  We present results from high-resolution, optical to near-IR imaging of host
stars of Kepler Objects of Interest (KOIs), identified in the original Kepler
field. Part of the data were obtained under the Kepler imaging follow-up
observation program over seven years (2009 - 2015). Almost 90% of stars that
are hosts to planet candidates or confirmed planets were observed. We combine
measurements of companions to KOI host stars from different bands to create a
comprehensive catalog of projected separations, position angles, and magnitude
differences for all detected companion stars (some of which may not be bound).
Our compilation includes 2297 companions around 1903 primary stars. From
high-resolution imaging, we find that ~10% (~30%) of the observed stars have at
least one companion detected within 1" (4"). The true fraction of systems with
close (< ~4") companions is larger than the observed one due to the limited
sensitivities of the imaging data. We derive correction factors for planet
radii caused by the dilution of the transit depth: assuming that planets orbit
the primary stars or the brightest companion stars, the average correction
factors are 1.06 and 3.09, respectively. The true effect of transit dilution
lies in between these two cases and varies with each system. Applying these
factors to planet radii decreases the number of KOI planets with radii smaller
than 2 R_Earth by ~2-23% and thus affects planet occurrence rates. This effect
will also be important for the yield of small planets from future transit
missions such as TESS.
