Answer to Question #182708 in Optics for Khushi

Question

Explain the meaning of coherence length.

Answer 1

Coherence length is a measure of temporal coherence, expressed as the propagation distance over which the coherence significantly decays.

The coherence length can be used for quantifying the degree of temporal (not spatial!) coherence as the propagation length (and thus propagation time) over which coherence degrades significantly. It is defined as the coherence time times the vacuum velocity of light.

For light with a Lorentzian optical spectrum resulting from a random walk of the optical phase, the coherence length can be calculated as

$L_{coh} = cτ_{coh} = \frac{c}{πΔν}$

where Δν is the (full width at half-maximum) linewidth (optical bandwidth). This coherence length is the propagation length after which the magnitude of the coherence function has dropped to the value of 1/e.

The reason for often using the term coherence length instead of coherence time is that the optical time delays involved in some experiments are often determined by optical path lengths.