= Delay-range resolution in Fourier transform spectroscopy
{title2=$\delta\lambda\propto\lambda^2/L$}
A <Michelson interferometer> mirror displacement $x$ changes round-trip <optical path difference> by $2x$, giving delay $\tau=2x/c$. An interferogram recorded over a finite delay range is multiplied by a window; the recovered spectrum is the true spectrum convolved with that window's <Fourier transform>. Its characteristic <frequency> resolution scales inversely with delay range. Consequently a mirror travel range $L$ gives $\delta\nu\propto c/L$ and $\delta\lambda\simeq(\lambda^2/c)\delta\nu\propto\lambda^2/L$. Numerical width factors depend on the scan definition, window and resolution criterion; the inverse-travel scaling does not.
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