Free spectral range of an echelle grating
= Free spectral range of an echelle grating
At fixed incident and central outgoing angles, the <grating equation> gives $m\lambda_m=K=d(\sin\alpha+\sin\beta_0)$. Adjacent central wavelengths are separated by
$$
\lambda_m-\lambda_{m+1}=\frac K{m(m+1)}\sim\frac{\lambda_m}m.
$$
This is the usual adjacent-order <free spectral range>. A detector width of approximately $q\Delta\lambda_{\rm FSR}$, where $q$ is the <grating dispersion>, covers one such interval.