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Wave interference
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==== Light source requirements ==== The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap. Conventional light sources emit waves of differing frequencies and at different times from different points in the source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as [[Sodium-vapor lamp|sodium-]] or [[mercury-vapor lamp]]s have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes.<ref>{{cite book |first=W. H. |last=Steel |title=Interferometry |year=1986 |publisher=Cambridge University Press |location=Cambridge |isbn=0-521-31162-4 }}</ref> All interferometry prior to the invention of the laser was done using such sources and had a wide range of successful applications. A [[laser beam]] generally approximates much more closely to a monochromatic source, and thus it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give spurious interference fringes which can result in errors. Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements.<ref>{{cite journal | last1 = Pfleegor | first1 = R. L. | last2 = Mandel | first2 = L. | year = 1967 | title = Interference of independent photon beams | doi = 10.1103/physrev.159.1084 | journal = Phys. Rev. | volume = 159 | issue = 5| pages = 1084–1088 | bibcode = 1967PhRv..159.1084P }}</ref> This has also been observed for widefield interference between two incoherent laser sources.<ref>{{cite journal|last=Patel|first=R.|author2=Achamfuo-Yeboah, S. |author3=Light R.|author4=Clark M.|title= Widefield two laser interferometry|journal=Optics Express|date=2014|volume=22|issue=22|pages=27094–27101|url=https://www.osapublishing.org/oe/abstract.cfm?uri=oe-22-22-27094|bibcode=2014OExpr..2227094P|doi=10.1364/OE.22.027094|pmid=25401860|doi-access=free}}</ref> It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.<ref name="Born and Wolf">{{cite book |first1=Max |last1=Born |author-link=Max Born |first2=Emil |last2=Wolf |year=1999 |title=[[Principles of Optics]] |publisher=Cambridge University Press |location=Cambridge |isbn=0-521-64222-1 }}</ref>
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