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Michelson interferometer
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==Configuration== [[File:Michelson interferometer with labels.svg|thumb|300x300px|Figure 2. Path of [[light]] in Michelson interferometer.]] A Michelson interferometer consists minimally of mirrors ''M<sub>1</sub>'' & ''M<sub>2</sub>'' and a [[beam splitter]] ''M'' (although a [[diffraction grating]] is also used<ref>{{Cite journal | doi=10.1364/OE.409185| title=Fully symmetric dispersionless stable transmission-grating Michelson interferometer| year=2020| last1=Kolesnichenko| first1=Pavel| last2=Wittenbecher| first2=Lukas| last3=Zigmantas| first3=Donatas| journal=Optics Express| volume=28| issue=25| pages=37752β37757| doi-access=free| pmid=33379604| bibcode=2020OExpr..2837752K}}</ref>). In Fig 2, a source ''S'' emits light that hits the beam splitter (in this case, a plate beamsplitter) surface ''M'' at point ''C''. ''M'' is partially reflective, so part of the light is transmitted through to point ''B'' while some is reflected in the direction of ''A''. Both beams recombine at point ''C' ''to produce an interference pattern incident on the detector at point ''E'' (or on the retina of a person's eye). If there is a slight angle between the two returning beams, for instance, then an imaging detector will record a sinusoidal ''fringe pattern'' as shown in Fig. 3b. If there is perfect spatial alignment between the returning beams, then there will not be any such pattern but rather a constant intensity over the beam dependent on the differential pathlength; this is difficult, requiring very precise control of the beam paths. Fig. 2 shows use of a coherent (laser) source. Narrowband spectral light from a [[Gas-discharge lamp|discharge]] or even white light can also be used, however to obtain significant interference contrast it is required that the differential pathlength is reduced below the [[coherence length]] of the light source. That can be only [[micrometre|micrometer]]s for white light, as discussed below. If a lossless beamsplitter is employed, then one can show that optical [[Conservation of energy|energy is conserved]]. At every point on the interference pattern, the power that is ''not'' directed to the detector at ''E'' is rather present in a beam (not shown) returning in the direction of the source. [[File:Michelson interferometer fringe formation.svg|thumb|left|300px|Figure 3. Formation of fringes in a Michelson interferometer]] [[File:The Fringe formed by the Michelson interferometer.jpg|thumb|This photo shows the fringe pattern formed by the Michelson interferometer, using monochromatic light (sodium D lines).]] As shown in Fig. 3a and 3b, the observer has a direct view of mirror ''M<sub>1</sub>'' seen through the beam splitter, and sees a reflected image ''M'<sub>2</sub>'' of mirror ''M<sub>2</sub>''. The fringes can be interpreted as the result of interference between light coming from the two virtual images ''S'<sub>1</sub>'' and ''S'<sub>2</sub>'' of the original source ''S''. 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. 3a, the optical elements are oriented so that ''S'<sub>1</sub>'' and ''S'<sub>2</sub>'' are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to ''M<sub>1</sub>'' and ''M'<sub>2</sub>'' (fringes of equal [[inclination]]). If, as in Fig. 3b, ''M<sub>1</sub>'' and ''M'<sub>2</sub>'' are tilted with respect to each other, the interference fringes will generally take the shape of [[conic sections]] (hyperbolas), but if ''M<sub>1</sub>'' and ''M'<sub>2</sub>'' overlap, the fringes near the axis will be straight, parallel, and equally spaced (fringes of equal thickness). If S is an extended source rather than a point source as illustrated, the fringes of Fig. 3a must be observed with a telescope set at infinity, while the fringes of Fig. 3b will be localized on the mirrors.<ref name=Hariharan2007>{{cite book|last=Hariharan|first=P.|title=Basics of Interferometry, Second Edition|date=2007|publisher=Elsevier|isbn=978-0-12-373589-8}}</ref>{{rp|17}}
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