  Computationally-efficient wave-front reconstruction techniques for
astronomical adaptive optics systems have seen a great development in the past
decade. Algorithms developed in the spatial-frequency (Fourier) domain have
gathered large attention specially for high-contrast imaging systems.
  In this paper we present the Wiener filter (resulting in the maximization of
the Strehl-ratio) and further develop formulae for the anti-aliasing Wiener
filter that optimally takes into account high-order wave-front terms folded
in-band during the sensing (i.e. discrete sampling) process.
  We employ a continuous spatial-frequency representation for the forward
measurement operators and derive the Wiener filter when aliasing is explicitly
taken into account. We further investigate and compare to classical estimates
using least-squares filters the reconstructed wave-front, measurement noise and
aliasing propagation coefficients as a function of the system order. Regarding
high-contrast systems, we provide achievable performance results as a function
of an ensemble of for ward models for the Shack-Hartmann wave-front sensor
(using sparse and non-sparse representations) and compute point-spread function
raw intensities.
  We find that for a 32x32 single-conjugated adaptive optics system the
aliasing propagation coefficient is roughly 60% of the least-squares filters
whereas the noise propagation is around 80%. Contrast improvements of factors
of up to 2 are achievable across the field in H-band. For current and next
generation high-contrast imagers, despite better aliasing mitigation,
anti-aliasing Wiener filtering cannot be used as a stand-alone method and must
therefore be used in combination with optical spatial filters deployed before
image formation takes actual place.
