the bulk of the sub-mm emission is expected to arise. In the right panel in Fig. \[fig:dndz\_mi\], we plot the $i$-band absolute magnitude versus redshift for the DR7 and DR9 QSO sample. The DR9 QSO sample, apart from being at higher redshift, also extends to fainter objects.

In Fig. \[fig:hers\_helms\_dr7\_9\], we plot the sky distribution of the selected SDS DR7 and DR9 quasars in the region covered by the HeRS and HeLMS survey. Out of consideration for space, the distributions of the quasars in the Boötes, Lockman-SWIRE and [*XMM*]{}-LSS field are not shown here. For the DR7 QSO sample, we select all quasars at $0.15<z<2.5$ with $i$-band magnitude $<19.1$ (corrected for Galactic extinction) in the Boötes and Lockman-SWIRE region and $<19.9$ in the HeRS and HeLMS region. Based on visual inspection and lack of angular completeness masks, we assume that the angular completeness of the DR7 quasars is uniform. More discussion on this issue is presented in Section 3.1. For the DR9 QSO sample, we select all quasars at $2.2<z<3.5$ and “uniform $>0$” in Boötes, [*XMM*]{}-LSS, HeRS and HeLMS. We use DR9 quasar angular completeness masks from White et al. (2012) to model the completeness variations across the sky.

We 