and $K$-corrections. The cuts are as follows:

-   Circularized half-light radius in the range $1.5 \leq R_{e,c} <
        10~\mathrm{kpc}$.

-   Sérsic index $n < 4$. Roughly 97% of injected $n=1$ profiles have a recovered $n < 4$ (see §\[sec:sims\]).

-   Absolute mean surface brightness within $R_e$ $\langle\mu\rangle_{e,\mathrm{abs},F814W} >
            24.1~\mathrm{mag}~\mathrm{arcsec}^{-2}$. For radial profiles and estimating the total abundance in each cluster, only UDGs with a mean surface brightness within $R_e$ brighter than $\langle\mu\rangle_{e,F814W} = 26.9~\mathrm{mag}~\mathrm{arcsec}^{-2}$ are included, this is the 50% completeness limit (see § \[sec:sims\]).

-   Axis ratio $q \equiv b/a > 0.3$. Coma UDGs are prolate with $\langle q
        \rangle \sim 0.7$ [@burkert2017] and [@chen2010] found no Virgo dwarfs flatter than 0.35. This also has the benefit of removing edge-on disks and lensing arcs.

-   Photometric redshift $z_{\mathrm{phot}} < 1$, if available. Not every UDG candidate has a match in the ASTRODEEP catalogs, but this removes known high-$z$ background objects.

-   Within the WFC3/IR footprint for uniform photometric redshift accuracy.

The selection in size and surface brightness parameter space is shown in Figure \[fig:udg\_selection\].

Photometric redshifts for all 6 clusters were obtained from the <span style="font-variant:small-caps;">ASTRODEEP</span> catalogs [@castellano2016; @merlin2016; @bradac2019]. We matched our catalog to that of <span style="font-variant:small-caps;">ASTRODEEP</span> 