Distribution of ‘centre’ measurements for the 1000 instrumental profiles shown in Fig. A.1, where the centre estimator used is indicated at the top of the panel. Since we were interested in quantifying the stability (distribution width) of each centre estimator under small perturbations of the IP, the distributions plotted were shifted to have zero median. The dashed white vertical lines show the limits of the central 68% of the distribution and the text above the lines gives their values in units pixel. Ranking centre estimators from the most stable to the least stable, we get: ψ(−0. 5) = ψ(0. 5), the median, the mean, and the mode.