Free electron lasers emit powerful and coherent radiation in a wide wavelength range extending to hard X-rays. This radiation is also characterized by a high degree of polarization that is generally linear and depends on the undulator properties. The possibility of controlling the polarization state of the radiation is an important option for free electron lasers that is critical for a large class of experiments. Such control can be achieved using variable polarization undulators or alternatively via the crossed polarized undulator scheme. We report the results of an extensive study for the characterization of the crossed-polarized undulator scheme in a number of different configurations. A simple model, based on Gaussian mode beam propagation, is presented and used to reproduce the experimental results obtained at the seeded free electron laser FERMI. A good agreement is found between the model and the experiment allowing us to understand the impact of the wavefront properties of the radiation coming from the consecutive undulators on the output radiation. The model is used not only for characterizing the control of the polarization but also for the control of the transverse mode.