Editing Michelson interferometer (section)

==Source bandwidth==
[[File:Michelson interferometer using white light.png|thumb|400px|Figure 4. Michelson interferometers using a white light source]]
White light has a tiny [[coherence length]] and is difficult to use in a Michelson (or [[Mach–Zehnder]]) interferometer. Even a narrowband (or "quasi-monochromatic") spectral source requires careful attention to issues of [[chromatic dispersion]] when used to illuminate an interferometer. The two optical paths must be practically equal for all wavelengths present in the source. This requirement can be met if both light paths cross an equal thickness of glass of the same [[Dispersion (optics)|dispersion]]. In Fig.&nbsp;4a, the horizontal beam crosses the beam splitter three times, while the vertical beam crosses the beam splitter once. To equalize the dispersion, a so-called compensating plate identical to the substrate of the beam splitter may be inserted into the path of the vertical beam.<ref name=Hariharan2007/>{{rp|16}} In Fig.&nbsp;4b, we see using a cube beam splitter already equalizes the pathlengths in glass. The requirement for dispersion equalization is eliminated by using extremely narrowband light from a laser.

The extent of the fringes depends on the [[coherence length]] of the source. In Fig.&nbsp;3b, the yellow [[sodium light]] used for the fringe illustration consists of a pair of closely spaced lines, [[Fraunhofer lines|D<sub>1</sub> and D<sub>2</sub>]], implying that the interference pattern will blur after several hundred fringes. Single longitudinal mode [[laser]]s are highly coherent and can produce high contrast interference with differential pathlengths of millions or even billions of wavelengths. On the other hand, using white (broadband) light, the central fringe is sharp, but away from the central fringe the fringes are colored and rapidly become indistinct to the eye.

Early experimentalists attempting to detect the Earth's velocity relative to the supposed [[luminiferous aether]], such as Michelson and Morley (1887)<ref name=Michelson1887/> and Miller (1933),<ref>{{cite journal | url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.5.203 | doi=10.1103/RevModPhys.5.203 | title=The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth | date=1933 | last1=Miller | first1=Dayton C. | journal=Reviews of Modern Physics | volume=5 | issue=3 | pages=203–242 | bibcode=1933RvMP....5..203M | url-access=subscription }}</ref> used quasi-monochromatic light only for initial alignment and coarse path equalization of the interferometer. Thereafter they switched to white (broadband) light, since using [[white light interferometry]] they could measure the point of ''absolute phase'' equalization (rather than phase modulo 2π), thus setting the two arms' pathlengths equal.<ref name=Michelson1881>{{cite journal |last=Michelson |first=A.A. |title=The Relative Motion of the Earth and the Luminiferous Ether|journal=American Journal of Science |date=1881 |volume=22 |issue=128 |pages=120–129 |url=http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether |doi=10.2475/ajs.s3-22.128.120 |bibcode=1881AmJS...22..120M|s2cid=130423116 }}</ref><ref group=note>Michelson (1881) wrote, "... when they [the fringes using sodium light] were of convenient width and of maximum sharpness, the sodium flame was removed and the lamp again substituted. The screw ''m'' was then slowly turned till the bands reappeared. They were then of course colored, except the central band, which was nearly black."</ref><ref>{{cite journal|author=Shankland, R.S.|title=Michelson–Morley experiment|journal=American Journal of Physics|date=1964|volume=31|issue=1|pages=16–35|doi=10.1119/1.1970063|bibcode = 1964AmJPh..32...16S }}</ref><ref group=note>Shankland (1964) wrote concerning the 1881 experiment, p. 20: "''The interference fringes were found by first using a sodium light source and after adjustment for maximum visibility, the source was changed to white light and the colored fringes then located. White-light fringes were employed to facilitate observation of shifts in position of the interference pattern.''" And concerning the 1887 experiment, p. 31: "''With this new interferometer, the magnitude of the expected shift of the white-light interference pattern was 0.4 of a fringe as the instrument was rotated through an angle of 90° in the horizontal plane. (The corresponding shift in the Potsdam interferometer had been 0.04 fringe.)''"</ref> More importantly, in a white light interferometer, any subsequent "fringe jump" (differential pathlength shift of one wavelength) would always be detected.