Invited Article: Refined analysis of synchrotron radiation for NIST's SURF III facility.

We have developed a new method for the exact calculation of synchrotron radiation for the National Institute of Standards and Technology Synchrotron Ultraviolet Radiation Facility, SURF III. Instead of using the Schwinger formula, which is only an approximation, we develop formulae based on Graf's addition theorem for Bessel functions and accurate asymptotic expansions for Hankel functions and Bessel functions. By measuring the radiation intensity profile at two distances from the storage ring, we also confirm an apparent vertical emittance that is consistent with the vertical betatron oscillations that are intentionally introduced to extend beam lifetime by spreading the electron beam spatially. Finally, we determine how much diffraction by beamline apertures enhances the spectral irradiance at an integrating sphere entrance port at the end station. This should eliminate small but treatable components of the uncertainty budget that one should consider when using SURF III or similar synchrotrons as standard, calculable sources of ultraviolet and other radiation.