Calibration of I_E against Gaia. The upper panels display the colour transformation between Gaia-DR3 photometry (converted to the AB magnitude system) and I_E for Milky-Way stars in the ERO fields towards Dorado (left panel), Perseus (middle), and NGC 2403 (right). In the lower sub-panels, the residual difference between the predicted and observed I_E photometry is plotted. The coloured symbols represent observations, as determined from stacked images using photometry in a large aperture and the pre-launch ZP, that is a stack ZP of 30 as described in Sect. 7. An average foreground extinction is applied to the synthetic photometry, as adequate for each line of sight; the empirical data have not been dereddened. Two extinction vectors are shown in each figure, both for A_V = 0.5, with one appropriate for the bluest stars and one for the reddest ones. Coincidentally the extinction vector is almost aligned with the colour-transformation curve at all colours; as a result extinction corrections of up to A_V = 1 change I_E,obs − I_E,pred by less than 0.01 magnitude.