Spectrometer Instrumental Bandpass

Ignoring the effects of the image height, the instrumental bandpass B is given by

B = P sup(w',w")    (8-12)

where P is the reciprocal linear dispersion, w' is the image width, w" is the width of the exit slit, and sup(w',w") is the greater of its arguments:

sup(w',w") = w' if w'>w",  w" otherwise    (8-13)

As P is usually expressed in nm/mm, the widths w' and w" must be expressed in millimeters to obtain the bandpass B in nanometers.

In cases where the image of the entrance slit is wider than the exit slit (that is, w' > w"), the instrumental bandpass is said to be imaging limited, whereas in those cases where the exit slit is wider than the image of the entrance slit (w' < w"), the instrumental bandpass is said to be slit limited. [When an imaging-limited optical system is imaging limited due primarily to the grating, either because of the resolving power of the grating or due to its wavefront errors, the system is said to be grating limited.]

In the design of optical spectrometers, the widths of the entrance and exit slits are chosen by balancing spectral resolution (which improves as the slits become narrower, to a limit) and optical throughput (which improves as the slits widen, up to a limit). Ideally, the exit slit width is matched to the width of the image of the entrance slit  – this optimizes both resolution and throughput. This optimum may only be achievable for one wavelength, the resolution of the other wavelengths generally being either slit-limited or imaging-limited (with suboptimal throughput likely as well).