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Coherence length

In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence. The significance is that interference will be strong within a coherence length of the source, but not beyond it. This concept is also commonly used in telecommunication engineering.

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In long-distance transmission systems, the coherence length may be reduced by propagation factors such as dispersion, scattering, and diffraction.

In radio-band systems, the coherence length is approximated by

$L={c \over \Delta f}$ ,

where $c$ is the speed of light in a vacuum, $n$ is the refractive index of the medium, and $Δ f$ is the bandwidth of the source.

In optical communications, the coherence length $L$ is given approximately by

$L={\lambda^2 \over n \Delta\lambda}$ ,

where $λ$ is the central wavelength of the source, $n$ is the refractive index of the medium, and $Δλ$ is the spectral width of the source.

Coherence length is usually applied to the optical regime.

The expression above is a frequently used approximation. Due to ambiguities in the definition of spectral width of a source, however, the following definition of coherence length has been suggested^{[citation needed]}:

The coherence length is the optical path length difference of a self-interfering laserbeam which corresponds to a 50% fringe visibility, where the fringe visibility is defined as

$V = {I_{max} - I_{min} \over I_{max} + I_{min}}$ ,

where $I$ is the fringe intensity.

Helium-neon lasers have a typical coherence length of 20 cm, while semiconductor lasers reach some 100 m. Fiber lasers can have coherence lengths exceeding 100 km.