= Optical coherence length
{title2=$L_c=c\tau_c$}
= Coherence length
{synonym}
In this temporal sense, the <optical coherence length> is $L_c=c\tau_c$, where $c$ is the <vacuum> <speed of light> and $\tau_c$ is an explicitly chosen <optical coherence time>. It measures a delay as a vacuum-equivalent path difference; it does not measure transverse <spatial optical coherence>. https://www.rp-photonics.com/coherence_length.html[Rüdiger Paschotta, RP Photonics Encyclopedia, Coherence Length: temporal definition and path difference]{ref}.
For the stipulated $1\,\mathrm{GHz}$ profiles, the $1/e$ convention gives $L_c\approx9.54269\,\mathrm{cm}$ for the Lorentzian and $15.8896\,\mathrm{cm}$ for the Gaussian. In a <vacuum> <Michelson interferometer>, changing one mirror position by $x$ changes the round-trip delay by $2x/c$, so the mirror travel to either of these delays is $L_c/2$. In a medium, convert physical travel using the actual group delay, which can depend on <frequency>. For a narrow line centered at <vacuum> <wavelength> $\lambda_0$, differentiating $\nu=c/\lambda$ gives $\Delta\nu\approx c\Delta\lambda/\lambda_0^2$; this small-width approximation must use consistently defined spectral widths.
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