Coherence Length - Formulas

Formulas

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

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

In optical communications, the coherence length is given by

where is the central wavelength of the source, is the refractive index of the medium, and is the spectral width of the source. If the source has a Gaussian spectrum with FWHM spectral width, then a path offset of ± will reduce the fringe visibility to 50%.

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:

The coherence length can be measured using a Michelson interferometer and is the optical path length difference of a self-interfering laser beam which corresponds to a fringe visibility, where the fringe visibility is defined as

where is the fringe intensity.

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

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