that are brighter than a source plane limiting magnitude can then be found by simply counting the number of sources brighter than the limiting magnitude in the source plane after correcting for lensing. A simple Poisson uncertainty is attached to this value.

We then calculated the area of the background sky within which EROs were detectable in the relevant cluster field in the following manner. An ERO with a source plane magnitude of $K'_{\rm{source}}$ will appear in the image plane of the relevant cluster with a magnitude brighter than an image plane detection limit of $K'_{\rm{det}}$, if it is magnified by a factor greater than $\mu_{\rm{min}} = 10^{-0.4(K'_{\rm{det}}-K'_{\rm{source}})}$. The area in the source plane within which such a galaxy would be detected in that cluster is thus $A$($\mu_{\rm{min}}$), where $A$($\mu_{\rm{min}}$) is the area of the $z_{\rm{source}} = 1.5$ source plane behind each cluster that lies within the CISCO field of view, and is magnified by a factor greater than $\mu_{\rm{min}}$(figure 8). Therefore, we can derive the surface number density from the dividing number of galaxies by $A$($\mu_{min}$).

Corrected Surface Density of EROs
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The derived surface densities for each cluster field are 2.43 arcmin$^{-2}$ for $R_{\rm{c}}-K' \geq$ 5.3 in MS 