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.
Read more about this topic: Coherence Length
Famous quotes containing the word formulas:
“That’s the great danger of sectarian opinions, they always accept the formulas of past events as useful for the measurement of future events and they never are, if you have high standards of accuracy.”
—John Dos Passos (1896–1970)
“It is sentimentalism to assume that the teaching of life can always be fitted to the child’s interests, just as it is empty formalism to force the child to parrot the formulas of adult society. Interests can be created and stimulated.”
—Jerome S. Bruner (20th century)
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (1877–1962)