  This paper introduces a novel wavefront sensing approach that relies on the
Fourier analysis of a single conventional direct image. In the high Strehl
ratio regime, the relation between the phase measured in the Fourier plane and
the wavefront errors in the pupil can be linearized, as was shown in a previous
work that introduced the notion of generalized closure-phase, or kernel-phase.
The technique, to be usable as presented requires two conditions to be met: (1)
the wavefront errors must be kept small (of the order of one radian or less)
and (2) the pupil must include some asymmetry, that can be introduced with a
mask, for the problem to become solvable. Simulations show that this asymmetric
pupil Fourier wavefront sensing or APF-WFS technique can improve the Strehl
ratio from 50 to over 90 % in just a few iterations, with excellent photon
noise sensitivity properties, suggesting that on-sky close loop APF-WFS is
possible with an extreme adaptive optics system.
