Difference of the inserted and recovered magnitudes of artificial stars inserted into the combined image of the K_s-band data in 2008 plotted vs. the magnitude. A high-order polynomial fit to the median and the standard deviation (multiplied by a factor of 1.5) of the magnitude difference within magnitude bins of 1   mag are shown as well. The vertical dotted line indicates the maximum K_s-band magnitude at K_s = 19   mag of stars to be used for the proper motion analysis.