Cumulative number counts vs. flux for the AGNs in the 0.5 − 2.0 keV energy band. The black curve is from Lehmer et al. (2012); the blue dotted curve represents one realization of an AGN population used for the simulation. The purple dotted line indicates the AGN flux cut (≥1 × 10⁻¹⁵ ergs s⁻¹ cm²) for the 90% encircled energy fraction when removing the AGN contamination at the stage of the spectral fitting (Sect. 3.2.5).