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In almost all of the studies devoted to the time delay and the frequencyshift of light, the calculations are based on the integration of the nullgeodesic equations. However, the above-mentioned effects can be calculatedwithout integrating the geodesic equations if one is able to determine thebifunction $\Omega(x_A, x_B)$ giving half the squared geodesic distance betweentwo points $x_A$ and $x_B$ (this bifunction may be called Synge's worldfunction). In this lecture, $\Omega(x_A, x_B)$ is determined up to the order$1/c^3$ within the framework of the PPN formalism. The case of a stationarygravitational field generated by an isolated, slowly rotating axisymmetric bodyis studied in detail. The calculation of the time delay and the frequency shiftis carried out up to the order $1/c^4$. Explicit formulae are obtained for thecontributions of the mass, of the quadrupole moment and of the internal angularmomentum when the only post-Newtonian parameters different from zero are$\beta$ and $\gamma$. It is shown that the frequency shift induced by the massquadrupole moment of the Earth at the order $1/c^3$ will amount to $10^{-16}$in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission.Other contributions are briefly discussed.

A universal tool for determining the time delay and the frequency shift of light: Synge's world function