# 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 ${\displaystyle \Delta \lambda }$, and is closely related to the resolving power of the spectrograph, defined as

${\displaystyle R={\lambda \over \Delta \lambda }}$,

where ${\displaystyle \Delta \lambda }$ is the smallest difference in wavelengths that can be distinguished at a wavelength of ${\displaystyle \lambda }$. 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.[1]

## Doppler effect

The spectral resolution can also be expressed in terms of physical quantities, such as velocity; then it describes the difference between velocities ${\displaystyle \Delta v}$  that can be distinguished through the Doppler effect. Then, the resolution is ${\displaystyle \Delta v}$  and the resolving power is

${\displaystyle R={c \over \Delta v}}$

where ${\displaystyle c}$  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.[2] Resolving power, R, is given by the transition wavenumber, wavelength or frequency, divided by the resolution.[3]