The spectral resolution of a spectrograph, or, more generally, of a

frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...

, is a measure of its ability to resolve features in the

electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...

. It is usually denoted by

\Delta\lambda

, and is closely related to the resolving power of the spectrograph, defined as

R = \frac,

where

\Delta\lambda

is the smallest difference in

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

s that can be distinguished at a wavelength of

\lambda

. For example, the

Space Telescope Imaging Spectrograph The Space Telescope Imaging Spectrograph (STIS) is a spectrograph, also with a camera mode, installed on the Hubble Space Telescope. Aerospace engineer Bruce Woodgate of the Goddard Space Flight Center was the principal investigator and crea ...

(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 The European Organisation for Astronomical Research in the Southern Hemisphere, commonly referred to as the European Southern Observatory (ESO), is an intergovernmental research organisation made up of 16 member states for ground-based ast ...

Very Large Telescope The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m acro ...

, 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,

where

c

is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

. The STIS example above then has a spectral resolution of 51

km/s The metre per second is the unit of both speed (a scalar quantity) and velocity (a vector quantity, which has direction and magnitude) in the International System of Units (SI), equal to the speed of a body covering a distance of one metre in a ...

IUPAC definition

IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...

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.

References

{{reflist

Doppler effect

IUPAC definition

See also

References

Further reading