The spectral resolution or resolving power of a spectrograph is a
measure of its ability to resolve features in the electromagnetic
spectrum. The resolving power is understood as the inverse relative
spectral resolution, e.g. the wavelength divided by the smallest
wavelength difference that can be distinguished by the spectrograph.
When relating to spectrometry, the term chromatic resolving power is
often used.

The image a distant point source forms at
the focal plane of an optical telescope lens or camera lens is actually
a Fraunhofer diffraction pattern. The lens opening plays the role of
the aperture. The image formed by an extended composite source is
therefore a superposition of many airy disks. The resolution of a
detail in the image therefore depends on the size of the individual
Airy disks. If D is the diameter of the lens opening, then the angular
radius of an Airy disk is approximately 1.22 l/D.
This is also the approximate minimum angular seperation between two
equal point sources such that they can be just barely resolved, because
at this angular separation the central maximum of the image of one
source falls on the first minimum of the other. This condition for
optical resolution is known as the **Rayleigh criterion**.

In
the case of a rectangular aperture, of width b, such as the entrance
and exit slits or a spectrograph, the minimum angular separation
according to the Rayleigh criterion is just l/b. The intensity of the saddle point is 8/p^{2}=0.81 times the maximum intensity.

For instruments based on multiple beam interferences, such as the Fabry-Perot interferometer, the *Taylor criterion*
is more convenient to use, because there are no fringes used for the
definition of the local minimum. According to this convention, two
equal lines are considered resolved if the individual curves cross at
the half intensity, point or either line alone.

The two
conventions are often not clearly distinguished, and many people use
the Taylor criterion still referring to Lord Raleigh. In real life, the
capability of distinguishing between to separate spectral feature
depends not only on their separation, but also on the signal to noise
ratio. For noisy signals, the "real" resolution may be much worse then
the Rayleigh or Taylor criteria would predict. If the signal to noise
ratio is high, data processing technique may allow separating two
spectral features much closer than their Full Width at Half Maximum
(FWHM). The latter statement is particularly true more information on
the expected line shapes is available than just the experimental
results.