  In suitably chosen domains of space-time, the world function may be a
powerful tool for modelling the deflection of light and the time/frequency
transfer. In this paper we work out a recursive procedure for expanding the
world function into a perturbative series of ascending powers of the Newtonian
gravitational constant G. We show rigorously that each perturbation term is
given by a line integral taken along the unperturbed geodesic between two
points. Once the world function is known, it becomes possible to determine the
time transfer functions giving the propagation time of a photon between its
emission and its reception. We establish that the direction of a light ray as
measured in the 3-space relative to a given observer can be derived from these
time transfer functions, even if the metric is not stationary. We show how to
deduce these functions up to any given order in G from the perturbative
expansion of the world function. To illustrate the method, we carry out the
calculation of the world function and of the time transfer function outside a
static, spherically symmetric body up to the order G^2, the metric containing
three arbitrary parameters.
