## 1 Introduction  
The observation of known stellar fields by [PERSON], [PERSON] and [PERSON] during the 1919 (29 May) eclipse brought confirmation of [PERSON]'s general relativity (GR) theory into public awareness. It measured the apparent positions during the eclipse of a few stars, within a few degrees from the Sun, compared to their unperturbed relative positions. The concept is shown in Figure 1: the stars' true positions are marked in red, and their photons would follow the dashed lines if the Sun were not present; the space-time curvature induced by gravitation generates the curved photon trajectories (solid lines), so that the apparent star positions (in blue), seen by the observer on the straight (dotted) line prolongation of the incoming photon direction, are displaced away from the Sun. The measured angular variation was interpreted in terms of light deflection, providing an estimate of the \(\gamma\) parameter of the parametrized post-Newtonian (PPN) formulation of gravity theories [1] with a precision of \(\sim\)10%. The current best estimate of \(\gamma\), from a single pass of the Cassini probe behind the Sun, is in the \(10^{-5}\) range [2]. The expectations for the Gaia mission [3], currently offering its Data Release 3 (DR3) catalog [4; 5], are in the \(10^{-6}\) range [6], after initial hopes of an even better photon limit [7]. We recall that, apart from the intrinsic value of fundamental physics, the implications for our modern technology are paramount; without GR taken into account, in fact, the clocks used in GPS satellites would be faster than nominally identical ground-based clocks by about 45 us per day (partially mitigated by a 7 us/day counter-effect from special relativity), resulting in \(\sim\)10 km of error accumulated each day ([[https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System](https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System)]([https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System](https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System)), accessed on 13 December 2023) [8]. The issue is partially mitigated by design, scaling the actual on-board clock rate to the correct average value; nonetheless, real-time corrections are still required to achieve the precision level we are used to relying on in everyday life, not to mention the most demanding applications (high-precision surveying, autonomous driving, and so on). With future developments of human activity in space, deployment of positioning systems on inter-planetary scale may be considered, with even more demanding needs for correct relativistic description [9]. Light deflection is an unavoidable first-order contribution to the complex trajectory of photons in the GR universe, affected by all gravitational sources and phenomena. In a simple framework [10], an observer at a distance \(d\) from the center of the Sun (mass \(M_{\bigodot}\)) will see a star outwardly displaced by an amount \(\delta\varphi\) with respect to its unperturbed angle \(\varphi\) to the Sun:  
\[\delta\varphi=(1+\gamma)\frac{G\,M_{\bigodot}}{c^{2}\,d}\cot(\varphi/2)\,. \tag{1}\]  
The peak value at the Sun's limb is about \(1^{\prime\prime}.75\), still retaining a non-negligible value for micro-arcsecond (hereafter, \(\mu\)as) astrometry over most of the sky: at \(90^{\circ}\) from the Sun, it is about 4 milli-arcsec (hereafter, mas). Gaia observes in a range of angular distance to the Sun \(45^{\circ}\leq\varphi\leq 135^{\circ}\), where light deflection is in the range \(9.8\,\mathrm{mas}\geq\delta\varphi\geq 1.7\,\mathrm{mas}\), respectively. The relevance of deflection measurement can be appreciated from the consideration that GR acts as a cosmological attractor for scalar-tensor gravitation theories, with expected deviations from unity of \(\gamma\) in the \(10^{-5}\) to \(10^{-7}\) range [11].