Top panel: simulated luminosity function (number of sources per magnitude bin) for the contiguous GBTDS fields. This luminosity function includes all luminous sources, not just binaries (see Figure 3). The field latitudes are labeled by the different colored lines; longitudes are not labeled for readability. The gray shaded regions F146_Vega > 23.5 mag denote the background-dominated regime. Bottom panel: cumulative source density distribution, zoomed in on the region of optimal astrometric sensitivity. The horizontal dashed lines denote 1/10, 1/30, and 1/50 sources per beam, which are a proxy for the amount of crowding (discussed in Section 6.2.2).