Editing Interferometry (section)

===Physics and astronomy===
[[File:Emmaalexander inter dishes.png|thumb|right|Interferometry is used in radio astronomy, with timing offsets of D sin θ]]
In physics, one of the most important experiments of the late 19th century was the famous "failed experiment" of [[Michelson–Morley experiment|Michelson and Morley]] which provided evidence for [[special relativity]]. Recent repetitions of the Michelson–Morley experiment perform heterodyne measurements of beat frequencies of crossed cryogenic [[optical resonator]]s. Fig&nbsp;7 illustrates a resonator experiment performed by Müller et al. in 2003.<ref name=Muller2003>{{cite journal|author1=Müller, H. |author2=Herrmann, S. |author3=Braxmaier, C. |author4=Schiller, S. |author5=Peters, A. |title=Modern Michelson–Morley experiment using cryogenic optical resonators|journal=Phys. Rev. Lett. |volume=91 |issue=2 |pages=020401 |date=2003 |doi=10.1103/PhysRevLett.91.020401 |arxiv=physics/0305117 |bibcode = 2003PhRvL..91b0401M|pmid=12906465|s2cid=15770750 }}</ref> 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<sup>−17</sup> level.<ref>{{Cite journal | last1 = Eisele | first1 = C. | last2 = Nevsky | first2 = A. | last3 = Schiller | first3 = S. | title = Laboratory Test of the Isotropy of Light Propagation at the 10-17 Level | doi = 10.1103/PhysRevLett.103.090401 | journal = Physical Review Letters | volume = 103 | issue = 9 | pages = 090401 | year = 2009 | pmid =  19792767|bibcode = 2009PhRvL.103i0401E | s2cid = 33875626 }}</ref><ref>{{Cite journal | last1 = Herrmann | first1 = S. | last2 = Senger | first2 = A. | last3 = Möhle | first3 = K. | last4 = Nagel | first4 = M. | last5 = Kovalchuk | first5 = E. | last6 = Peters | first6 = A. | doi = 10.1103/PhysRevD.80.105011 | title = Rotating optical cavity experiment testing Lorentz invariance at the 10-17 level | journal = Physical Review D | volume = 80 | issue = 10 | pages = 105011 | year = 2009|arxiv = 1002.1284 |bibcode = 2009PhRvD..80j5011H | s2cid = 118346408 }}</ref>

{| cellspacing="0" border="0" style="margin:1em auto;"
|-
|[[File:MMX with optical resonators.svg|border|250px]]<br/><span style="font-size:87%; line-height: 1.3em;">Figure 7. Michelson–Morley experiment with <br/>cryogenic optical resonators</span>
|[[File:Fourier transform spectrometer.png|border|270px]]<br/><span style="font-size:87%; line-height: 1.3em;">Figure 8. Fourier transform spectroscopy</span>
|<br/><span style="font-size:87%; line-height: 1.3em;">Figure 9. A picture of the solar corona taken <br/>with the LASCO C1 coronagraph</span>
|}

Michelson interferometers are used in tunable narrow band optical filters<ref name=Scherrer1995>{{cite journal|last=Scherrer|first=P.H. |author2=Bogart, R.S. |author3=Bush, R.I. |author4=Hoeksema, J. |author5=Kosovichev, A.G. |author6=Schou, J. |title=The Solar Oscillations Investigation – Michelson Doppler Imager |journal=Solar Physics|date=1995|volume=162 |issue=1–2 |pages=129–188 |bibcode = 1995SoPh..162..129S |doi = 10.1007/BF00733429 |s2cid=189848134 }}</ref> and as the core hardware component of [[Fourier transform spectroscopy|Fourier transform spectrometers]].<ref name=Stroke1965>{{cite journal|last=Stroke|first=G.W.|author2=Funkhouser, A.T.|title=Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers|journal=Physics Letters|date=1965|volume=16|issue=3|pages=272–274|doi=10.1016/0031-9163(65)90846-2|url=http://deepblue.lib.umich.edu/bitstream/2027.42/32013/1/0000055.pdf|access-date=2 April 2012|bibcode = 1965PhL....16..272S |hdl=2027.42/32013|hdl-access=free}}</ref>

