 Spectral Resolution
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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.

## 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. Resolving power, R, is given by the transition wavenumber, wavelength or frequency, divided by the resolution.