Distributions of RA_out-RA_in (blue, top) and Dec_out-Dec_in (orange, top). The filled histograms indicate subsamples of very bright sources with detection likelihoods >100. The full samples and the sub-samples have a median ΔRA= 1.2″ (vertical blue line) and a median ΔDec= −1.0″ (vertical orange line). The lower panel displays the distribution of input-output separation in terms of the ratio to the ID positional uncertainty in comparison with the Rayleigh distribution. The blue histogram shows the raw measurements. The distribution after correcting the detected positions for the median offsets is plotted in green. Then we further multiply the measured positional uncertainty by a factor of 1.25 and plot the distribution in red.