When used as a tunable narrow band filter, Michelson interferometers exhibit a number of advantages and disadvantages when compared with competing technologies such as [[Fabry–Pérot interferometer]]s or [[Lyot filter]]s. 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 Fabry–Pérot 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.<ref name=Gary2004>{{cite web|author=Gary, G.A.|author2=Balasubramaniam, K.S.|title=Additional Notes Concerning the Selection of a Multiple-Etalon System for ATST|url=http://atst.nso.edu/files/docs/TN-0027.pdf|publisher=Advanced Technology Solar Telescope|access-date=29 April 2012|url-status=dead|archive-url=https://web.archive.org/web/20100810222938/http://atst.nso.edu/files/docs/TN-0027.pdf|archive-date=10 August 2010}}</ref>

Fig.&nbsp;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, 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.<ref name=OPIFourier>{{cite web|title=Spectrometry by Fourier transform|url=http://www.optique-ingenieur.org/en/courses/OPI_ang_M02_C05/co/Contenu_32.html|publisher=OPI – Optique pour l'Ingénieur|access-date=3 April 2012}}</ref>

Fig.&nbsp;9 shows a doppler image of the solar corona made using a tunable Fabry-Pérot 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 coronal plasma velocity towards or away from the satellite camera.

Fabry–Pérot thin-film etalons are used in narrow bandpass filters capable of selecting a single spectral line for imaging; for example, the [[H-alpha]] line or the [[Calcium#H and K lines|Ca-K]] line of the Sun or stars. Fig.&nbsp;10 shows an [[Extreme ultraviolet Imaging Telescope]] (EIT) image of the Sun at 195&nbsp;Ångströms (19.5 nm), corresponding to a spectral line of multiply-ionized iron atoms.<ref name=SOHO_EIT2003>{{cite web|title=Halloween 2003 Solar Storms: SOHO/EIT Ultraviolet, 195 Ã|date=2 April 2008|url=http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003500/|publisher=NASA/Goddard Space Flight Center Scientific Visualization Studio|access-date=20 June 2012|archive-date=23 April 2014|archive-url=https://web.archive.org/web/20140423134932/http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003500/|url-status=dead}}</ref> 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&nbsp;nm each. The layer thicknesses were tightly controlled so that at the desired wavelength, reflected photons from each layer interfered constructively.

The [[LIGO|Laser Interferometer Gravitational-Wave Observatory]] (LIGO) uses two 4-km [[Fabry–Pérot interferometer|Michelson–Fabry–Pérot interferometers]] for the detection of [[gravitational wave]]s.<ref name=LIGO>{{cite web|title=LIGO-Laser Interferometer Gravitational-Wave Observatory |url=http://www.ligo.caltech.edu/ |publisher=Caltech/MIT |access-date=4 April 2012}}</ref> In this application, the Fabry–Pérot 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 [[first observation of gravitational waves]] occurred on September 14, 2015.<ref name="Nature_11Feb16">{{cite journal |title=Einstein's gravitational waves found at last |journal=Nature News |url=http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |date=11 February 2016 |last1=Castelvecchi |first1=Davide |last2=Witze |first2=Alexandra |doi=10.1038/nature.2016.19361 |s2cid=182916902 |access-date=11 February 2016|url-access=subscription }}</ref>

The Mach–Zehnder interferometer's relatively large and freely accessible working space, and its flexibility in locating the fringes has made it the interferometer of choice for [[Flow visualization|visualizing flow]] in wind tunnels,<ref name=Chevalerias1957>{{Cite journal | last1 = Chevalerias | first1 = R. | last2 = Latron | first2 = Y. | last3 = Veret | first3 = C. | doi = 10.1364/JOSA.47.000703 | title = Methods of Interferometry Applied to the Visualization of Flows in Wind Tunnels | journal = Journal of the Optical Society of America | volume = 47 | issue = 8 | pages = 703 | year = 1957| bibcode = 1957JOSA...47..703C }}</ref><ref name=Ristic>{{cite web|last=Ristić|first=Slavica|title=Flow visualization techniques in wind tunnels – optical methods (Part II) |url=http://www.vti.mod.gov.rs/ntp/rad2007/2-07/rist/rist.pdf |publisher=Military Technical Institute, Serbia |access-date=6 April 2012}}</ref> 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.<ref name=HariharanBasics2007/>{{rp|18,93–95}}

