI)
1043:
Neutron interferometry has been used to investigate the
1584:
unsporulated oocyst, differential interference contrast
4950:
Yang, C.-H.; Wax, A; Dasari, R.R.; Feld, M.S. (2002).
4053:"Interferential Devices â TwymanâGreen Interferometer"
2380:
Principles of physics: a calculus-based text, Volume 1
1805:
1803:
1801:
1799:
1797:
1157:, in which light interferes between two branches of a
547:
Figure 4. Four examples of common-path interferometers
57:
to extract information. Interferometry typically uses
5936:
2954:. Advanced Technology Solar Telescope. Archived from
1795:
1793:
1791:
1789:
1787:
1785:
1783:
1781:
1779:
1777:
1271:
to optical frequencies. At each step of the chain, a
684:
Figure 6. Three amplitude-splitting interferometers:
3960:
Malacara, D. (2007). "TwymanâGreen Interferometer".
3794:"Neutron interferometry: A tale of three continents"
1526:
Figure 22. Typical optical setup of single point OCT
4390:. National Research Council, Canada. Archived from
1748:Bunch, Bryan H; Hellemans, Alexander (April 2004).
1619:
analysis of planar silicon semiconductor processing
904:
Laser Interferometer Gravitational-Wave Observatory
752:a reflectivity of 0.95 for the high-finesse image.
4281:Anderson, R.; Bilger, H.R.; Stedman, G.E. (1994).
1749:
1246:Optical heterodyne detection is used for coherent
374:The law of interference of light was described by
223:light will be split into two identical beams by a
5174:"Holographic Interferometry: Nondestructive tool"
4182:Journal of Micro/Nanolithography, MEMS, and MOEMS
3537:"Quantum interference of large organic molecules"
1896:History of the Principle of Interference of Light
1118:to control and measure the wavelengths of light.
644:Figure 5. Two wavefront splitting interferometers
503:(superhet), invented in 1917-18 by U.S. engineer
5202:"PIA01762: Space Radar Image of Kilauea, Hawaii"
4778:
4776:
4774:
2465:. Physics Department, Westminster School, London
2437:"Interferential devices â Fizeau Interferometer"
2006:"The superhet or superheterodyne radio receiver"
895:line of the Sun or stars. Fig. 10 shows an
5368:Optical Interferometry for Biology and Medicine
4548:Harasaki, A.; Schmit, J.; Wyant, J. C. (2000).
4543:
4541:
2538:Optical Interferometry for Biology and Medicine
2115:. Discovery Publishing House. pp. 97â110.
1153:MachâZehnder interferometers are being used in
4815:Sommargren, G. E. (1986). US Patent 4,594,003.
3052:"Einstein's gravitational waves found at last"
2460:"How does a MachâZehnder interferometer work?"
1078:Figure 13. Optical flat interference fringes.
852:Figure 9. A picture of the solar corona taken
612:Wavefront splitting versus amplitude splitting
27:Measurement method using interference of waves
5267:DvoĆĂĄkovĂĄ, P.; Bajgar, V.; Trnka, J. (2007).
5146:. Dover Publications, Inc. pp. 229â230.
4825:Ferraro, P.; Paturzo, M.; Grilli, S. (2007).
4665:"Interferometry: Technology and Applications"
982:is an astronomical interferometer located in
8:
5234:Journal of Physics E: Scientific Instruments
2490:(engd). California Institute of Technology.
5167:
5165:
5163:
4550:"Improved vertical-scanning interferometry"
2516:. Fachbereich Physik, UniversitĂ€t OsnabrĂŒck
1637:Phase-contrast x-ray imaging (introduction)
1625:Angle-resolved low-coherence interferometry
1515:
1098:of the light waves are greatly exaggerated.
833:Figure 7. MichelsonâMorley experiment with
822:
661:molecules large enough to be seen under an
4925:Bulletin of the Polish Academy of Sciences
4722:
4720:
4215:Burge, J. H.; Zhao, C.; Dubin, M. (2010).
2358:. American Association of Physics Teachers
1612:. These structures can be made visible by
707:is shown as it might be set up to test an
5816:
5724:
5694:
5692:
5672:
5587:
5435:
5313:
4751:
4749:
4658:
4656:
4654:
4584:
4496:
4477:Journal of the Optical Society of America
4333:RF and Microwave Applications and Systems
4132:
4095:
4028:
4018:
3911:
3846:
3817:
3658:
3605:
3568:
3495:
3390:
3304:
3241:
3173:
3094:Journal of the Optical Society of America
2924:
2805:
2693:
2458:Zetie, K.P.; Adams, S.F.; Tocknell, R.M.
2161:
2052:
1976:
1974:
1972:
1970:
1860:
1462:Electronic speckle pattern interferometry
1134:modes except the single one of interest.
150:give information about the difference in
3279:
3277:
2326:. In Buschhorn, G. W.; Wess, J. (eds.).
2212:"Interference Fringes with Feeble Light"
1443:Interferometric synthetic aperture radar
1346:
1332:
1308:
1256:
1199:
1073:
916:first observation of gravitational waves
846:Figure 8. Fourier transform spectroscopy
679:
639:
542:
178:
170:
116:, mechanical stress/strain measurement,
31:
5943:
4663:Olszak, A.G.; Schmit, J.; Heaton, M.G.
4366:"Self-heterodyne Linewidth Measurement"
3995:"On the Correction of Optical Surfaces"
2888:Stroke, G.W.; Funkhouser, A.T. (1965).
2186:"Interferential Devices â Introduction"
1740:
1558:
1415:
1179:extremely large astronomical telescopes
1106:Fabry-PĂ©rot etalons are widely used in
4263:
4253:
3134:. Military Technical Institute, Serbia
2570:Michelson, A.A.; Morley, E.W. (1887).
1663:, or high resolution x-ray detectors.
1141:Figure 14. TwymanâGreen Interferometer
5293:Moustafa, N. A.; Hendawi, N. (2003).
4730:. Newport Corporation. Archived from
3286:"Optical interferometry in astronomy"
1756:. Houghton Mifflin Harcourt. p.
1752:The History of Science and Technology
1445:(InSAR) is a radar technique used in
908:MichelsonâFabryâPĂ©rot interferometers
897:Extreme ultraviolet Imaging Telescope
460:). A weak input signal of frequency f
437:Homodyne versus heterodyne detection
7:
1837:"Widefield two laser interferometry"
1632:average cell nuclei size increases.
5336:Buga, A.; Jokela, J.; Putrimas, R.
5097:"Typical profilometry measurements"
3647:Physical Chemistry Chemical Physics
2981:"Spectrometry by Fourier transform"
2377:Serway, R.A.; Jewett, J.W. (2010).
