Beam brightness

A beam intensity or photon flux per transverse phase-space volume, with any spectral bandwidth convention stated. In the far-from-diffraction-limited case with fixed flux and negligible dispersion contributions, brightness scales inversely with ${\epsilon }_x{\epsilon }_y$.

Photon source widths combine electron and diffraction widths in quadrature. At fixed optics, reducing electron emittance eventually has little effect when both radiation size and divergence dominate. This criterion differs from comparing emittances alone if the optical beta function is not matched to the diffraction ellipse.