  We consider the formally determined inverse problem of recovering an unknown
time-dependent potential function from the knowledge of the restriction of the
solution of the wave equation to a small subset, subject to a single external
source. We show that one can determine the potential function, up to the
natural obstruction for the problem, by using a single source placed in the
exterior of the spacetime domain and subsequently measuring the solution in a
small neighborhood outside of the spacetime domain. The approach is based on
considering a dense collection of light rays and constructing a source function
that combines a countable collection of sources that each generates a wave
packet near a light ray in the collection. We show that measuring the solution
corresponding to that single source simultaneously determines the light ray
transform along all the light rays in the collection. The result then follows
from injectivity of the light ray transform. Our proof also provides a
reconstruction algorithm.
