  In an investigation of the cause of the cosmic microwave background decrement
in the field of the z = 3.8 quasar pair PC1643+4631, we have carried out a
study to photometrically estimate the redshifts of galaxies in deep
multi-colour optical images of the field taken with the WHT. To examine the
possibility that a massive cluster of galaxies lies in the field, we have
attempted to recover simulated galaxies with intrinsic colours matching those
of the model galaxies used in the photometric redshift estimation. We find that
when such model galaxies are added to our images, there is considerable scatter
of the recovered galaxy redshifts away from the model value; this scatter is
larger than that expected from photometric errors and is the result of
confusion, simply due to ground-based seeing, between objects in the field. We
have also compared the likely efficiency of the photometric redshift technique
against the colour criteria used to select z>3 galaxies via the strong colour
signature of the Lyman-limit break. We find that these techniques may
significantly underestimate the true surface density of z>3, due to confusion
between the high-redshift galaxies and other objects near the line of sight. We
argue that the actual surface density of z=3 galaxies may be as much as 6 times
greater than that estimated by previous ground-based studies, and note that
this conclusion is consistent with the surface density of high-redshift objects
found in the HDF. Finally, we conclude that all ground-based deep field surveys
are inevitably affected by confusion, and note that reducing the effective
seeing in ground-based images will be of paramount importance in observing the
distant universe.
