Astrometric measurements relative to the first epoch. The crosses show the positions of HD 135344 Ab, which moves eastward. The colored circles show the positions of the suspected background sources in the IRDIS field of view, which are connected with dotted lines between epochs. The dashed line shows the track for a stationary background source, and the gray circles and squares indicate the three SPHERE and three GRAVITY epochs, respectively, after the initial detection. The small dots represent a sample of Gaia sources within 0.1 deg from HD 135344 A (see main text for details). The colors indicate a specific epoch, for example, all pink markers correspond to 2021 Jul. 16.