worry about contamination for very faint (R=25-27) objects.

As our astrometric accuracy heavily depends on the signal-to-noise ratio of the object (i.e. objects with low photon counts are centered with lower accuracy) and the off-axis angle of the object (there is a significant degradation of the PSF of increasing off-axis angles), the total area covered by the sum of the error circles is quite large, around 3900 arcsec$^2$. In Figure \[magdist\], we show the magnitude distribution of our selected primary optical counterparts and the expected magnitude distribution of random field galaxies over this area, based on galaxy number counts [@metcalfe2001; @jones1991]. Contamination by random field galaxies becomes a serious problem beyond R $\sim24$ and they start to dominate beyond R $\sim26$, the practical limit of our imaging survey.

Therefore, extra caution is required in making sure that the [*right*]{} optical object is identified as the counterpart. This is not always trivial as the optical spectra do not always show clear signatures of active nuclei (AGNs). In some cases we had to observe every object in the error circle. Fortunately this turns out to be feasible. At R $\sim24$ and fainter, deblending is not a serious challenge (using both automated and 