Editing Diffraction (section)

== Coherence ==
{{main|Coherence (physics)}}

The description of diffraction relies on the interference of waves emanating from the same source taking different paths to the same point on a screen. In this description, the difference in phase between waves that took different paths is only dependent on the effective path length. This does not take into account the fact that waves that arrive at the screen at the same time were emitted by the source at different times. The initial phase with which the source emits waves can change over time in an unpredictable way. This means that waves emitted by the source at times that are too far apart can no longer form a constant interference pattern since the relation between their phases is no longer time independent.<ref name=Halliday>{{citation|last1=Halliday|first1=David|last2=Resnick|first2=Robert|last3=Walker|first3=Jerl|title=Fundamental of Physics | publisher=John Wiley and Sons, Inc. | location=USA|edition=7th | isbn=978-0-471-23231-5|year=2005|url-access=registration|url=https://archive.org/details/isbn_0471216437}}</ref>{{rp|p=919}}

The length over which the phase in a beam of light is correlated is called the [[coherence length]]. In order for interference to occur, the path length difference must be smaller than the coherence length. This is sometimes referred to as spectral coherence, as it is related to the presence of different frequency components in the wave. In the case of light emitted by an [[Energy level|atomic transition]], the coherence length is related to the lifetime of the excited state from which the atom made its transition.<ref name="Fowles1975">{{cite book|author=Grant R. Fowles | title=Introduction to Modern Optics | year=1975|publisher=Courier Corporation|isbn=978-0-486-65957-2}}</ref>{{rp|pp=71–74}}<ref name="Hecht2002">{{cite book | last = Hecht | first = Eugene | title = Optics | year=2002 | location=United States of America | publisher=Addison Wesley | edition= 4th| isbn=978-0-8053-8566-3 | language=en}}</ref>{{rp|pp=314–316}}

If waves are emitted from an extended source, this can lead to incoherence in the transversal direction. When looking at a cross section of a beam of light, the length over which the phase is correlated is called the transverse coherence length. In the case of Young's double-slit experiment, this would mean that if the transverse coherence length is smaller than the spacing between the two slits, the resulting pattern on a screen would look like two single-slit diffraction patterns.<ref name="Fowles1975"/>{{rp|pp=74–79}}

In the case of particles like electrons, neutrons, and atoms, the coherence length is related to the spatial extent of the wave function that describes the particle.<ref name="IchimiyaCohen2004">{{cite book | author1=Ayahiko Ichimiya|author2=Philip I. Cohen|title=Reflection High-Energy Electron Diffraction |url=https://books.google.com/books?id=AUVbPerNxTcC | date=13 December 2004| publisher=Cambridge University Press|isbn=978-0-521-45373-8|url-status=live |archive-url=https://web.archive.org/web/20170716041343/https://books.google.com/books?id=AUVbPerNxTcC | archive-date=16 July 2017}}</ref>{{rp|p=107}}