990:Astronomical optical interferometry
492:. These new frequencies are called
468:with a strong reference frequency f
36:Figure 1. The light path through a
4336:. CRC Press. pp. 14.1â14.17.
4226:. Vol. 7739. p. 773902.
2947:Gary, G.A.; Balasubramaniam, K.S.
1639:. For a more in-depth review, see
1606:differential interference contrast
1269:cesium or other atomic time source
25:
4076:Sensors and Actuators B: Chemical
2322:Arndt, M.; Zeilinger, A. (2004).
1724:Very-long-baseline interferometry
1678:Coherence scanning interferometry
1479:A method of establishing precise
1467:When lasers were first invented,
1357:coherence scanning interferometry
1299:coherence scanning interferometry
970:very long baseline interferometry
781:environmental temperature control
594:Zernike phase-contrast microscope
5982:
5970:
5958:
5946:
5924:
5073:. Lumetrics, Inc. Archived from
4757:"How Phase Interferometers work"
4625:Advances in Optics and Photonics
4055:. OPI â Optique pour l'IngĂ©nieur
2983:. OPI â Optique pour l'IngĂ©nieur
2188:. OPI â Optique pour l'IngĂ©nieur
1704:List of types of interferometers
1589:
1573:
1561:
1533:
1519:
1430:
1418:
1128:wavelength-division multiplexing
1126:etalons. In telecommunications,
918:occurred on September 14, 2015.
839:
826:
676:Amplitude-splitting inferometers
617:Wavefront splitting inferometers
586:point diffraction interferometer
511:. In this circuit, the incoming
5649:"Phase-sensitive x-ray imaging"
5071:"Coating Thickness Measurement"
1530:
1229:frequency division multiplexing
1070:Engineering and applied science
863:Fourier transform spectrometers
650:Young's interference experiment
627:Young's interference experiment
590:lateral shearing interferometer
194:Interference (wave propagation)
5468:"Optical Coherence Tomography"
5401:"Optical Coherence Tomography"
5143:Laser, Light of a Million Uses
4759:. Graham Optical Systems. 2011
3293:Reports on Progress in Physics
2763:10.1103/PhysRevLett.103.090401
1985:. RP Photonics Consulting GmbH
1983:"Optical Heterodyne Detection"
533:Double path versus common path
156:Fourier transform spectroscopy
47:is a technique which uses the
1:
3379:Astron. Astrophys. Suppl. Ser
2712:10.1103/PhysRevLett.91.020401
1685:(HST FGS are interferometers)
854:with the LASCO C1 coronagraph
5647:Fitzgerald, Richard (2000).
5560:Journal of Biomedical Optics
5475:Journal of Biomedical Optics
5119:"Holographic interferometry"
4106:10.1016/0925-4005(93)87008-D
3432:Phil. Trans. R. Soc. Lond. A
2917:10.1016/0031-9163(65)90846-2
2541:. Springer. pp. 17â26.
2511:"FabryâPerot Interferometer"
2383:. Brooks Cole. p. 905.
2330:. Springer. pp. 35â52.
1641:Phase-contrast X-ray imaging
1554:Optical coherence tomography
1546:optical coherence tomography
1252:optical fiber communications
1195:computer-generated holograms
1051:that is at the basis of the
835:cryogenic optical resonators
812:which provided evidence for
527:Optical heterodyne detection
5099:. Novacam Technologies, Inc
2579:American Journal of Science
2484:Ashkenas, Harry I. (1950).
2289:American Journal of Physics
2208:Ingram Taylor, Sir Geoffrey
1943:. Oxford University Press.
1377:TwymanâGreen interferometer
1375:Fig. 19 illustrates a
1337:Figure 18. Lunate cells of
1155:integrated optical circuits
870:FabryâPĂ©rot interferometers
716:MachâZehnder interferometer
606:scatterplate interferometer
565:MachâZehnder interferometer
561:TwymanâGreen interferometer
366:for a discussion of this.)
160:astronomical interferometer
6031:
5614:Gastrointestinal Endoscopy
5172:Fein, H (September 1997).
4867:10.1002/9780470135976.ch15
4793:10.1002/9780470135976.ch14
3865:10.1103/PhysRevD.78.042003
3771:(2nd ed.). Springer.
3323:10.1088/0034-4885/66/5/203
3260:10.1103/PhysRevB.82.155303
2824:10.1103/PhysRevD.80.105011
2439:. Optique pour l'Ingénieur
1964:Nolte, Interference,pg.111
1694:Interferometric visibility
1683:Fine Guidance Sensor (HST)
1542:Central serous retinopathy
1400:Holographic interferometry
1385:is a technique which uses
1383:Holographic interferometry
1297:(SWLI) or by the ISO term
1295:white light interferometry
763:, Laser Unequal Path, and
732:FabryâPĂ©rot interferometer
573:common-path interferometer
553:double-path interferometer
539:Common-path interferometer
536:
320:. If, as in Fig. 2b,
231:itself or a change in the
191:
5626:10.1016/j.gie.2006.10.016
5254:10.1088/0022-3735/4/4/004
4711:10.1080/09500349514550341
3993:Michelson, A. A. (1918).
3970:10.1002/9780470135976.ch2
3937:10.1002/9780470135976.ch1
3736:10.1017/S1431927602029938
3624:10.1103/RevModPhys.84.157
3594:Reviews of Modern Physics
3484:The Astrophysical Journal
3064:10.1038/nature.2016.19361
2636:Reviews of Modern Physics
2599:10.2475/ajs.s3-34.203.333
2086:10.1002/9780470135976.ch3
1905:10.1007/978-3-0348-8652-9
1610:bright field illumination
1187:Extremely Large Telescope
1053:Pauli exclusion principle
654:constructive interference
110:biomolecular interactions
88:(and its applications to
5538:. Carl Zeiss, Oberkochen
5366:Nolte, David D. (2012).
5315:10.21608/ejs.2003.150160
5181:The Industrial Physicist
4691:Journal of Modern Optics
4388:"Optical Frequency Comb"
3284:Monnier, John D (2003).
3192:10.1103/PhysRevA.59.1615
2656:10.1103/RevModPhys.5.203
2535:Nolte, David D. (2012).
1937:Nolte, David D. (2023).
1812:Basics of Interferometry
1699:Interference lithography
1455:synthetic aperture radar
1328:piezoelectric transducer
1029:. Around 1990 the first
1023:electron interferometers
1019:wave character of matter
966:Earth-rotation synthesis
557:Michelson interferometer
501:superheterodyne receiver
414:Michelson Interferometer
364:Michelson interferometer
38:Michelson interferometer
5705:Applied Physics Letters
5428:10.1126/science.1957169
5183:: 37â39. Archived from
4893:. Veeco. Archived from
4507:10.1364/JOSAA.13.000832
4194:2006JMM&M...5b3009N
4151:10.1126/science.1119678
3401:1999A&AS..138..135M
2743:Physical Review Letters
2353:"Simple Lloyd's Mirror"
2008:. Radio-Electronics.com
1719:Superposition principle
1483:baselines, invented by
1293:also known as scanning
1262:frequency measurements.
