  We write the curvature of spacetime in terms of the excitation probability of
particle detectors ultra-rapidly coupled to a quantum field. More precisely, we
provide an expansion for the excitation probability of a smeared UDW detector
delta-coupled to a real scalar quantum field in a curved background. Using a
short distance expansion for the Wightman function, we express the excitation
probability of a detector as the transition probability in Minkowski spacetime
plus correction terms written as a function of the curvature tensors and the
detector size. Comparing the excitation probability in curved spacetimes with
its flat analog, we are able to express the components of the Ricci and Riemann
curvature tensors as a function of physically measurable excitation
probabilities of different shaped detectors.
