The spectral resolution of a
spectrograph
An optical spectrometer (spectrophotometer, spectrograph or spectroscope) is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify mat ...
, or, more generally, of a
frequency spectrum, 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
, and is closely related to the resolving power of the spectrograph, defined as
where
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, tr ...
s that can be distinguished at a wavelength of
. 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 creato ...
(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
An echelle grating (from French ''échelle'', meaning "ladder") is a type of diffraction grating characterised by a relatively low groove density, but a groove shape which is optimized for use at high incidence angles and therefore in high diffract ...
'' (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
that can be distinguished through the
Doppler effect
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, ...
. Then, the resolution is
and the resolving power is
where
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 fo ...
. The STIS example above then has a spectral resolution of 51
km/s.
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.
See also
*
Angular resolution
Angular resolution describes the ability of any image-forming device such as an Optical telescope, optical or radio telescope, a microscope, a camera, or an Human eye, eye, to distinguish small details of an object, thereby making it a major det ...
*
Resolution (mass spectrometry)
In mass spectrometry, resolution is a measure of the ability to distinguish two peaks of slightly different mass-to-charge ratios ''ΔM'', in a mass spectrum.
Resolution and resolving power
There are two different definitions of resolution a ...
References
{{reflist
Further reading
*Kim Quijano, J., et al. (2003), ''STIS Instrument Handbook'', Version 7.0, (Baltimore: STScI)
*Frank L. Pedrotti, S.J. (2007), ''Introduction to optics'', 3rd version, (San Francisco)
Spectroscopy