  The Integrated Sachs-Wolfe (ISW) effect is a large-angle modulation of the
cosmic microwave background (CMB), generated when CMB photons traverse evolving
potential wells associated with large scale structure (LSS). Recent efforts
have been made to reconstruct maps of the ISW signal using information from
surveys of galaxies and other LSS tracers, but investigation into how survey
systematics affect their reliability has so far been limited. Using simulated
ISW and LSS maps, we study the impact of galaxy survey properties and
systematic errors on the accuracy of reconstructed ISW signal. We find that
systematics that affect the observed distribution of galaxies along the line of
sight, such as photo-z and bias-evolution related errors, have a relatively
minor impact on reconstruction quality. In contrast, however, we find that
direction-dependent calibration errors can be very harmful. Specifically, we
find that in order to avoid significant degradation of our reconstruction
quality statistics, direction-dependent number density fluctuations due to
systematics must be controlled so that their variance is smaller than $10^{-6}$
(which corresponds to a 0.1% calibration). Additionally, we explore the
implications of our results for attempts to use reconstructed ISW maps to shed
light on the origin of large-angle CMB alignments. We find that there is only a
weak correlation between the true and reconstructed angular momentum
dispersion, which quantifies alignment, even for reconstructed ISW maps which
are fairly accurate overall.