1027:neutron interferometers
635:Rayleigh interferometer
282:of the original source
5466:Fercher, A.F. (1996).
3913:10.5194/amt-5-329-2012
3452:10.1098/rsta.2001.0977
3153:Paris, M.G.A. (1999).
3114:10.1364/JOSA.47.000703
2410:. NASA. Archived from
2246:Zeitschrift fĂŒr Physik
1893:Kipnis, Nahum (1991).
1810:Hariharan, P. (2007).
1714:Seismic interferometry
1352:
1344:
1314:
1263:
1231:(FDM). For example, a
1213:fibre optic gyroscopes
1205:
1183:Thirty Meter Telescope
1142:
1099:
1087:
1014:both clearly visible.
999:three major facilities
986:
945:
805:
697:
645:
548:
517:intermediate frequency
505:Edwin Howard Armstrong
212:or some other form of
189:
176:
41:
18:Optical interferometry
5276:Engineering Mechanics
4468:Larkin, K.G. (1996).
3765:Tonomura, A. (1999).
3541:Nature Communications
2219:Proc. Camb. Phil. Soc
1709:Ramsey interferometry
1366:Linnik interferometer
1350:
1336:
1312:
1260:
1209:Ring laser gyroscopes
1203:
1140:
1093:
1077:
995:Astronomical "seeing"
978:
939:
910:for the detection of
906:(LIGO) uses two 4-km
803:
796:Physics and astronomy
765:Linnik interferometer
705:Fizeau interferometer
683:
643:
582:fibre optic gyroscope
578:Sagnac interferometer
546:
410:Hermann von Helmholtz
384:Augustin-Jean Fresnel
192:Further information:
184:monochromatic light (
182:
174:
112:, surface profiling,
76:, optical metrology,
59:electromagnetic waves
35:
5933:at Wikimedia Commons
5512:on 25 September 2018
5140:Hecht, Jeff (1998).
5030:10.1364/ol.26.001864
4979:10.1364/OL.27.000077
4859:Optical Shop Testing
4785:Optical Shop Testing
4645:10.1364/AOP.7.000001
4577:10.1364/AO.39.002107
4413:Paschotta, RĂŒdiger.
4364:Paschotta, RĂŒdiger.
4330:Golio, Mike (2007).
4020:10.1073/pnas.4.7.210
3962:Optical Shop Testing
3929:Optical Shop Testing
3353:"Cosmic Calibration"
3209:on 10 September 2016
2417:on 25 September 2018
2109:Verma, R.K. (2008).
2078:Optical Shop Testing
2054:10.1364/OE.19.024546
1981:Paschotta, RĂŒdiger.
1862:10.1364/OE.22.027094
1503:Biology and medicine
1491:traceable scale for
1361:Mirau interferometer
1301:(CSI), CSI exploits
1273:frequency multiplier
1177:The latest proposed
1161:that are externally
1045:AharonovâBohm effect
1031:atom interferometers
1025:, later followed by
931:quantum entanglement
810:Michelson and Morley
507:and French engineer
382:The French engineer
214:electromagnetic wave
152:optical path lengths
148:interference fringes
6010:Optical instruments
5854:1995Natur.373..595D
5801:2016NatPh..12..830M
5754:1996Natur.384..335W
5717:2002ApPhL..81.3287D
5665:2000PhT....53g..23F
5572:2005JBO....10e1604W
5487:1996JBO.....1..157F
5420:1991Sci...254.1178H
5376:2012oibm.book.....N
5246:1971JPhE....4..277B
5022:2001OptL...26.1864H
4971:2002OptL...27...77Y
4703:1995JMOp...42..389D
4637:2015AdOP....7....1D
4569:2000ApOpt..39.2107H
4489:1996JOSAA..13..832L
4439:Proceedings of SPIE
4302:1994AmJPh..62..975A
4232:2010SPIE.7739E..02B
4143:2005Sci...310.1653O
4127:(5754): 1653â1657.
4088:1993SeAcB..10..209H
4011:1918PNAS....4..210M
3904:2012AMT.....5..329M
3857:2008PhRvD..78d2003D
3819:10.1051/epn/2009802
3810:2009ENews..40f..24K
3768:Electron Holography
3728:2002MiMic...8..447L
3669:2013PCCP...1514696E
3616:2012RvMP...84..157H
3553:2011NatCo...2..263G
3506:2008ApJ...684L..95Z
3444:2002RSPTA.360..969B
3409:10.1051/aas:1999496
3315:2003RPPh...66..789M
3252:2010PhRvB..82o5303H
3184:1999PhRvA..59.1615P
3106:1957JOSA...47..703C
2909:1965PhL....16..272S
2859:1995SoPh..162..129S
2816:2009PhRvD..80j5011H
2755:2009PhRvL.103i0401E
2704:2003PhRvL..91b0401M
2648:1933RvMP....5..203M
2591:1887AmJS...34..333M
2547:2012oibm.book.....N
2301:1974AmJPh..42....4J
2258:1961ZPhy..161..454J
2154:2020OExpr..2837752K
2148:(25): 37752â37757.
2045:2011OExpr..1924546P
2039:(24): 24546â24556.
1853:2014OExpr..2227094P
1847:(22): 27094â27101.
1193:. In recent years,
1122:are multiple layer
1037:Electron holography
912:gravitational waves
777:luminiferous aether
663:electron microscope
406:Albert A. Michelson
6015:Plasma diagnostics
5897:10.1038/nm0496-473
5077:on 29 October 2013
4734:on 7 November 2012
3964:. pp. 46â96.
3792:Klein, T. (2009).
3716:Microsc. Microanal
3677:10.1039/C3CP51500A
3561:10.1038/ncomms1263
2867:10.1007/BF00733429
2266:10.1007/BF01342460
1353:
1345:
1340:Nepenthes khasiana
1315:
1287:frequency standard
1264:
1206:
1143:
1108:telecommunications
1100:
1088:
1060:general relativity
987:
984:Chajnantor Plateau
950:aperture synthesis
946:
818:optical resonators
814:special relativity
806:
723:, on the order of
698:
646:
549:
443:homodyne detection
190:
177:
55:superimposed waves
42:
5929:Media related to
5848:(6515): 595â598.
5809:10.1038/nphys3734
5748:(6607): 335â338.
