Illustration of the POKER correction for two different 114 arcmin² fields. Top row: CO+[C_I] masks corresponding to the two fields, as well as the [C_II] sources (red points). Bottom row: APS of the masked [C_II] source maps, with or without correction of mask aliasing (labelled ‘Poker’ and ‘Masked’, respectively). On the left-hand side, the mask covers 44% of the sky patch (dashed blue line) but masks only 29% of the [C_II] sources (dashed green line). POKER returns an output power spectrum that has the correct shape (flat, up to the sample variance) but that is overestimated by a factor of (1-0.29)/(1-0.44) = 1.27. This is the dashed red line, and it matches the average level of the output APS. On the right-hand side, the mask covers only 36% of the sky patch but 58% of the sources. Hence, the output APS returned by POKER is underestimated by (1-0.58)/(1-0.36) = 0.65.