  We present a complete analysis of the light rays within the linearized,
weak-field approximation of a Schwarzschild-like metric describing the
gravitational field of an isolated, spherically symmetric body. We prove in
this context the existence of two time transfer functions and we obtain these
functions in an exact closed-form. We are led to distinguish two regimes. In
the first regime, the two time transfer functions correspond to rays which are
confined in regions of spacetime where the weak-field approximation is valid.
Such a regime occurs in gravitational lensing configurations with double images
of a given source. We find the general expressions of the angular separation
and the difference in light travel time between the two images. In the second
regime, there exists only one time transfer function corresponding to a light
ray remaining in a region of weak field. Performing a Taylor expansion of this
function with respect to the gravitational constant, we obtain the Shapiro time
delay completed by a series of so-called "enhanced terms". The enhanced terms
beyond the third order are new.
