Spectral resolution

The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by $$\Delta\lambda$$, and is closely related to the resolving power of the spectrograph, defined as $$R = \frac{\lambda}{\Delta\lambda},$$ where $$\Delta\lambda$$ is the smallest difference in wavelengths that can be distinguished at a wavelength of $$\lambda$$. For example, the Space Telescope Imaging Spectrograph (STIS) can distinguish features 0.17 nm apart at a wavelength of 1000 nm, giving it a resolution of 0.17 nm and a resolving power of about 5,900. An example of a high resolution spectrograph is the Cryogenic High-Resolution IR Echelle Spectrograph (CRIRES+) installed at ESO's Very Large Telescope, which has a spectral resolving power of up to 100,000.

Doppler effect
The spectral resolution can also be expressed in terms of physical quantities, such as velocity; then it describes the difference between velocities $$\Delta v$$ that can be distinguished through the Doppler effect. Then, the resolution is $$\Delta v$$ and the resolving power is $$R = \frac{c}{\Delta v},$$ where $$c$$ is the speed of light. The STIS example above then has a spectral resolution of 51 km/s.

IUPAC definition
IUPAC defines resolution in optical spectroscopy as the minimum wavenumber, wavelength or frequency difference between two lines in a spectrum that can be distinguished. Resolving power, R, is given by the transition wavenumber, wavelength or frequency, divided by the resolution.