[en] The spectral brightness of the radiation in a long undulator chain with an external periodic FODO lattice is derived, taking into account the space-angular distribution of the electron beam. Given the convolution of the electron and photon beam distributions, the brightness is explicitly presented via the phase advance per cell and the number of FODO lattices along the undulators chain. The radiation brightness for several focusing lattice arrangements for the European XFEL SASE1 beamline are evaluated numerically and compared with the analytical predictions. (paper)