= Pixel sampling of a grating spectrum
A normal-incidence <diffraction grating> of pitch $D$ has order $m$ at $D\sin\theta=m\lambda$ and angular separation $\Delta\theta\simeq m\Delta\lambda/(D\cos\theta)$. A lens whose axis follows the selected order maps a small angular interval to $\Delta x\simeq f\Delta\theta$. Detector pixels substantially smaller than this separation are needed; two pixels per resolution interval correspond to $t\lesssim\Delta x/2$. If instead detector coordinates obey $x=f\tan\theta$ relative to the original axis, the scale is $\Delta x\simeq f\sec^2\theta\,\Delta\theta$. A numerical pixel limit therefore requires an optical layout and a sampling criterion as well as the <resolving power of a diffraction grating>.
Back to article page
