  Ground based optical telescopes are seriously affected by atmospheric
turbulence induced aberrations. Understanding properties of these aberrations
is important both for instruments design and image restoration methods
development. Because the point spread function can reflect performance of the
whole optic system, it is appropriate to use the point spread function to
describe atmospheric turbulence induced aberrations. Assuming point spread
functions induced by the atmospheric turbulence with the same profile belong to
the same manifold space, we propose a non-parametric point spread function --
PSF-NET. The PSF-NET has a cycle convolutional neural network structure and is
a statistical representation of the manifold space of PSFs induced by the
atmospheric turbulence with the same profile. Testing the PSF-NET with
simulated and real observation data, we find that a well trained PSF--NET can
restore any short exposure images blurred by atmospheric turbulence with the
same profile. Besides, we further use the impulse response of the PSF-NET,
which can be viewed as the statistical mean PSF, to analyze interpretation
properties of the PSF-NET. We find that variations of statistical mean PSFs are
caused by variations of the atmospheric turbulence profile: as the difference
of the atmospheric turbulence profile increases, the difference between
statistical mean PSFs also increases. The PSF-NET proposed in this paper
provides a new way to analyze atmospheric turbulence induced aberrations, which
would be benefit to develop new observation methods for ground based optical
telescopes.
