Brilliance (radiation)

In optics and laser technology, brilliance describes the bundling of a beam of electromagnetic radiation .

definition

The brilliance is defined as the number of photons per time , area , solid angle and within a narrow wavelength range : ${\displaystyle B}$ ${\displaystyle \Delta N}$ ${\displaystyle t}$ ${\displaystyle A}$ ${\displaystyle \Delta \Omega }$

${\displaystyle B={\frac {\Delta N}{t\cdot A\cdot \Delta \Omega \cdot {\frac {\Delta \lambda }{\lambda }}}}}$

The spectral brilliance is given, for example, in the unit Schwinger  (Sch; after Julian Seymour Schwinger ):

${\displaystyle 1{\text{Sch}}={\frac {1{\rm {Photon}}}{\rm {s\cdot (mm)^{2}\cdot (mrad)^{2}\cdot 0{,}1\,\%\,{\text{Bandbreite}}}}}}$

The brilliance is equal to the spectral radiance divided by the energy per photon ( ): ${\displaystyle L_{\Omega \lambda }}$ ${\displaystyle {\tfrac {E}{\Delta N}}}$

${\displaystyle B={\frac {L_{\Omega \lambda }}{E/\Delta N}}={\frac {E}{t\cdot A\cdot \Delta \Omega \cdot {\frac {\Delta \lambda }{\lambda }}}}\cdot {\frac {\Delta N}{E}}}$

Like radiance, brilliance is based on a unit wavelength interval (or a unit frequency interval) as a measure of the spectral bandwidth . This reference is necessary because the spectral brilliance is related to the dispersion (the wavelength and frequency dependent refraction) as follows :

${\displaystyle B={\frac {\frac {\Delta N}{t}}{\Delta \Omega \cdot {\frac {\Delta W}{W}}}}}$

Here is the relative spectral bandwidth of the radiation. ${\displaystyle {\tfrac {\Delta W}{W}}}$

meaning

As a measure of the quality of radiation, brilliance is particularly relevant in the case of new types of devices for generating synchrotron radiation , e.g. B. the free-electron laser .

According to Liouville's theorem , the brilliance of a source - unlike intensity and divergence - cannot be changed by optics.

The brilliance describes the effects of the spatial (radiation cross-section and solid angle) and the temporal coherence (time and bandwidth interval) of a beam source . The corresponding minimum products in the denominator ( as well as ) and thus the maximum brilliance are not given by Heisenberg's uncertainty relation, but are a manifestation of the wave nature (time is not defined as a non-commuting operator in classical quantum mechanics , see Complete set of commuting observables ). Area- spatial frequency - (cf. e.g. Van-Cittert-Zernike theorem ) or time-frequency relationship (cf. e.g. Wiener-Chintschin theorem ) - describable by integral transformations, e.g. B. Fourier transform . ${\displaystyle A\cdot \Delta \Omega }$ ${\displaystyle t\cdot {\tfrac {\Delta \lambda }{\lambda }}}$

See also

• Beam parameter product

Individual evidence

1. ^ ^{A b} Ingolf V. Hertel, Claus Peter Schulz: Atoms, Molecules and Optical Physics. Atomic Physics and Basics of Spectroscopy . Springer, 2008, ISBN 978-3-540-30613-9 , pp. 424 ( definition of brilliance in Google book search).
2. ↑ Jens Falta, Thomas Möller: Research with Synchrotron Radiation: An Introduction to the Basics and Applications. Vieweg + Teubner, Wiesbaden 2010, ISBN 978-3-519-00357-1 , p. 214 ( limited preview in the Google book search).
3. ↑ Ludwig Bergmann , Heinz low , Clemens Schaefer (eds.): Textbook of experimental physics: Optics: Wave and particle optics . Walter de Gruyter, 2004, ISBN 978-3-11-017081-8 , p. 1000 .