  The decay of gravitational potentials in the presence of dark energy leads to
an additional, late-time contribution to anisotropies in the cosmic microwave
background (CMB) at large angular scales. The imprint of this so-called
integrated Sachs-Wolfe (ISW) effect to the CMB angular power spectrum has been
detected and studied in detail, but reconstructing its spatial contributions to
the CMB $\textit{map}$, which would offer the tantalizing possibility of
separating the early- from the late-time contributions to CMB temperature
fluctuations, is more challenging. Here we study the technique for
reconstructing the ISW map based on information from galaxy surveys and focus
in particular on how its accuracy is impacted by the presence of photometric
calibration errors in input galaxy maps, which were previously found to be a
dominant contaminant for ISW signal estimation. We find that both including
tomographic information from a single survey and using data from multiple,
complementary galaxy surveys improve the reconstruction by effectively
self-calibrating the estimator against spurious power contributions from
calibration errors. A high-fidelity reconstruction further requires one to
account for the contribution of calibration errors to the observed galaxy power
spectrum in the model used to construct the ISW estimator. We find that if the
photometric calibration errors in galaxy surveys can be independently
controlled at the level required to obtain unbiased dark energy constraints,
then it is possible to reconstruct ISW maps with excellent accuracy using a
combination of maps from two galaxy surveys with properties similar to Euclid
and SPHEREx.
