  The next generation of large aperture ground based telescopes will offer the
opportunity to perform accurate stellar photometry in very crowded fields. This
future capability will allow one to study in detail the stellar population in
distant galaxies. In this paper we explore the effect of photometric errors on
the stellar metallicity distribution derived from the color distribution of the
Red Giant Branch stars in the central regions of galaxies at the distance of
the Virgo cluster. We focus on the analysis of the Color-Magnitude Diagrams at
different radii in a typical giant Elliptical galaxy obtained from synthetic
data constructed to exemplify observations of the European Extremely Large
Telescope. The simulations adopt the specifications of the first light high
resolution imager MICADO and the expected performance of the Multi-Conjugate
Adaptive Optics Module MAORY. We find that the foreseen photometric accuracy
allows us to recover the shape of the metallicity distribution with a
resolution $\lesssim 0.4$ dex in the inner regions ($\mu_{\rm B}$ = 20.5 mag
arcsec$^{-2}$) and $\simeq 0.2$ dex in regions with $\mu_{\rm B}$ = 21.6 mag
arcsec$^{-2}$, that corresponds to approximately half of the effective radius
for a typical giant elliptical in Virgo. At the effective radius ($\mu_{\rm B}
\simeq 23$ mag arcsec$^{-2}$), the metallicity distribution is recovered with a
resolution of $\simeq 0.1$ dex. It will thus be possible to study in detail the
metallicity gradient of the stellar population over (almost) the whole
extension of galaxies in Virgo. We also evaluate the impact of moderate
degradations of the Point Spread Function from the assumed optimal conditions
and find similar results, showing that this science case is robust.
