Detection schemes for quantum vacuum diffraction and birefringence

Motivated by recent experimental initiatives, such as at the Helmholtz International Beamline for Extreme Fields (HIBEF) at the European X-ray Free Electron Laser (XFEL), we calculate the birefringent scattering of x-rays at the combined field of two optical (or near-optical) lasers and compare various scenarios. % In order to facilitate an experimental detection of quantum vacuum diffraction and birefringence, special emphasis is placed on scenarios where the initial and final x-ray photons differ not just in polarization, but also in propagation direction (corresponding to scattering angles in the mrad regime) and possibly energy.