  Birefringence is one of the fascinating properties of the vacuum of quantum
electrodynamics (QED) in strong electromagnetic fields. The scattering of
linearly polarized incident probe photons into a perpendicularly polarized mode
provides a distinct signature of the optical activity of the quantum vacuum and
thus offers an excellent opportunity for a precision test of non-linear QED.
Precision tests require accurate predictions and thus a theoretical framework
that is capable of taking the detailed experimental geometry into account. We
derive analytical solutions for vacuum birefringence which include the
spatio-temporal field structure of a strong optical pump laser field and an
x-ray probe. We show that the angular distribution of the scattered photons
depends strongly on the interaction geometry and find that scattering of the
perpendicularly polarized scattered photons out of the cone of the incident
probe x-ray beam is the key to making the phenomenon experimentally accessible
with the current generation of FEL/high-field laser facilities.
