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A detection of the predicted anticorrelation between 21cm and either Ly-alphaor H-alpha from the Epoch of Reionization (EOR) would be a powerful probe ofthe first galaxies. While 3D intensity maps isolate foregrounds in lowk_\parallel modes, infrared surveys cannot yet match the field of view andredshift resolution of radio intensity mapping experiments. In contrast, 2D(i.e., broad band) infrared intensity maps can be measured with currentexperiments and are limited by foregrounds instead of photon or thermal noise.We show 2D experiments can measure most of the 3D fluctuation power at k<0.2Mpc^-1 while preserving its correlation properties. However, we showforegrounds pose two challenges: (1) simple geometric effects producepercent-level correlations between radio and infrared fluxes, even if theirluminosities are uncorrelated; and (2) radio and infrared foreground residualscontribute sample variance noise to the cross spectrum. The first challengedemands better foreground masking and subtraction, while the second demandslarge fields of view to average away uncorrelated radio and infrared power.Using radio observations from the Murchison Widefield Array and near-infraredobservations from the Asteroid Terrestrial-impact Last Alert System, we set anupper limit on residual foregrounds of the 21cm--Ly-alpha cross power spectrumat z\sim7 of \Delta^2<181 kJy/sr * mK (95\%) at \ell\sim800. We predict levelsof foreground correlation and sample variance noise in future experiments,showing that higher resolution surveys such as LOFAR, SKA-LOW, and the DarkEnergy Survey can start to probe models of the 21cm--Ly\alpha EOR crossspectrum.

Foreground and sensitivity analysis for broad band (2D) 21cm--Ly-alpha and 21cm--H-alpha correlation experiments probing the Epoch of Reionization