5726:10.1063/1.1516611
5711:(17): 3287â3289.
5674:10.1063/1.1292471
5580:10.1117/1.2102767
5495:10.1117/12.231361
5414:(5035): 1178â81.
5385:978-1-4614-0889-5
5153:978-0-486-40193-5
5016:(23): 1864â1866.
4876:978-0-470-13597-6
4802:978-0-470-13597-6
4563:(13): 2107â2115.
4447:10.1117/12.140770
4415:"Frequency Combs"
4343:978-0-8493-7219-3
4240:10.1117/12.857816
4202:10.1117/1.2203366
3979:978-0-470-13597-6
3946:978-0-470-13597-6
3892:Atmos. Meas. Tech
3841:(42003): 042003.
3778:978-3-540-64555-9
3653:(35): 14696â700.
3438:(1794): 969â986.
3230:Physical Review B
3162:Physical Review A
3127:RistiÄ, Slavica.
2961:on 10 August 2010
2794:Physical Review D
2556:978-1-4614-0889-5
2496:10.7907/D0V1-MJ80
2390:978-0-534-49143-7
2337:978-3-540-20201-1
2309:10.1119/1.1987592
2163:10.1364/OE.409185
2122:978-81-8356-114-3
2095:978-0-470-13597-6
1914:978-3-0348-9717-4
1821:978-0-12-373589-8
1767:978-0-618-22123-3
1729:Zero spacing flux
1582:Toxoplasma gondii
1551:
1550:
1493:geodetic networks
1370:surface metrology
1003:This linked video
859:
858:
730:The heart of the
598:Fresnel's biprism
447:carrier frequency
408:, while visiting
94:quantum mechanics
16:(Redirected from
6022:
5987:
5986:
5975:
5974:
5963:
5962:
5961:
5951:
5950:
5949:
5942:
5928:
5917:
5916:
5880:
5874:
5873:
5862:10.1038/373595a0
5837:
5831:
5830:
5820:
5780:
5774:
5773:
5762:10.1038/384335a0
5737:
5731:
5730:
5728:
5696:
5687:
5686:
5676:
5644:
5638:
5637:
5608:
5602:
5601:
5591:
5554:
5548:
5547:
5545:
5543:
5537:
5528:
5522:
5521:
5519:
5517:
5511:
5505:. Archived from
5472:
5463:
5457:
5456:
5454:
5452:
5439:
5405:
5396:
5390:
5389:
5363:
5357:
5356:
5354:
5352:
5342:
5333:
5327:
5326:
5324:
5322:
5317:
5299:
5290:
5284:
5283:
5273:
5264:
5258:
5257:
5229:
5223:
5220:
5214:
5213:
5211:
5209:
5204:. NASA/JPL. 1999
5198:
5192:
5191:
5189:
5178:
5169:
5158:
5157:
5137:
5131:
5130:
5128:
5126:
5115:
5109:
5108:
5106:
5104:
5093:
5087:
5086:
5084:
5082:
5067:
5061:
5057:
5051:
5048:
5042:
5041:
5005:
4999:
4998:
4956:
4947:
4941:
4940:
4938:
4936:
4922:
4913:
4907:
4906:
4904:
4902:
4887:
4881:
4880:
4854:
4848:
4845:
4839:
4838:
4836:
4834:
4822:
4816:
4813:
4807:
4806:
4780:
4769:
4768:
4766:
4764:
4753:
4744:
4743:
4741:
4739:
4724:
4715:
4714:
4686:
4680:
4679:
4677:
4675:
4669:
4660:
4649:
4648:
4620:
4614:
4613:
4611:
4609:
4603:
4597:. Archived from
4588:
4554:
4545:
4536:
4535:Standardization.
4532:
4526:
4525:
4523:
4521:
4516:on 10 March 2020
4515:
4509:. Archived from
4500:
4474:
4465:
4459:
4458:
4433:
4427:
4426:
4424:
4422:
4410:
4404:
4403:
4401:
4399:
4384:
4378:
4377:
4375:
4373:
4361:
4355:
4354:
4352:
4350:
4327:
4321:
4320:
4318:
4316:
4287:
4278:
4272:
4271:
4265:
4261:
4259:
4251:
4221:
4212:
4206:
4205:
4177:
4171:
4170:
4136:
4134:cond-mat/0512691
4116:
4110:
4109:
4099:
4071:
4065:
4064:
4062:
4060:
4049:
4043:
4042:
4032:
4022:
3990:
3984:
3983:
3957:
3951:
3950:
3924:
3918:
3917:
3915:
3883:
3877:
3876:
3850:
3830:
3824:
3823:
3821:
3798:Europhysics News
3789:
3783:
3782:
3762:
3756:
3755:
3711:
3705:
3704:
3662:
3642:
3636:
3635:
3609:
3589:
3583:
3582:
3572:
3532:
3526:
3525:
3499:
3478:
3472:
3471:
3427:
3421:
3420:
3394:
3392:astro-ph/9907031
3374:
3368:
3367:
3365:
3363:
3349:
3343:
3342:
3308:
3306:astro-ph/0307036
3290:
3281:
3272:
3271:
3245:
3225:
3219:
3218:
3216:
3214:
3208:
3202:. Archived from
3177:
3175:quant-ph/9811078
3168:(2): 1615â1621.
3159:
3150:
3144:
3143:
3141:
3139:
3133:
3124:
3118:
3117:
3089:
3083:
3082:
3080:
3078:
3047:
3041:
3040:
3038:
3036:
3025:
3019:
3018:
3016:
3014:
3009:on 23 April 2014
2999:
2993:
2992:
2990:
2988:
2977:
2971:
2970:
2968:
2966:
2960:
2953:
2944:
2938:
2937:
2935:
2933:
2928:
2894:
2885:
2879:
2878:
2853:(1â2): 129â188.
2842:
2836:
2835:
2809:
2789:
2783:
2782:
2738:
2732:
2731:
2697:
2677:
2671:
2670:
2631:
2625:
2624:
2622:
2621:
2615:
2609:. Archived from
2585:(203): 333â345.
2576:
2567:
2561:
2560:
2532:
2526:
2525:
2523:
2521:
2515:
2509:Betzler, Klaus.
2506:
2500:
2499:
2481:
2475:
2474:
2472:
2470:
2464:
2455:
2449:
2448:
2446:
2444:
2433:
2427:
2426:
2424:
2422:
2416:
2409:
2401:
2395:
2394:
2374:
2368:
2367:
2365:
2363:
2357:
2351:Carroll, Brett.
