  Identifying galaxy clusters through overdensities of galaxies in photometric
surveys is the oldest and arguably the most economic and mass-sensitive
detection method, compared to X-ray and Sunyaev-Zel'dovich Effect surveys that
detect the hot intracluster medium. However, a perennial problem has been the
mapping of optical 'richness' measurements on to total cluster mass. Emitted at
a conformal distance of 14 Gpc, the cosmic microwave background acts as a
backlight to all intervening mass in the Universe, and therefore has been
gravitationally lensed. Here we present a calibration of cluster optical
richness at the 10 per cent level by measuring the average cosmic microwave
background lensing convergence measured by Planck towards the positions of
large numbers of optically-selected clusters, detecting the deflection of
photons by haloes of total mass of the order 10**14 solar masses. Although
mainly aimed at the study of larger-scale structures, the Planck lensing
reconstruction can yield nearly unbiased results for stacked clusters on
arcminute scales. The lensing convergence only depends on the redshift integral
of the fractional overdensity of matter, so this approach offers a clean
measure of cluster mass over most of cosmic history, largely independent of
baryon physics.
