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