2348:
2342:
2341:
2319:
2313:
2312:
2284:
2278:
2277:
2241:
2235:
2234:
2232:
2230:
2216:
2204:
2198:
2197:
2195:
2193:
2182:
2176:
2175:
2165:
2133:
2127:
2126:
2106:
2100:
2099:
2073:
2067:
2066:
2056:
2024:
2018:
2017:
2015:
2013:
2001:
1995:
1994:
1992:
1990:
1978:
1965:
1962:
1956:
1954:
1934:
1928:
1925:
1919:
1918:
1890:
1884:
1881:
1875:
1874:
1864:
1832:
1826:
1825:
1814:. Elsevier Inc.
1807:
1772:
1771:
1755:
1745:
1647:interferometry,
1593:
1577:
1565:
1547:
1537:
1527:
1523:
1516:
1434:
1422:
1237:cable television
1172:optical switches
1148:coherence length
1120:Dichroic filters
961:Very Large Array
923:visualizing flow
855:
847:
843:
836:
830:
823:
785:coherence length
771:Michelson-Morley
721:coherence length
602:zero-area Sagnac
474:local oscillator
418:Edward W. Morley
396:Hippolyte Fizeau
352:
342:
332:
301:
291:
277:
267:
250:
235:along the path.
233:refractive index
167:Basic principles
136:refractive index
102:particle physics
21:
6030:
6029:
6025:
6024:
6023:
6021:
6020:
6019:
5995:
5994:
5993:
5981:
5969:
5959:
5957:
5947:
5945:
5937:
5921:
5920:
5885:Nature Medicine
5882:
5881:
5877:
5839:
5838:
5834:
5782:
5781:
5777:
5739:
5738:
5734:
5698:
5697:
5690:
5646:
5645:
5641:
5610:
5609:
5605:
5556:
5555:
5551:
5541:
5539:
5535:
5530:
5529:
5525:
5515:
5513:
5509:
5470:
5465:
5464:
5460:
5450:
5448:
5403:
5398:
5397:
5393:
5386:
5365:
5364:
5360:
5350:
5348:
5340:
5335:
5334:
5330:
5320:
5318:
5297:
5292:
5291:
5287:
5271:
5266:
5265:
5261:
5231:
5230:
5226:
5221:
5217:
5207:
5205:
5200:
5199:
5195:
5187:
5176:
5171:
5170:
5161:
5154:
5139:
5138:
5134:
5124:
5122:
5121:. Oquagen. 2008
5117:
5116:
5112:
5102:
5100:
5095:
5094:
5090:
5080:
5078:
5069:
5068:
5064:
5058:
5054:
5049:
5045:
5007:
5006:
5002:
4954:
4949:
4948:
4944:
4934:
4932:
4920:
4915:
4914:
4910:
4900:
4898:
4897:on 9 April 2012
4889:
4888:
4884:
4877:
4861:. p. 667.
4856:
4855:
4851:
4846:
4842:
4832:
4830:
4824:
4823:
4819:
4814:
4810:
4803:
4787:. p. 547.
4782:
4781:
4772:
4762:
4760:
4755:
4754:
4747:
4737:
4735:
4726:
4725:
4718:
4688:
4687:
4683:
4673:
4671:
4667:
4662:
4661:
4652:
4622:
4621:
4617:
4607:
4605:
4604:on 25 July 2010
4601:
4552:
4547:
4546:
4539:
4533:
4529:
4519:
4517:
4513:
4498:10.1.1.190.4728
4472:
4467:
4466:
4462:
4435:
4434:
4430:
4420:
4418:
4412:
4411:
4407:
4397:
4395:
4394:on 5 March 2012
4386:
4385:
4381:
4371:
4369:
4363:
4362:
4358:
4348:
4346:
4344:
4329:
4328:
4324:
4314:
4312:
4310:10.1119/1.17656
4296:(11): 975â985.
4285:
4280:
4279:
4275:
4262:
4252:
4219:
4214:
4213:
4209:
4179:
4178:
4174:
4118:
4117:
4113:
4097:10.1.1.556.5526
4073:
4072:
4068:
4058:
4056:
4051:
4050:
4046:
3992:
3991:
3987:
3980:
3959:
3958:
3954:
3947:
3926:
3925:
3921:
3885:
3884:
3880:
3832:
3831:
3827:
3791:
3790:
3786:
3779:
3764:
3763:
3759:
3713:
3712:
3708:
3644:
3643:
3639:
3591:
3590:
3586:
3534:
3533:
3529:
3480:
3479:
3475:
3429:
3428:
3424:
3376:
3375:
3371:
3361:
3359:
3351:
3350:
3346:
3288:
3283:
3282:
3275:
3227:
3226:
3222:
3212:
3210:
3206:
3157:
3152:
3151:
3147:
3137:
3135:
3131:
3126:
3125:
3121:
3091:
3090:
3086:
3076:
3074:
3049:
3048:
3044:
3034:
3032:
3027:
3026:
3022:
3012:
3010:
3001:
3000:
2996:
2986:
2984:
2979:
2978:
2974:
2964:
2962:
2958:
2951:
2946:
2945:
2941:
2931:
2929:
2897:Physics Letters
2892:
2887:
2886:
2882:
2844:
2843:
2839:
2791:
2790:
2786:
2740:
2739:
2735:
2695:physics/0305117
2682:Phys. Rev. Lett
2679:
2678:
2674:
2633:
2632:
2628:
2619:
2617:
2613:
2574:
2569:
2568:
2564:
2557:
2534:
2533:
2529:
2519:
2517:
2513:
2508:
2507:
2503:
2483:
2482:
2478:
2468:
2466:
2462:
2457:
2456:
2452:
2442:
2440:
2435:
2434:
2430:
2420:
2418:
2414:
2407:
2403:
2402:
2398:
2391:
2376:
2375:
2371:
2361:
2359:
2355:
2350:
2349:
2345:
2338:
2321:
2320:
2316:
2286:
2285:
2281:
2243:
2242:
2238:
2228:
2226:
2214:
2206:
2205:
2201:
2191:
2189:
2184:
2183:
2179:
2135:
2134:
2130:
2123:
2108:
2107:
2103:
2096:
2075:
2074:
2070:
2026:
2025:
2021:
2011:
2009:
2003:
2002:
1998:
1988:
1986:
1980:
1979:
1968:
1963:
1959:
1951:
1936:
1935:
1931:
1926:
1922:
1915:
1892:
1891:
1887:
1882:
1878:
1834:
1833:
1829:
1822:
1809:
1808:
1775:
1768:
1747:
1746:
1742:
1737:
1669:
1659:x-ray sources,
1597:
1594:
1585:
1578:
1569:
1566:
1545:
1539:
1538:
1525:
1524:
1505:
1438:
1435:
1426:
1423:
1278:frequency combs
1086:curved surface.
