Kepler and K2 data analysis reported in the literature is mostly based on
aperture photometry. Because of Kepler's large, undersampled pixels and the
presence of nearby sources, aperture photometry is not always the ideal way to
obtain high-precision photometry and, because of this, the data set has not
been fully exploited so far. We present a new method that builds on our
experience with undersampled HST images. The method involves a point-spread
function (PSF) neighbour-subtraction and was specifically developed to exploit
the huge potential offered by the K2 "super-stamps" covering the core of dense
star clusters. Our test-bed targets were the NGC 2158 and M 35 regions observed
during the K2 Campaign 0. We present our PSF modeling and demonstrate that, by
using a high-angular-resolution input star list from the Asiago Schmidt
telescope as the basis for PSF neighbour subtraction, we are able to reach
magnitudes as faint as Kp~24 with a photometric precision of 10% over 6.5
hours, even in the densest regions. At the bright end, our photometric
precision reaches ~30 parts-per-million. Our method leads to a considerable
level of improvement at the faint magnitudes (Kp>15.5) with respect to the
classical aperture photometry. This improvement is more significant in crowded
regions. We also extracted raw light curves of ~60,000 stars and detrended them
for systematic effects induced by spacecraft motion and other artifacts that
harms K2 photometric precision. We present a list of 2133 variables.Comment: 27 pages (included appendix), 2 tables, 25 figures (5 in low
resolution). Accepted for publication in MNRAS on November 05, 2015. Online
materials will be available on the Journal website soo
