## 3 Results
### Optical Parameter Calibration  
The light deflection effect acts purely in the radial direction with respect to the nominal observing geometry and instrument symmetry (e.g., Figure 4). Therefore, the measurement is mostly sensitive to disturbances affecting the radial component of the electro-optical response parameters.  
Several optical aberrations have a radial dependence, usually different from that of deflection (Equation (1)). The instrument response may be most effectively calibrated by observation of known stellar fields, e.g., in off-eclipse periods. The concept of relative astrometry calibration is discussed, e.g., in [30], which discusses how the local reference frame, materialized by the observed Gaia DR3 sources, can be consolidated by simple model fitting to the measurements. The basic idea is recalled hereafter.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Limiting Magnitude** & **0.5 Years** & **1 Year** & **2 Years** & **3 Years** \\ \hline \(G=12\) mag & 1.60 & 1.11 & 0.787 & 0.643 \\ \(G=14\) mag & 1.49 & 1.01 & 0.713 & 0.582 \\ \(G=16\) mag & 1.44 & 0.94 & 0.665 & 0.543 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mission performance: relative precision, in \(10^{-7}\) units, on the estimate of light deflection.  
Figure 7: GLADE mission performance over a three-year lifetime.  
It is convenient to express positions in terms of local radial and tangential coordinates, respectively, in angular \((\rho,\tau)\) and linear \((r,t)\) units. We can rewrite Equation (1) as \(\rho_{D}=\rho+(1+\gamma)f(\rho)\), where \(\rho\) is the nominal angle of the star with respect to the current Sun position and \(\rho_{D}\) is the observed (deflected) position, through the PPN parameter \(\gamma\). Then, a star at angular coordinates \((\rho,\tau)\) is projected through the EFL \(F\) of an ideal telescope to the linear FP position  
\[r=F\rho_{D}\,,\;\;\;t=F\tau\,. \tag{4}\]  
The detected position of a star may be affected, e.g., by a deviation \(\delta\gamma\) from unity of the \(\gamma\) parameter or by an EFL variation \(\delta F\), as  
\[r+\delta r=F(1+\frac{\delta F}{F})(\rho_{D}+\delta\gamma f(\rho))\,,\;\;\;t+ \delta t=F(1+\frac{\delta F}{F})\tau\,. \tag{5}\]  
Therefore, tangential coordinates are basically unaffected by deflection (which is basically radial) and its uncertainty, allowing us to decouple the issue of EFL calibration from the deflection measurement.  
The self-calibration potential of GLADE can be glimpsed, e.g., in the case of a focal plane image including \(N\) stars, with photo-center estimate errors following the photon-limited astrometric noise described by Equation (2) and shown in Figure 6 at the level of a few 0.1 \(\mu\)as for intermediate exposure and magnitude. The EFL must match the measured and cataloged star positions. It may be noted that catalog errors are systematic on an individual basis, but they act collectively as random errors since each star is affected by its own error within known uncertainty.  
We assume a typical catalog position error \(\sigma_{t}\simeq 10\,\mu\)as for each of \(N\simeq 20\) stars uniformly distributed on any \(L=15^{\prime}\) chip (typical separation \(\Delta\tau\sim 1^{\prime}\)) in average observing conditions. Therefore, the EFL precision on individual field exposures (over a few hours) is of the order of  
\[\frac{\sigma(s)}{s}\simeq\frac{\sigma_{t}}{\Delta\tau}=\simeq 1.7\times 10^{-7}\,, \tag{6}\]  
which is quite adequate to the mission goal, since it is well below the random error on the same time scale (of order \(10^{-6}\)), and it will be further averaged throughout the measurements.