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Kepler and K2 data analysis reported in the literature is mostly based onaperture photometry. Because of Kepler's large, undersampled pixels and thepresence of nearby sources, aperture photometry is not always the ideal way toobtain high-precision photometry and, because of this, the data set has notbeen fully exploited so far. We present a new method that builds on ourexperience with undersampled HST images. The method involves a point-spreadfunction (PSF) neighbour-subtraction and was specifically developed to exploitthe huge potential offered by the K2 "super-stamps" covering the core of densestar clusters. Our test-bed targets were the NGC 2158 and M 35 regions observedduring the K2 Campaign 0. We present our PSF modeling and demonstrate that, byusing a high-angular-resolution input star list from the Asiago Schmidttelescope as the basis for PSF neighbour subtraction, we are able to reachmagnitudes as faint as Kp~24 with a photometric precision of 10% over 6.5hours, even in the densest regions. At the bright end, our photometricprecision reaches ~30 parts-per-million. Our method leads to a considerablelevel of improvement at the faint magnitudes (Kp>15.5) with respect to theclassical aperture photometry. This improvement is more significant in crowdedregions. We also extracted raw light curves of ~60,000 stars and detrended themfor systematic effects induced by spacecraft motion and other artifacts thatharms K2 photometric precision. We present a list of 2133 variables.

A PSF-based approach to Kepler/K2 data. I. Variability within the K2 Campaign 0 star clusters M 35 and NGC 2158