Beam Shape Effects on Grating Spectrometer Resolution

The collimated optical beam in a grating spectrometer may be circular or elliptical in cross section, so that different parts of the beam illuminate different numbers of grooves on the grating. Here we estimate the consequent loss in spectral resolution relative to that obtained with a beam which illuminates a fixed number of grooves. For representative diffraction resolution functions, the effect is to reduce the intrinsic resolving power of the spectrometer by about 13%, exclusive of other contributions such as finite entrance slit width.