  Vacuum birefringence is one of the most striking predictions of strong field
quantum electrodynamics: Probe photons traversing a strong field region can
indirectly sense the applied "pump" electromagnetic field via quantum
fluctuations of virtual charged particles which couple to both pump and probe
fields. This coupling is sensitive to the field alignment and can effectively
result in two different indices of refraction for the probe photon polarization
modes giving rise to a birefringence phenomenon. In this article we perform a
dedicated theoretical analysis of the proposed discovery experiment of vacuum
birefringence at a x-ray free electron laser/optical high-intensity laser
facility. Describing both pump and probe laser pulses realistically in terms of
their macroscopic electromagnetic fields, we go beyond previous analyses by
accounting for various effects not considered before in this context. Our study
facilitates stringent quantitative predictions and optimizations of the signal
in an actual experiment.
