Editing Coherence (physics) (section)

=== Examples ===
<gallery caption="Spatial coherence" perrow="5">
File:spatial coherence infinite ex1.png|<small>Figure 5: A plane wave with an infinite [[coherence length]].</small>
File:spatial coherence infinite ex2.png|<small>Figure 6: A wave with a varying profile (wavefront) and infinite coherence length.</small>
File:spatial coherence finite.png|<small>Figure 7: A wave with a varying profile (wavefront) and finite coherence length.</small>
File:spatial coherence pinhole.png|<small>Figure 8: A wave with finite coherence area is incident on a pinhole (small aperture). The wave will [[diffraction|diffract]] out of the pinhole. Far from the pinhole the emerging spherical wavefronts are approximately flat. The coherence area is now infinite while the coherence length is unchanged.</small>
File:spatial coherence detector.png|<small>Figure 9: A wave with infinite coherence area is combined with a spatially shifted copy of itself. Some sections in the wave interfere constructively and some will interfere destructively. Averaging over these sections, a detector with length D will measure reduced [[interference visibility]]. For example, a misaligned [[Mach–Zehnder interferometer]] will do this.</small>
</gallery>

Consider a tungsten light-bulb filament. Different points in the filament emit light independently and have no fixed phase-relationship. In detail, at any point in time the profile of the emitted light is going to be distorted. The profile will change randomly over the coherence time <math>\tau_c</math>. Since for a white-light source such as a light-bulb <math>\tau_c</math> is small, the filament is considered a spatially incoherent source. In contrast, a radio [[Phased array|antenna array]], has large spatial coherence because antennas at opposite ends of the array emit with a fixed phase-relationship. Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow.

Holography requires temporally and spatially coherent light. Its inventor, [[Dennis Gabor]], produced successful holograms more than ten years before lasers were invented. To produce coherent light he passed the monochromatic light from an emission line of a [[mercury-vapor lamp]] through a pinhole spatial filter.

In February 2011 it was reported that [[helium]] atoms, cooled to near [[absolute zero]] / [[Bose–Einstein condensate]] state, can be made to flow and behave as a coherent beam as occurs in a laser.<ref>{{cite journal
 |last1=Hodgman |first1=S. S.
 |last2=Dall |first2=R. G.
 |last3=Manning |first3=A. G.
 |last4=Baldwin |first4=K. G. H.
 |last5=Truscott |first5=A. G.
 |year=2011
 |title=Direct Measurement of Long-Range Third-Order Coherence in Bose-Einstein Condensates
 |journal=[[Science (journal)|Science]]
 |volume=331 |issue=6020 |pages=1046–1049
 |bibcode=2011Sci...331.1046H
 |doi=10.1126/science.1198481
 |pmid=21350171
|s2cid=5336898
 }}</ref><ref>{{cite web
 |last=Pincock |first=S.
 |date=25 February 2011
 |title=Cool laser makes atoms march in time
 |url=http://www.abc.net.au/science/articles/2011/02/25/3149175.htm
 |work=[[ABC Science]]
 |publisher=[[ABC News Online]]
 |access-date=2011-03-02
}}</ref>