Mach–Zehnder interferometers are also used to study one of the most counterintuitive predictions of quantum mechanics, the phenomenon known as [[quantum entanglement]].<ref name=Paris1999>{{cite journal |last=Paris |first=M.G.A. |title=Entanglement and visibility at the output of a Mach–Zehnder interferometer |journal=Physical Review A |date=1999 |volume=59 |issue=2 |pages=1615–1621 |url=http://qinf.fisica.unimi.it/~paris/PDF/visent.pdf |access-date=2 April 2012 |arxiv=quant-ph/9811078 |bibcode=1999PhRvA..59.1615P |doi=10.1103/PhysRevA.59.1615 |s2cid=13963928 |archive-date=10 September 2016 |archive-url=https://web.archive.org/web/20160910074215/http://qinf.fisica.unimi.it/~paris/PDF/visent.pdf |url-status=dead }}</ref><ref name=Haack2010>{{Cite journal | last1 = Haack | first1 = G. R. | last2 = Förster | first2 = H. | last3 = Büttiker | first3 = M. | title = Parity detection and entanglement with a Mach–Zehnder interferometer | doi = 10.1103/PhysRevB.82.155303 | journal = Physical Review B | volume = 82 | issue = 15 | pages = 155303 | year = 2010|arxiv = 1005.3976 |bibcode = 2010PhRvB..82o5303H | s2cid = 119261326 }}</ref>

[[Image:USA.NM.VeryLargeArray.02.jpg|thumb |300px |right |Figure 11. The [[Very Large Array|VLA]] interferometer]]

An astronomical interferometer achieves high-resolution observations using the technique of [[aperture synthesis]], mixing signals from a cluster of comparatively small telescopes rather than a single very expensive monolithic telescope.<ref name=astro/>

Early [[radio telescope]] interferometers used a single baseline for measurement. Later astronomical interferometers, such as the [[Very Large Array]] illustrated in Fig&nbsp;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 information in multiple orientations by taking repeated measurements, a technique called ''Earth-rotation synthesis''. Baselines thousands of kilometers long were achieved using [[very long baseline interferometry]].<ref name=astro>{{cite journal|url=http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf|doi=10.1088/0034-4885/66/5/203|title=Optical interferometry in astronomy|date=2003|last1=Monnier|first1=John D|journal=Reports on Progress in Physics|volume=66|pages=789–857|arxiv = astro-ph/0307036 |bibcode = 2003RPPh...66..789M|issue=5 |hdl=2027.42/48845|s2cid=887574}}</ref>

[[File:Cosmic Calibration.jpg|left|thumb|[[Atacama Large Millimeter Array|ALMA]] is an astronomical interferometer located in [[Llano de Chajnantor Observatory|Chajnantor Plateau]]<ref>{{cite web|title=Cosmic Calibration|url=https://www.eso.org/public/images/potw1641a/|website=www.eso.org|access-date=10 October 2016}}</ref>]]

[[Astronomical optical interferometry]] 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&nbsp;μm stability in a 100&nbsp;m baseline. Optical interferometric measurements require high sensitivity, low noise detectors that did not become available until the late 1990s. [[Astronomical seeing|Astronomical "seeing"]], 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.<ref name=Malbet1999>{{cite journal|last=Malbet|first=F.|author2=Kern, P. |author3=Schanen-Duport, I. |author4=Berger, J.-P. |author5=Rousselet-Perraut, K. |author6= Benech, P. |title=Integrated optics for astronomical interferometry|journal=Astron. Astrophys. Suppl. Ser. |date=1999 |volume=138 |pages=135–145 |bibcode = 1999A&AS..138..135M |doi = 10.1051/aas:1999496 | arxiv=astro-ph/9907031|s2cid=15342344}}</ref><ref name=Baldwin2002>{{cite journal |last=Baldwin |first=J.E. |author2=Haniff, C.A. |title=The application of interferometry to optical astronomical imaging |journal=Phil. Trans. R. Soc. Lond. A |date=2002 |volume=360 |pages=969–986 |doi=10.1098/rsta.2001.0977 |pmid=12804289 |issue=1794|bibcode = 2002RSPTA.360..969B |s2cid=21317560 }}</ref> Despite these technical difficulties, [[List of astronomical interferometers at visible and infrared wavelengths|three major facilities]] are now in operation offering resolutions down to the fractional milliarcsecond range.

