For a given set of incidence angle α and diffraction angle β, the grating equation is satisfied for a different wavelength λ for each integral diffraction order m. Thus, light of several wavelengths (each in a different order) will be diffracted along the same direction: light of wavelength λ in order m is diffracted along the same direction as light of wavelength λ/2 in order 2m, etc.
The range of wavelengths in a given spectral order for which superposition of light from adjacent orders does not occur is called the free spectral range Fλ. It can be calculated directly from its definition: in order m, the wavelength of light that diffracts along the direction of λ in order m+1 is λ + Δλ, where
λ + Δλ = (m+1)/m λ (2-28)
from which
Fλ = Δλ = λ/m (2-29)
The concept of free spectral range applies to all gratings capable of operation in more than one diffraction order, but it is particularly important in the case of echelles, because they operate in high orders with correspondingly short free spectral ranges.
Free spectral range and order sorting are intimately related, since grating systems with greater free spectral ranges may have less need for filters (or cross-dispersers) that absorb or diffract light from overlapping spectral orders. This is one reason why first-order applications are widely popular.
For footnotes and additional insights into diffraction grating topics like this one, download our free MKS Diffraction Gratings Handbook (8th Edition)
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