  Modern Giant Segmented Mirror Telescopes (GSMTs) like the Extremely Large
Telescope, which is currently under construction, depend heavily on Adaptive
Optics (AO) systems to correct for atmospheric distortions. However, a residual
blur always remains in the astronomical images corrected by Single Conjugate AO
(SCAO) systems due to fitting and bandwidth errors, which can mathematically be
described by a convolution of the true image with a point spread function
(PSF). Due to the nature of the turbulent atmosphere and its correction, the
PSF is spatially varying, which is known as aniosplanatic effect. The PSF
serves, e.g., as a quality measure for the science images and therefore needs
to be known as accurately as possible.
  In this paper, we present an algorithm for PSF reconstruction in directions
apart from the guide star direction in an SCAO system adapted to the needs of
GSMTs focused on estimating the contribution of the anisoplanatic and
generalized fitting error to the PSF. In particular, the PSF reconstruction
algorithm for Single Conjugate Adaptive Optics from (Wagner, 2018) is combined
with an algorithm for time-dependent atmospheric tomography from (Niebsch,
2021) to obtain a direction dependent reconstruction of the post-AO PSF.
  Results obtained in an end-to-end simulation tool show a qualitatively good
reconstruction of the PSF compared to the PSF calculated directly from the
simulated incoming wavefront as well as a stable performance with respect to
imprecise knowledge of atmospheric parameters.