The [[Wave–particle duality|wave character of matter]] can be exploited to build interferometers. The first examples of matter interferometers were [[electron interferometer]]s, later followed by [[neutron interferometer]]s. Around 1990 the first [[atom interferometer]]s were demonstrated, later followed by interferometers employing molecules.<ref>{{Cite journal | last1 = Gerlich | first1 = S. | last2 = Eibenberger | first2 = S. | last3 = Tomandl | first3 = M. | last4 = Nimmrichter | first4 = S. | last5 = Hornberger | first5 = K. | last6 = Fagan | first6 = P. J. | last7 = Tüxen | first7 = J. | last8 = Mayor | first8 = M. | last9 = Arndt | first9 = M. | title = Quantum interference of large organic molecules | doi = 10.1038/ncomms1263 | journal = Nature Communications | volume = 2 | pages = 263– | year = 2011 | pmid =  21468015| pmc =3104521 |bibcode = 2011NatCo...2..263G }}</ref><ref>{{Cite journal|last1=Hornberger|first1=Klaus|last2=Gerlich|first2=Stefan|last3=Haslinger|first3=Philipp|last4=Nimmrichter|first4=Stefan|last5=Arndt|first5=Markus|date=2012-02-08|title=\textit{Colloquium} : Quantum interference of clusters and molecules|journal=Reviews of Modern Physics|volume=84|issue=1|pages=157–173|doi=10.1103/RevModPhys.84.157|bibcode=2012RvMP...84..157H|arxiv=1109.5937|s2cid=55687641}}</ref><ref>{{Cite journal|last1=Eibenberger|first1=Sandra|last2=Gerlich|first2=Stefan|last3=Arndt|first3=Markus|last4=Mayor|first4=Marcel|last5=Tüxen|first5=Jens|date=2013-08-14|title=Matter–wave interference of particles selected from a molecular library with masses exceeding 10000 amu|journal=Physical Chemistry Chemical Physics|volume=15|issue=35|doi=10.1039/C3CP51500A|issn=1463-9084|bibcode=2013PCCP...1514696E|pages=14696–700|pmid=23900710|arxiv=1310.8343|s2cid=3944699}}</ref>

[[Electron holography]] 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.<ref>{{cite journal |last1=Lehmann |first1=M| last2= Lichte| first2= H |title=Tutorial on off-axis electron holography |journal=Microsc. Microanal. |volume=8 |issue=6 |pages=447–66 |date=December 2002 |pmid=12533207 |doi=10.1017/S1431927602029938 |bibcode=2002MiMic...8..447L|s2cid=37980394}}</ref> This technique was developed to enable greater resolution in electron microscopy than is possible using conventional imaging techniques. The resolution of conventional electron microscopy is not limited by electron wavelength, but by the large aberrations of electron lenses.<ref name=Tonomura1999>{{cite book|last=Tonomura|first=A.|title=Electron Holography|edition=2nd|date=1999|publisher=Springer|isbn=978-3-540-64555-9 |url=https://books.google.com/books?id=ghn_GeKbRo0C}}</ref>

Neutron interferometry has been used to investigate the [[Aharonov–Bohm effect]], to examine the effects of gravity acting on an elementary particle, and to demonstrate a strange behavior of [[fermions]] that is at the basis of the [[Pauli exclusion principle]]: 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.<ref name=Klein2009>{{Cite journal | last1 = Klein | first1 = T. | title = Neutron interferometry: A tale of three continents | doi = 10.1051/epn/2009802 | journal = Europhysics News | volume = 40 | issue = 6 | pages = 24–26| year = 2009|bibcode =  2009ENews..40f..24K| doi-access = free }}</ref>

Atom interferometry techniques are reaching sufficient precision to allow laboratory-scale tests of [[general relativity]].<ref name=Dimopoulos2008>{{cite journal|title= General Relativistic Effects in Atom Interferometry|last=Dimopoulos|first=S.|author2=Graham, P.W. |author3=Hogan, J.M. |author4= Kasevich, M.A. |journal=Phys. Rev. D |date=2008|volume=78|issue=42003 |pages=042003|doi=10.1103/PhysRevD.78.042003 |bibcode = 2008PhRvD..78d2003D |arxiv = 0802.4098 |s2cid=119273854}}</ref>

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 column concentration of trace gases such as ozone and carbon monoxide above the instrument.<ref>{{cite journal|last=Mariani|first=Z.|author2=Strong, K.|author3= Wolff, M.|display-authors= etal|date=2012|title=Infrared measurements in the Arctic using two Atmospheric Emitted Radiance Interferometers|journal=Atmos. Meas. Tech.|volume=5|issue=2|pages=329–344|doi=10.5194/amt-5-329-2012|bibcode = 2012AMT.....5..329M |doi-access=free}}</ref>