Abstract
Three long straight sections with double-mini beta-y lattice were created in the Taiwan Photon Source (TPS) for which the effects of focusing elements and phase shifters between the collinear undulators result in incorrect calculations of the brilliance while assuming a Gaussian-approximation. Therefore, an on-axis Wigner distribution function (WDF), which includes effects of wave phenomena, is a natural way to measure the intensity of synchrotron radiation and is used in this article as the definition of brilliance.