  We present an in-situ method to measure the birefringence of a single vacuum
window by means of microwave spectroscopy on an ensemble of cold atoms.
Stress-induced birefringence can cause an ellipticity in the polarization of an
initially linearly-polarized laser beam. The amount of ellipticity can be
reconstructed by measuring the differential vector light shift of an atomic
hyperfine transition. Measuring the ellipticity as a function of the linear
polarization angle allows us to infer the amount of birefringence $\Delta n$ at
the level of $10^{-8}$ and identify the orientation of the optical axes. The
key benefit of this method is the ability to separately characterize each
vacuum window, allowing the birefringence to be precisely compensated in
existing vacuum apparatuses.
