  Directly imaging exoplanets is challenging because quasi-static phase
aberrations in the pupil plane (speckles) can mimic the signal of a companion
at small angular separations. Kernel phase, which is a generalization of
closure phase (known from sparse aperture masking), is independent of pupil
plane phase noise to second order and allows for a robust calibration of full
pupil, extreme adaptive optics observations. We applied kernel phase combined
with a principal component based calibration process to a suitable but not
optimal, high cadence, pupil stabilized L' band ($3.8~\mu\text{m}$) data set
from the ESO archive. We detect eight low-mass companions, five of which were
previously unknown, and two have angular separations of
$\sim0.8$-$1.2~\lambda/D$ (i.e. $\sim80$-$110~\text{mas}$), demonstrating that
kernel phase achieves a resolution below the classical diffraction limit of a
telescope. While we reach a $5\sigma$ contrast limit of $\sim1/100$ at such
angular separations, we demonstrate that an optimized observing strategy with
more diversity of PSF references (e.g. star-hopping sequences) would have led
to a better calibration and even better performance. As such, kernel phase is a
promising technique for achieving the best possible resolution with future
space-based telescopes (e.g. JWST), which are limited by the mirror size rather
than atmospheric turbulence, and with a dedicated calibration process also for
extreme adaptive optics facilities from the ground.
