 Detector pixels and optical layout

The angular dispersion at the chosen order isFor a collecting lens with its axis directed along the selected second-order beam, the local focal-plane separation isA basic one-pixel separation criterion is therefore $\boxed{t\lesssim 55\mu \mathrm{m}}$. A more reliable two-pixels-per-resolution-interval choice is $\boxed{t\lesssim 27\mu \mathrm{m}}$. Finite pixels integrate the pattern, so sampling and pixel response should not degrade the grating's optical resolution.

This pixel sampling of a grating spectrum depends on the layout and criterion, neither of which is fully specified. If the detector is instead described by $x=f\tan \theta$ relative to the incident-axis coordinate, the derivative contains an additional ${\sec }^2\theta$ and gives $65.0\mu \mathrm{m}$ separation, or about $32\mu \mathrm{m}$ for two-pixel sampling. The more approximate paraxial mapping $x\simeq fm\lambda /D$ gives $50\mu \mathrm{m}$. These are stated alternatives rather than one falsely precise universal pixel width.