Effects of the cuts in redshift for z_s < z_cl + 0.1 on the expected log N–log S of lensed X-ray sources in the soft (upper panel) and hard (lower panel) bands. The upper red lines show the total number counts from the model by Gilli et al. (2007), and the lower blue lines show the number counts expected for the lensed sources (z_s < z_cl + 0.1) on the basis of Gilli et al. (2007). The shaded areas are the CDFS number counts from Luo et al. (2017). The hard-band flux limits in Luo et al. (2017) given in 2−7 keV are converted into 2−10 keV by assuming Γ = 1.8. The predictions from Gilli et al. (2007) are multiplied by a factor of 0.8 to be consistent with the CDFS results.