We simulate the focusing of partial coherent beams produced by fourth-generation storage rings. We used a new software tool to perform coherent mode decomposition of the undulator radiation in 1D. The analysis of a focusing system based on x-ray lenses, shows the shift and degradation of the focus when the numerical aperture is reduced by a slit. The pairing of two transfocators to assure a fixed focal position is studied in terms of beam sizes and coherent fraction. The results show that the synchrotron source imaged by two paired undulators is highly dependent on the aperture used to control the coherence fraction, and simple concepts based on geometrical optics cannot be applied.