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It is often suggested that the emittance coupling of a storage ring should be adjusted to the so-called diffraction limit corresponding to the shortest wavelength of interest. For 1 A radiation this leads to a typical requirement of 8 pm rad vertical emittance. In ultralow-emittance storage rings like the MAX IV 3 GeV storage ring this corresponds to a comparably large setting of the emittance coupling (2.5%). This approach, however, does not produce the brightest radiation and needs to be revisited taking into account that overall photon brightness depends on the emittances of the electron beam and the intrinsic photon beam. This paper summarizes an analytic approach to maximizing brightness as a function of emittance coupling while retaining sufficient lifetime. Instead of "meeting the diffraction limit", we further reduce the coupling, thus increasing both the brightness and transverse coherence of the emitted radiation. We derive that reducing the MAX IV 3 GeV storage ring's vertical emittance to 2 pm rad (0.6% coupling) will increase brightness and transverse coherence by almost a factor two while 10 h overall lifetime can still be achieved.
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