  We present a new method for photometering objects in galaxy clusters. We
introduce a mode-filtering technique for removing spatially variable
backgrounds, improving both detection and photometric accuracy (roughly halving
the scatter in the red sequence compared to previous catalogs of the same
clusters). This method is based on robustly determining the distribution of
background pixel values and should provide comparable improvement in
photometric analysis of any crowded fields. We produce new multiwavelength
catalogs for the 25 CLASH cluster fields in all 16 bandpasses from the UV
through the near IR, as well as rest-frame magnitudes. A comparison with
spectroscopic values from the literature finds a ~30% decrease in the redshift
deviation from previously-released CLASH photometry. This improvement in
redshift precision, in combination with a detection scheme designed to maximize
purity, yields a substantial upgrade in cluster member identification over the
previous CLASH galaxy catalog. We construct luminosity functions for each
cluster, reliably reaching depths of at least 4.5 mag below M* in every case,
and deeper still in several clusters. We measure M* , $\alpha$, and their
redshift evolution, assuming the cluster populations are coeval, and find
little to no evolution of $\alpha$, $-0.9\lesssim\langle\alpha\rangle\lesssim
-0.8$, and M* values consistent with passive evolution. We present a catalog of
galaxy photometry, photometric and spectroscopic redshifts, and rest-frame
photometry for the full fields of view of all 25 CLASH clusters. Not only will
our new photometric catalogs enable new studies of the properties of CLASH
clusters, but mode-filtering techniques, such as those presented here, should
greatly enhance the data quality of future photometric surveys of crowded
fields.
