  We present deep V and I photometry for the open cluster NGC 4815 and four
surrounding Galactic fields down to a limiting magnitude $V\sim25$. These data
are used to study cluster spatial extension by means of star counts, and to
derive the luminosity (LF) and mass function (MF). The radius turns out to be
$3.6\pm0.3 arcmin$ at V=19.0 level, whereas the mass amounts at $880\pm230
m_{\odot}$ down to V=20.8. From the color-magnitude diagram, we obtain the LFs
in the V and I bands, using both the standard histogram and an adaptive kernel.
After correction for incompleteness and field star contamination, the LFs have
been transformed into the present day mass functions (PDMF). The PDMFs from the
V and I photometry can be represented as a power-law with a slope $\alpha =
3.1\pm0.3$ and $\alpha = 2.9\pm0.3$ (the \cite{salp55} MF in this notation has
a slope $\alpha = 2.35$) respectively, in the mass range $2.5 \leq
\frac{m}{m_{\odot}} \leq 0.8$. Below this mass, the MF cannot be considered as
representative of the cluster IMF, as it is the result of the combined effect
of strong irregularities in the stellar background, probable internal dynamical
evolution of the cluster and/or interaction of the cluster with the dense
Galactic field. Unresolved binaries and mass segregation can only flatten the
apparent derived IMF, so we expect that the real IMF must be steeper than the
quoted slope by an unknown amount.
