Stellar reddening map from DESI imaging and spectroscopy

We present new Galactic reddening maps of the high Galactic latitude sky using DESI imaging and spectroscopy. We directly measure the reddening of 2.6 million stars by comparing the observed stellar colors in $g-r$ and $r-z$ from DESI imaging with the synthetic colors derived from DESI spectra from the first two years of the survey. The reddening in the two colors is on average consistent with the \cite{fitzpatrick_correcting_1999} extinction curve with $R_\mathrm{V}=3.1$. We find that our reddening maps differ significantly from the commonly used \cite{schlegel_maps_1998} (SFD) reddening map (by up to 80 mmag in $E(B-V)$), and we attribute most of this difference to systematic errors in the SFD map. To validate the reddening map, we select a galaxy sample with extinction correction based on our reddening map, and this yields significantly better uniformity than the SFD extinction correction. Finally, we discuss the potential systematic errors in the DESI reddening measurements, including the photometric calibration errors that are the limiting factor on our accuracy. The $E(g-r)$ and $E(g-r)$ maps presented in this work, and for convenience their corresponding $E(B-V)$ maps with SFD calibration, are publicly available.