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The decay of gravitational potentials in the presence of dark energy leads toan additional, late-time contribution to anisotropies in the cosmic microwavebackground (CMB) at large angular scales. The imprint of this so-calledintegrated Sachs-Wolfe (ISW) effect to the CMB angular power spectrum has beendetected and studied in detail, but reconstructing its spatial contributions tothe CMB $\textit{map}$, which would offer the tantalizing possibility ofseparating the early- from the late-time contributions to CMB temperaturefluctuations, is more challenging. Here we study the technique forreconstructing the ISW map based on information from galaxy surveys and focusin particular on how its accuracy is impacted by the presence of photometriccalibration errors in input galaxy maps, which were previously found to be adominant contaminant for ISW signal estimation. We find that both includingtomographic information from a single survey and using data from multiple,complementary galaxy surveys improve the reconstruction by effectivelyself-calibrating the estimator against spurious power contributions fromcalibration errors. A high-fidelity reconstruction further requires one toaccount for the contribution of calibration errors to the observed galaxy powerspectrum in the model used to construct the ISW estimator. We find that if thephotometric calibration errors in galaxy surveys can be independentlycontrolled at the level required to obtain unbiased dark energy constraints,then it is possible to reconstruct ISW maps with excellent accuracy using acombination of maps from two galaxy surveys with properties similar to Euclidand SPHEREx.

Integrated Sachs-Wolfe map reconstruction in the presence of systematic errors