Like many astronomical missions and data sets, the NASA Kepler satellite imaging is crowded; there is no part of the imaging that contains reliably isolated stars. For this reason, it is hard to infer (from the data) the point-spread function of the instrument simply; any PSF inference requires modeling the images as a crowded image of many overlapping stars (of unknown brightnesses and positions). However, when a star is subject to a planetary or stellar transit, the change in the scene during the transit should be modeled well as a PSF-shaped deficit. So we should be able to infer the PSF from these deficits. The transits are rare, so they rarely overlap. They are also very faint (low-amplitude) events, but (a) the eclipsing-binary stellar transits are not so faint (and very common), and (b) Kepler has good signal-to-noise even on planetary transits.
