= Coherence length from a finite spectral band
{title2=$\ell_c\sim[1/\lambda_{\min}-1/\lambda_{\max}]^{-1}$}
For <vacuum> <wavelength> endpoints $\lambda_{\min}<\lambda_{\max}$, the corresponding <frequency> span is $\Delta\nu=c(1/\lambda_{\min}-1/\lambda_{\max})$. The reciprocal-bandwidth estimate of <optical coherence time> is $\tau_c\sim1/\Delta\nu$, giving $\ell_c\sim c/\Delta\nu$. This endpoint conversion is valid even for a broad band, whereas $\ell_c\sim\lambda_0^2/\Delta\lambda$ requires a relatively narrow <optical spectrum>.
For constant spectral density per unit <frequency> in the band, the normalized <first-order optical coherence> is $g^{(1)}(\tau)=e^{-i2\pi\nu_0\tau}\sin(\pi\Delta\nu\tau)/(\pi\Delta\nu\tau)$. Its first zero occurs at $\tau=1/\Delta\nu$. A different spectral shape or a different contrast criterion changes the numerical <optical coherence length>; endpoints alone do not define an exact universal value.
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