  In vacuum high-intensity lasers can cause photon-photon interaction via the
process of virtual vacuum polarization which may be measured by the phase
velocity shift of photons across intense fields. In the optical frequency
domain, the photon-photon interaction is polarization-mediated described by the
Euler-Heisenberg effective action. This theory predicts the vacuum
birefringence or polarization dependence of the phase velocity shift arising
from nonlinear properties in quantum electrodynamics (QED). We suggest a method
to measure the vacuum birefringence under intense optical laser fields based on
the absolute phase velocity shift by phase-contrast Fourier imaging. The method
may serve for observing effects even beyond the QED vacuum polarization.
