Luminosity and mass function of galactic open clusters I. NGC 4815

We present deep V and I photometry for the open cluster NGC 4815 and four s urrounding Galactic fields down to a limiting magnitude V similar to 25. Th ese data are used to study cluster spatial extension by means of star count s, and to derive the luminosity (LF) and mass function (MF). The radius tur ns out to be 3.6 +/-0.3 arcmin at V = 19.0, whereas the mass is 880 +/- 230 m(circle dot) down to V = 20.8. From the color-magnitude diagram, we obtai n the LFs in the V and I bands, using both the standard histogram and an ad aptive kernel. After correction for incompleteness and field star contamina tion, the LFs mere transformed into the present day mass functions (PDMF). The PDMFs from the V and I photometry can be represented as a power-law wit h a slope alpha = 3.1 +/-0.3 and alpha = 2.9 +/-0.3 (the (Salpeter 1955) MF in this notation has a slope alpha = 2.35) respectively, in the mass range 2.5 less than or equal to m/m(circle dot) less than or equal to 0.8. Below this mass, the MF cannot be considered as representative of the cluster IM F, as it is m-a the result of the combined effect of strong irregularities in the stellar background, probable internal dynamical evolution of the clu ster and/or interaction of the cluster with the dense Galactic field. Unres olved binaries and mass segregation can only flatten the apparent derived I MF, so we expect that the real IMF must be steeper than the quoted slope by an unknown amount.