Ellipticity induced in vacuum birefringence

We consider signals of photon-photon scattering in laser-based, low energy experiments. In particular, we consider the ellipticity induced on a probe beam by a strong background field, and compare it with a recent worldline expression for the photon polarisation flip amplitude. When the probe and the background are plane waves, the ellipticity is equal to the flip amplitude. Here we investigate the ellipticity-amplitude relation for more physical fields.