at the object’s position from the <span style="font-variant:small-caps;">PSFEx</span> model.

Absolute magnitudes and physical sizes were computed from the GALFIT model parameters assuming all sources in an image lie at their respective cluster redshifts (Table \[tab:clusters\]). We circularized the effective radii using $R_{e,c} = R_e\sqrt{b/a}$. The mean surface brightness within $R_e$ was derived from the model magnitudes $m$ and effective radii using $$\langle\mu\rangle_{e} = m + 2.5\log(2 \pi R_{e,c}^2).$$ The absolute mean surface brightness is then calculated with $$\langle\mu\rangle_{e,abs} = \langle\mu\rangle_{e} -
    2.5\log(1+z)^4 - E(z) - K(z),$$ where $z$ is the cluster redshift, and $E(z)$ and $K(z)$ are the evolutionary and $K$-corrections, respectively [@graham2005], computed with EzGal [@ezgal] assuming a simple stellar population (SSP) with $[\mathrm{Fe}/\mathrm{H}] = -0.6$, a formation redshift of $z=2$ and a [@chabrier2003] IMF.

Ultra-diffuse galaxy selection {#sec:udgselection}
------------------------------

![image](figure1.png){width="99.00000%"}

Our UDG selection is very similar to that used in our previous work on Abell 2744 [@janssens2017], which in turn is based on the cuts used by [@vdb2016]. In this work, instead of transforming all the UDG $F814W$ surface brightnesses to the $r$-band, we instead transform the $r$-band surface brightness cut of $\langle\mu\rangle_{e,abs,r} > 23.8~\mathrm{mag}~\mathrm{arcsec}^{-2}$ into a $F814W$ cut using the same SSP described above for the evolutionary 