Beyond the current stages, astrometric observation will be able to attain the accuracy of a few microarcsecond (μas) or higher for some astrometric missions in the future. This tendency requires a practical framework that can satisfy the accuracy of μas. 

   In order to realize this purpose, by using the post-Newtonina method, the author generalizes the relativistic theories of light propagation by introducing two new parameters ς and η in the second post-Newtonian (2PN) order in this work, in addition to the parametrized post-Newtonian (PPN) parameters γ and β. ς and η respectively parametrize the spatial isotropic and anisotropic terms in g_ij at O(c⁻⁴) (see the table). 

   This new 2PN parametrized (2PPN) formalism includes the nonstationary gravitational fields and the influences of all kinds of relativistic effects. With the derivation of a gauge-invariant angle between the directions of two incoming photons, the author further discuss a practical astronomic observation, namely, an observer on a spacecraft measures the angle between the two incoming photons emitted separately from two spacecrafts which are all at an orbit circling the Sun at the same distance as the Earth. Given attaining a level of ∼1 μas for space astrometry missions in the near future, like LATOR mission, the terms at this level are listed in the following table.