Spectral Resolution vs. Grating Dimension
Question: What is the necessary dimension of a grating to reach the best system’s spectral resolution possible?
Theoretical resolution of a grating: R = m x n x a where m is the order of diffraction, n is the density of grooves (lines/mm) and a ist the grating’s dimension (mm). For n=1200 l/mm it is clear that a 30mm grating comes with R = 36000 which is far better compared to the system’s overall resolution (R = 4000). Hence one does not need an expensive large grating. 30 x 30 mm is more than enough as far as resolution is concerned.
In order to proof this dependancy I took Ne spectra covering various portions of the grating’s surface with a paper mask comprizing 2, 4 and 8mm openings:
