Delay-range resolution in Fourier transform spectroscopy ($\delta \lambda \propto {\lambda }^2/L$)

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.