  Adaptive optics (AO) is critical in astronomy, optical communications and
remote sensing to deal with the rapid blurring caused by the Earth's turbulent
atmosphere. But current AO systems are limited by their wavefront sensors,
which need to be in an optical plane non-common to the science image and are
insensitive to certain wavefront-error modes. Here we present a wavefront
sensor based on a photonic lantern fibre-mode-converter and deep learning,
which can be placed at the same focal plane as the science image, and is
optimal for single-mode fibre injection. By measuring the intensities of an
array of single-mode outputs, both phase and amplitude information on the
incident wavefront can be reconstructed. We demonstrate the concept with
simulations and an experimental realisation wherein Zernike wavefront errors
are recovered from focal-plane measurements to a precision of
$5.1\times10^{-3}\;\pi$ radians root-mean-squared-error.