1072:
957:radio telescope
940:Figure 11. The
853:
851:
850:
845:
844:
834:
832:
831:
798:
793:
773:
678:
619:
614:
541:
535:
513:radio frequency
491:
487:
483:
479:
471:
463:
439:
431:
372:
356:
350:
346:
340:
336:
330:
326:
318:
312:
305:
299:
295:
289:
281:
275:
271:
265:
261:
254:
248:
244:
196:
169:
132:Interferometers
28:
23:
22:
15:
12:
11:
5:
6028:
6026:
6018:
6017:
6012:
6007:
6005:Interferometry
5997:
5996:
5992:
5991:
5979:
5967:
5955:
5935:
5934:
5931:Interferometry
5919:
5918:
5891:(4): 473â475.
5875:
5832:
5795:(9): 830â834.
5789:Nature Physics
5775:
5732:
5688:
5639:
5620:(3): 487â491.
5603:
5549:
5531:Lang, Walter.
5523:
5481:(2): 157â173.
5458:
5391:
5384:
5358:
5328:
5308:(2): 225â229.
5285:
5259:
5240:(4): 277â279.
5224:
5215:
5193:
5190:on 2012-11-07.
5159:
5152:
5132:
5110:
5088:
5062:
5052:
5043:
5010:Optics Letters
5000:
4959:Optics Letters
4942:
4908:
4882:
4875:
4849:
4840:
4817:
4808:
4801:
4770:
4745:
4716:
4697:(2): 389â401.
4681:
4650:
4615:
4557:Applied Optics
4537:
4527:
4483:(4): 832â843.
4460:
4428:
4417:. RP Photonics
4405:
4379:
4368:. RP Photonics
4356:
4342:
4322:
4273:
4264:|journal=
4207:
4172:
4111:
4082:(3): 209â217.
4066:
4044:
4005:(7): 210â212.
3985:
3978:
3952:
3945:
3919:
3898:(2): 329â344.
3878:
3825:
3784:
3777:
3757:
3706:
3637:
3600:(1): 157â173.
3584:
3527:
3514:10.1086/592146
3473:
3422:
3369:
3344:
3299:(5): 789â857.
3273:
3236:(15): 155303.
3220:
3145:
3119:
3084:
3042:
3020:
2994:
2972:
2939:
2903:(3): 272â274.
2880:
2837:
2800:(10): 105011.
2784:
2733:
2672:
2642:(3): 203â242.
2626:
2562:
2555:
2527:
2501:
2476:
2450:
2428:
2396:
2389:
2369:
2343:
2336:
2314:
2279:
2252:(4): 454â474.
2236:
2199:
2177:
2142:Optics Express
2128:
2121:
2101:
2094:
2080:. p. 97.
2068:
2033:Optics Express
2019:
1996:
1966:
1957:
1950:978-0192869760
1949:
1929:
1920:
1913:
1885:
1876:
1841:Optics Express
1827:
1820:
1773:
1766:
1739:
1738:
1736:
1733:
1732:
1731:
1726:
1721:
1716:
1711:
1706:
1701:
1696:
1691:
1686:
1680:
1675:
1668:
1665:
1602:Phase contrast
1599:
1598:
1595:
1588:
1586:
1579:
1572:
1570:
1567:
1560:
1549:
1548:
1531:
1528:
1504:
1501:
1489:metrologically
1451:remote sensing
1440:
1439:
1436:
1429:
1427:
1424:
1417:
1191:null corrector
1181:, such as the
1170:to sensors to
1132:optical cavity
1082:flat surface,
1071:
1068:
944:interferometer
857:
856:
848:
837:
797:
794:
792:
789:
772:
769:
677:
674:
669:Lloyd's mirror
631:Lloyd's mirror
618:
615:
613:
610:
534:
531:
489:
488: â f
485:
481:
480: + f
477:
469:
461:
438:
435:
430:
427:
388:Francois Arago
371:
368:
354:
344:
334:
324:
316:
310:
303:
293:
279:
269:
259:
252:
242:
186:sodium D lines
168:
165:
106:plasma physics
45:Interferometry
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6027:
6016:
6013:
6011:
6008:
6006:
6003:
6002:
6000:
5990:
5985:
5980:
5978:
5973:
5968:
5966:
5956:
5954:
5944:
5940:
5932:
5927:
5923:
5922:
5914:
5910:
5906:
5902:
5898:
5894:
5890:
5886:
5879:
5876:
5871:
5867:
5863:
5859:
5855:
5851:
5847:
5843:
5836:
5833:
5828:
5824:
5819:
5814:
5810:
5806:
5802:
5798:
5794:
5790:
5786:
5779:
5776:
5771:
5767:
5763:
5759:
5755:
5751:
5747:
5743:
5736:
5733:
5727:
5722:
5718:
5714:
5710:
5706:
5702:
5695:
5693:
5689:
5684:
5680:
5675:
5670:
5666:
5662:
5658:
5654:
5653:Physics Today
5650:
5643:
5640:
5635:
5631:
5627:
5623:
5619:
5615:
5607:
5604:
5599:
5595:
5590:
5585:
5581:
5577:
5573:
5569:
5566:(5): 051604.
5565:
5561:
5553:
5550:
5534:
5527:
5524:
5508:
5504:
5500:
5496:
5492:
5488:
5484:
5480:
5476:
5469:
5462:
5459:
5447:
5443:
5438:
5433:
5429:
5425:
5421:
5417:
5413:
5409:
5402:
5395:
5392:
5387:
5381:
5377:
5373:
5369:
5362:
5359:
5346:
5339:
5332:
5329:
5316:
5311:
5307:
5303:
5302:Egypt. J. Sol
5296:
5289:
5286:
5282:(1/2): 37â44.
5281:
5277:
5270:
5263:
5260:
5255:
5251:
5247:
5243:
5239:
5235:
5228:
5225:
5219:
5216:
5203:
5197:
5194:
5186:
5182:
5175:
5168:
5166:
5164:
5160:
5155:
5149:
5145:
5144:
5136:
5133:
5120:
5114:
5111:
5098:
5092:
5089:
5076:
5072:
5066:
5063:
5056:
5053:
5047:
5044:
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5031:
5027:
5023:
5019:
5015:
5011:
5004:
5001:
4996:
4992:
4988:
4984:
4980:
4976:
4972:
4968:
4964:
4960:
4953:
4946:
4943:
4930:
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4912:
4909:
4896:
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4886:
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4878:
4872:
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4853:
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4779:
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4771:
4758:
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4717:
4712:
4708:
4704:
4700:
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4685:
4682:
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4389:
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4360:
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4311:
4307:
4303:
4299:
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4284:
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4274:
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4241:
4237:
4233:
4229:
4225:
4218:
4211:
4208:
4203:
4199:
4195:
4191:
4188:(2): 023009.
