  A majority of ultracold atom experiments utilize resonant absorption imaging
techniques to obtain the atomic density. To make well-controlled quantitative
measurements, the optical intensity of the probe beam must be precisely
calibrated in units of the atomic saturation intensity ${I_{\rm sat}}$. In
quantum gas experiments, the atomic sample is enclosed in an ultra-high vacuum
system that introduces loss and limits optical access; this precludes a direct
determination of the intensity. Here, we use quantum coherence to create a
robust technique for measuring the probe beam intensity in units of ${I_{\rm
sat}}$ via Ramsey interferometry. Our technique characterizes the ac Stark
shift of the atomic levels due to an off-resonant probe beam. Furthermore, this
technique gives access to the spatial variation of the probe intensity at the
location of the atomic cloud. By directly measuring the probe intensity just
before the imaging sensor our method in addition yields a direct calibration of
imaging system losses as well as the quantum efficiency of the sensor.
