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]

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]

See also

• Angular resolution
• Resolution (mass spectrometry)

References

1. - CRIRES Instrument page at ESO
2. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "resolution in optical spectroscopy".
3. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "resolving power, R, in optical spectroscopy".

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)