4187:
4183:
4176:
4173:
4168:
4164:
4160:
4156:
4152:
4148:
4144:
4140:
4135:
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4122:
4115:
4112:
4107:
4103:
4098:
4093:
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4077:
4070:
4067:
4054:
4048:
4045:
4040:
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4026:
4021:
4016:
4012:
4008:
4004:
4000:
3996:
3989:
3986:
3981:
3975:
3971:
3967:
3963:
3956:
3953:
3948:
3942:
3938:
3934:
3931:. p. 1.
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3879:
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3770:
3769:
3761:
3758:
3753:
3749:
3745:
3741:
3737:
3733:
3729:
3725:
3722:(6): 447â66.
3721:
3717:
3710:
3707:
3702:
3698:
3694:
3690:
3686:
3682:
3678:
3674:
3670:
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3641:
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3406:
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3398:
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3388:
3384:
3380:
3373:
3370:
3358:
3354:
3348:
3345:
3340:
3336:
3332:
3331:2027.42/48845
3328:
3324:
3320:
3316:
3312:
3307:
3302:
3298:
3294:
3287:
3280:
3278:
3274:
3269:
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3257:
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3249:
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3221:
3205:
3201:
3197:
3193:
3189:
3185:
3181:
3176:
3171:
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3163:
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3149:
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3130:
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3115:
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3099:
3095:
3088:
3085:
3073:
3069:
3065:
3061:
3057:
3053:
3046:
3043:
3031:. Caltech/MIT
3030:
3024:
3021:
3008:
3004:
2998:
2995:
2982:
2976:
2973:
2957:
2950:
2943:
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2927:
2926:2027.42/32013
2922:
2918:
2914:
2910:
2906:
2902:
2898:
2891:
2884:
2881:
2876:
2872:
2868:
2864:
2860:
2856:
2852:
2848:
2847:Solar Physics
2841:
2838:
2833:
2829:
2825:
2821:
2817:
2813:
2808:
2803:
2799:
2795:
2788:
2785:
2780:
2776:
2772:
2768:
2764:
2760:
2756:
2752:
2749:(9): 090401.
2748:
2744:
2737:
2734:
2729:
2725:
2721:
2717:
2713:
2709:
2705:
2701:
2696:
2691:
2688:(2): 020401.
2687:
2683:
2676:
2673:
2669:
2665:
2661:
2657:
2653:
2649:
2645:
2641:
2637:
2630:
2627:
2616:on 2016-03-07
2612:
2608:
2604:
2600:
2596:
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2588:
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2563:
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2310:
2306:
2302:
2298:
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2283:
2280:
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2267:
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2259:
2255:
2251:
2247:
2240:
2237:
2224:
2220:
2213:
2209:
2203:
2200:
2187:
2181:
2178:
2173:
2169:
2164:
2159:
2155:
2151:
2147:
2143:
2139:
2132:
2129:
2124:
2118:
2114:
2113:
2105:
2102:
2097:
2091:
2087:
2083:
2079:
2072:
2069:
2064:
2060:
2055:
2050:
2046:
2042:
2038:
2034:
2030:
2023:
2020:
2007:
2000:
1997:
1984:
1977:
1975:
1973:
1971:
1967:
1961:
1958:
1952:
1946:
1942:
1941:
1933:
1930:
1924:
1921:
1916:
1910:
1906:
1902:
1898:
1897:
1889:
1886:
1880:
1877:
1872:
1868:
1863:
1858:
1854:
1850:
1846:
1842:
1838:
1831:
1828:
1823:
1817:
1813:
1806:
1804:
1802:
1800:
1798:
1796:
1794:
1792:
1790:
1788:
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1784:
1782:
1780:
1778:
1774:
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1763:
1759:
1754:
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1744:
1741:
1734:
1730:
1727:
1725:
1722:
1720:
1717:
1715:
1712:
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1700:
1697:
1695:
1692:
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1684:
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1679:
1676:
1674:
1671:
1670:
1666:
1664:
1662:
1658:
1654:
1650:
1646:
1642:
1638:
1633:
1630:
1626:
1622:
1620:
1615:
1611:
1607:
1603:
1592:
1587:
1583:
1576:
1571:
1564:
1559:
1557:
1555:
1544:,imaged using
1543:
1536:
1532:
1529:
1522:
1518:
1517:
1514:
1511:
1502:
1500:
1496:
1494:
1490:
1486:
1482:
1477:
1475:
1470:
1469:laser speckle
1465:
1463:
1459:
1456:
1452:
1448:
1444:
1433:
1428:
1421:
1416:
1414:
1411:
1407:
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1378:
1373:
1371:
1367:
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1307:
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1300:
1296:
1290:
1288:
1284:
1279:
1274:
1270:
1259:
1255:
1253:
1249:
1248:Doppler lidar
1244:
1242:
1241:doppler radar
1238:
1234:
1233:coaxial cable
1230:
1225:
1222:
1221:optical fiber
1218:
1217:Sagnac effect
1214:
1210:
1202:
1198:
1196:
1192:
1188:
1184:
1180:
1175:
1173:
1169:
1168:RF modulators
1164:
1160:
1156:
1151:
1149:
1139:
1135:
1133:
1129:
1125:
1121:
1117:
1113:
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1104:
1097:
1092:
1085:
1081:
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1063:
1061:
1056:
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1038:
1034:
1032:
1028:
1024:
1020:
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1008:
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1000:
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991:
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958:
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951:
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932:
927:
924:
919:
917:
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909:
905:
900:
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890:
885:
881:
877:
875:
871:
866:
864:
849:
842:
838:
829:
825:
824:
821:
819:
815:
811:
802:
795:
790:
788:
786:
782:
778:
770:
768:
766:
762:
758:
753:
751:
747:
742:
737:
733:
728:
726:
722:
717:
712:
710:
706:
701:
695:
691:
687:
682:
675:
673:
670:
666:
664:
660:
655:
651:
642:
638:
636:
632:
628:
624:
616:
611:
609:
607:
603:
599:
595:
591:
587:
583:
579:
575:
574:
568:
566:
562:
558:
554:
545:
540:
532:
530:
528:
524:
522:
518:
514:
510:
506:
502:
497:
495:
475:
467:
459:
455:
450:
448:
444:
436:
434:
428:
426:
423:
419:
415:
411:
407:
403:
399:
397:
393:
392:Leon Foucault
389:
385:
380:
377:
369:
367:
365:
359:
353:
343:
333:
323:
319:
309:
302:
292:
285:
278:
268:
258:
251:
241:
236:
234:
230:
226:
225:beam splitter
222:
217:
215:
211:
206:
202:
195:
187:
181:
173:
166:
164:
161:
157:
153:
149:
145:
141:
140:optical paths
137:
133:
129:
127:
124:, and making
123:
119:
115:
114:microfluidics
111:
107:
103:
99:
95:
91:
87:
83:
79:
75:
72:
68:
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5884:
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5845:
5841:
5835:
5792:
5788:
5778:
5745:
5741:
5735:
5708:
5704:
5659:(7): 23â26.
