significant variation between the 6 clusters.

The geometrical completeness simulations are similar, but we only inject objects that would pass our selection criteria and that are brighter than the 50% completeness limit found above. We allow any location in the ACS and WFC3 overlap region to be chosen, informing the fraction of UDGs that may be lost due to projection against other sources or the intracluster light (ICL). The mimimum spacing of 150 pixels between injected objects is still enforced. The resulting radial completeness curves are shown in the right-hand panels of Figure \[fig:radial-profiles\], the rest of the figure is discussed later in the context of the radial density profiles of UDGs.

Ultra-compact dwarf selection
-----------------------------

![image](figure5.png){width="100.00000%"}

UCDs were selected from a separate catalog optimized for point source detection since even the largest UCDs [$r_h \sim 100~\mathrm{pc}$, @brodie2011] would be unresolved in the lowest redshift FF cluster. A median filter with a kernel size of 15 pixels was applied to the $F814W$ image of each field and subtracted off to remove low frequency power from the BCGs and the ICL. The resulting image was then used by <span style="font-variant:small-caps;">SExtractor</span> as the detection image in dual-image mode for all bands, with 