Free spectral range

The free spectral range(FSR) of a diffraction grating is the largest wavelength range for a given order that does not overlap the same range in an adjacent order. If the n^th order of $$lambda and (n+1)^th order of $$(lambda + Delta lambda) lie at the same angle, then:$$Delta lambda=lambda/(n+1)

In a Fabry-Pérot interferometer or etalon the wavelength separation between adjacent transmission peaks is called the FSR of the etalon, Δλ, and is given by:

:$$Deltalambda = frac{ lambda_0^2}{2nl cos heta + lambda_0 } approx frac{ lambda_0^2}{2nl cos heta }

where λ₀ is the central wavelength of the nearest transmission peak. The FSR is related to the full-width half-maximum, δλ, of any one transmission band by a quantity known as the "finesse":

:$$mathcal{F} = frac{Deltalambda}{deltalambda}=frac{pi}{2 arcsin(1/sqrt F)}.

This is commonly approximated (for "R" > 0.5) by

:$$mathcal{F} approx frac{pi sqrt{F{2}=frac{pi R^{1/2} }{(1-R)}

See also

Diffraction grating

Fabry-Pérot interferometer