5656:
5652:
5642:
5617:
5613:
5606:
5589:1721.1/87657
5563:
5559:
5552:
5540:. Retrieved
5526:
5514:. Retrieved
5507:the original
5478:
5474:
5461:
5449:. Retrieved
5411:
5407:
5394:
5370:. Springer.
5367:
5361:
5349:. Retrieved
5344:
5331:
5319:. Retrieved
5305:
5301:
5288:
5279:
5275:
5262:
5237:
5233:
5227:
5218:
5206:. Retrieved
5196:
5185:the original
5180:
5142:
5135:
5123:. Retrieved
5113:
5101:. Retrieved
5091:
5079:. Retrieved
5075:the original
5065:
5055:
5046:
5013:
5009:
5003:
4965:(2): 77â79.
4962:
4958:
4945:
4933:. Retrieved
4931:(2): 155â172
4928:
4924:
4911:
4899:. Retrieved
4895:the original
4885:
4858:
4852:
4843:
4831:. Retrieved
4820:
4811:
4784:
4761:. Retrieved
4736:. Retrieved
4732:the original
4694:
4690:
4684:
4672:. Retrieved
4628:
4624:
4618:
4606:. Retrieved
4599:the original
4586:10150/289148
4560:
4556:
4530:
4518:. Retrieved
4511:the original
4480:
4476:
4463:
4438:
4431:
4419:. Retrieved
4408:
4396:. Retrieved
4392:the original
4382:
4370:. Retrieved
4359:
4347:. Retrieved
4332:
4325:
4313:. Retrieved
4293:
4289:
4276:
4223:
4210:
4185:
4181:
4175:
4124:
4120:
4114:
4079:
4075:
4069:
4057:. Retrieved
4047:
4002:
3998:
3988:
3961:
3955:
3928:
3922:
3895:
3891:
3881:
3838:
3835:Phys. Rev. D
3834:
3828:
3804:(6): 24â26.
3801:
3797:
3787:
3767:
3760:
3719:
3715:
3709:
3650:
3646:
3640:
3597:
3593:
3587:
3544:
3540:
3530:
3487:
3483:
3476:
3435:
3431:
3425:
3382:
3378:
3372:
3360:. Retrieved
3356:
3347:
3296:
3292:
3233:
3229:
3223:
3211:. Retrieved
3204:the original
3165:
3161:
3148:
3136:. Retrieved
3122:
3097:
3093:
3087:
3075:. Retrieved
3055:
3045:
3033:. Retrieved
3023:
3011:. Retrieved
3007:the original
2997:
2985:. Retrieved
2975:
2963:. Retrieved
2956:the original
2942:
2930:. Retrieved
2900:
2896:
2883:
2850:
2846:
2840:
2797:
2793:
2787:
2746:
2742:
2736:
2685:
2681:
2675:
2667:
2639:
2635:
2629:
2618:. Retrieved
2611:the original
2582:
2578:
2565:
2537:
2530:
2518:. Retrieved
2504:
2486:
2479:
2467:. Retrieved
2453:
2441:. Retrieved
2431:
2419:. Retrieved
2412:the original
2399:
2379:
2372:
2360:. Retrieved
2346:
2327:
2317:
2292:
2288:
2282:
2249:
2245:
2239:
2227:. Retrieved
2222:
2218:
2202:
2190:. Retrieved
2180:
2145:
2141:
2131:
2111:
2104:
2077:
2071:
2036:
2032:
2022:
2010:. Retrieved
2004:Poole, Ian.
1999:
1987:. Retrieved
1960:
1939:
1932:
1923:
1895:
1888:
1879:
1844:
1840:
1830:
1811:
1751:
1743:
1661:x-ray optics
1634:
1623:
1600:
1581:
1552:
1510:nanoparticle
1506:
1497:
1485:Yrjö VÀisÀlÀ
1478:
1473:
1466:
1460:
1453:. Satellite
1441:
1412:
1408:
1404:
1396:
1392:
1381:
1374:
1354:
1338:
1320:
1316:
1291:
1265:
1245:
1226:
1207:
1176:
1152:
1144:
1116:spectroscopy
1105:
1101:
1083:
1079:
1064:
1057:
1042:
1035:
1016:
988:
965:
954:
947:
928:
920:
901:
891:line or the
886:
882:
878:
874:Lyot filters
867:
860:
807:
791:Applications
774:
761:TwymanâGreen
754:
749:
735:
729:
713:
709:optical flat
702:
699:
690:MachâZehnder
667:
647:
622:
620:
571:
569:
552:
550:
525:
498:
493:
451:
440:
432:
422:Case College
400:
381:
376:Thomas Young
373:
360:
348:
338:
328:
321:
314:
307:
297:
287:
283:
273:
263:
256:
246:
239:
237:
218:
197:
131:
130:
86:spectroscopy
78:oceanography
67:fiber optics
50:interference
48:
44:
43:
29:
4631:(1): 1â65.
4290:Am. J. Phys
3385:: 135â145.
3357:www.eso.org
3077:11 February
3056:Nature News
2295:(1): 4â11.
2112:Wave Optics
1653:synchrotron
1580:Figure 25.
1540:Figure 23.
1211:(RLGs) and
1011:CHARA array
741:focal plane
725:micrometers
694:Fabry PĂ©rot
509:Lucien LĂ©vy
494:heterodynes
402:Jules Jamin
229:path length
118:velocimetry
71:engineering
5999:Categories
5989:Technology
5081:28 October
3490:(2): L95.
3362:10 October
3100:(8): 703.
2620:2012-04-09
1955:pp. 99-108
1735:References
1689:Holography
1657:microfocus
1387:holography
1235:used by a
1096:wavelength
1007:Beta Lyrae
604:, and the
588:, and the
563:, and the
537:See also:
454:heterodyne
429:Categories
255:of mirror
144:incoherent
82:seismology
5953:Astronomy
5683:121322301
4493:CiteSeerX
4266:ignored (
4256:cite book
4092:CiteSeerX
3873:119273854
3848:0802.4098
3685:1463-9084
3660:1310.8343
3607:1109.5937
3497:0808.0932
3268:119261326
3243:1005.3976
3072:182916902
2875:189848134
2832:118346408
2807:1002.1284
2607:124333204
2274:121659705
2229:2 January
1673:Coherence
1303:coherence
1163:modulated
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