Spectral resolution
Encyclopedia
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
, and is closely related to the resolving power of the spectrograph, defined as
,
where
is the smallest difference in wavelength
s that can be distinguished at a wavelength of
. 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.
that can be distinguished through the Doppler effect
. Then, the resolution is
and the resolving power is
where
is the speed of light
. The STIS example above then has a spectral resolution of 51 km/s.
Spectrograph
A spectrograph is an instrument that separates an incoming wave into a frequency spectrum. There are several kinds of machines referred to as spectrographs, depending on the precise nature of the waves...
, or, more generally, of a frequency spectrum
Frequency spectrum
The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain. The frequency spectrum can be generated via a Fourier transform of the signal, and the resulting values are usually presented as amplitude and phase, both plotted versus frequency.Any signal...
, is a measure of its ability to resolve features in the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
. It is usually denoted by
, and is closely related to the resolving power of the spectrograph, defined as,where
is the smallest difference in wavelengthWavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s that can be distinguished at a wavelength of
. For example, the Space Telescope Imaging SpectrographSpace Telescope Imaging Spectrograph
The Space Telescope Imaging Spectrograph is a spectrograph, also with a camera mode, installed on the Hubble Space Telescope. It operated continuously from 1997 until a power supply failure in 2004. After repairs, it began operating again in 2009...
(STIS) can distinguish features 0.17 nm
Nanometre
A nanometre is a unit of length in the metric system, equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre .The nanometre is often used to express dimensions on the atomic scale: the diameter...
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
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
Echelle Spectrograph
Echelle grating
An echelle grating is a type of diffraction grating which is characterised by a relatively low groove density but is optimized for high diffraction orders. Echelle gratings are, like other types of diffraction grating, used in spectrometers and similar instruments, such as HARPS, and numerous...
(CRIRES) installed at ESO
ESO
ESO, as a three-letter abbreviation, may stand for:* European Southern Observatory* Ensemble Studios Online* English Symphony Orchestra* Edmonton Symphony Orchestra* Executive Stock Options...
's Very Large Telescope
Very Large Telescope
The Very Large Telescope is a telescope operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. The VLT consists of four individual telescopes, each with a primary mirror 8.2m across, which are generally used separately but can be used together to...
, 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 effectDoppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
. Then, the resolution is
and the resolving power iswhere
is the speed of lightSpeed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
. 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.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)