Editing Synchrotron light source (section)

== Spectral brightness ==

The primary figure of merit used to compare different sources of synchrotron radiation has been referred to as the "brightness", the "brilliance", and the "spectral brightness", with the latter term being recommended as the best choice by the Working Group on Synchrotron Nomenclature.<ref name=mills>{{cite journal |last1=Mills |first1=D. M. |last2=Helliwell |first2=J. R. |last3=Kvick |first3=Å. |last4=Ohta |first4=T. |last5=Robinson |first5=I. A. |last6=Authier |first6=A. |title=Report of the Working Group on Synchrotron Radiation Nomenclature – brightness, spectral brightness or brilliance? |journal=Journal of Synchrotron Radiation |date=1 May 2005 |volume=12 |issue=3 |pages=385 |doi=10.1107/S090904950500796X |pmid=15840926 |url=https://journals.iucr.org/s/issues/2005/03/00/es0344/ |access-date=8 April 2022|doi-access=free |bibcode=2005JSynR..12..385M }}</ref> Regardless of the name chosen, the term is a measure of the total [[flux]] of photons in a given six-dimensional [[phase space]] per unit [[Bandwidth (signal processing)|bandwidth]] (BW).<ref name="nielsen">{{cite book | last = Nielsen | first = Jens | title = Elements of modern X-ray physics | publisher = John Wiley | location = Chichester, West Sussex | year = 2011 | isbn = 9781119970156 }}</ref>

The spectral brightness is given by

: <math>B = \frac{\dot N_\text{ph}}{4 \pi^2 \sigma_x \sigma_y \sigma_{x'} \sigma_{y'} \frac{d\omega}{\omega}},</math>

where <math>\dot N_\text{ph}</math> is the number of photons per second in the beam, <math>\sigma_x</math> and <math>\sigma_y</math> are the [[root mean square]] values for the size of the beam in the axes perpendicular to the beam direction, <math>\sigma_{x'}</math> and <math>\sigma_{y'}</math> are the RMS values for the beam solid angle in the ''x'' and ''y'' dimensions, and <math display="inline">\frac{d\omega}{\omega}</math> is the relative bandwidth, or spread in beam frequency around the central frequency.<ref>{{cite book |last1=Wiedemann |first1=Helmut |title=Particle accelerator physics |date=2007 |publisher=Springer |location=Berlin |isbn=9783540490432 |page=782 |edition=3rd}}</ref> The customary value for bandwidth is 0.1%.{{r|mills}}

Spectral brightness has units of time<sup>−1</sup>&sdot;distance<sup>−2</sup>&sdot;angle<sup>−2</sup>&sdot;(% bandwidth)<sup>−1</sup>.