# Spectral resolution

### 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 = {\lambda\over\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.[1]

## Contents

• Doppler effect 1
• IUPAC definition 2
• References 4

## 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 = {c\over\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.[2] Resolving power, R, is given by the transition wavenumber, wavelength or frequency, divided by the resolution.[3]