Selection function of AMASCFI using the Millennium modified lightcones of Henriques et al. (2012). Top left: completeness as a function of redshift for haloes of M₂₀₀ > 10¹⁴ M_⊙. Top right:completeness as a function of halo mass. Bottom left: purity as computed for haloes of mass M₂₀₀ > 10¹³ M_⊙. In these three panels, blue, green, and red points respectively show the results for S∕N > 3, S∕N > 4, and S∕N> 5. Bottom right: two-dimensional histogram of the completeness in the (redshift, mass) parameter space for cluster candidates with S∕N > 4. The vertical dotted line at z = 0.7 shows the cut applied to compute GLFs (see Sect. 3.3) and the horizontal line the 90% purity limit.