  Modern Giant Segmented Mirror Telescopes (GSMT) like the Extremely Large
Telescope (ELT), currently under construction depend heavily on Adaptive Optics
(AO) systems to correct for atmospheric turbulence. To be able to correct wider
fields of view (FoV), Multi-Conjugate Adaptive Optics (MCAO) systems were
introduced, which use multiple guide stars to obtain an almost uniform
correction over the FoV. However, a residual blur remains in the astronmical
images due to the time delay stemming from the wavefront sensor (WFS)
integration time and temporal response of the deformable mirror(s) (DM). This
results in a blur which can be mathematically described by a convolution of the
true image with the point spread function (PSF). Due to the nature of the
atmosphere and its correction, the PSF is spatially varying.
  In this paper, we present an algorithm for MCAO PSF reconstruction adapted to
the needs of GSMTs in a storage efficient way. In particular, the PSF
reconstruction algorithm for Single Conjugate Adaptive Optics (SCAO) from [40]
is combined with an algorithm for atmospheric tomography from [33] to obtain a
direction dependent reconstruction of the post-AO PSF.
  Results obtained in an end-to-end simulation tool show qualitatively good
reconstruction of the PSF compared to the PSF calculated directly from the
simulated incoming wavefront. Furthermore, the used algorithm has a reasonable
runtime and memory consumption.
