  We establish a link between Fourier optics and a recent construction from the
machine learning community termed the kernel mean map. Using the Fraunhofer
approximation, it identifies the kernel with the squared Fourier transform of
the aperture. This allows us to use results about the invertibility of the
kernel mean map to provide a statement about the invertibility of Fraunhofer
diffraction, showing that imaging processes with arbitrarily small apertures
can in principle be invertible, i.e., do not lose information, provided the
objects to be imaged satisfy a generic condition. A real world experiment shows
that we can super-resolve beyond the Rayleigh limit.
