Linear dispersion defines the extent to which a spectral interval is spread out across the focal field of a spectrometer and is expressed in nm/mm, Å/mm, cm-1/mm, etc. For example, consider two spectrometers: one instrument disperses a 0.1 nm spectral segment over 1 mm while the other takes a 10 nm spectral segment and spreads it over 1 mm.

It is easy to imagine that fine spectral detail would be more easily identified in the first instrument than the second. The second instrument demonstrates “low” dispersion compared to the “higher” dispersion of the first. Linear dispersion is associated with an instrument’s ability to resolve fine spectral detail.

Linear dispersion perpendicular to the diffracted beam at a central wavelength, λ, is given by:

where LB is the effective exit focal length in mm and dx is the unit interval in mm along the focal field (see Fig. 2).

In a monochromator, LB is the arm length from the focusing mirror to the exit slit, or if the grating is concave, from the grating to the exit slit. Linear dispersion, therefore, varies directly with cos β, and inversely with the exit path length, LB, diffraction order (k), and groove density, n.

In a spectrograph, the linear dispersion for any wavelength other than the wavelength which is normal to the spectral plane will be modified by the cosine of the angle of inclination or tilt angle (γ) at wavelength λn. Fig. 3 shows a “flat field” spectrograph as used with a linear diode array.

Linear Dispersion