Observation bias due to the background reduction scheme. Both estimates from a Monte-Carlo simulation and the Eq. (A.4) are shown. Top panel: relation between the true mean number of counts λ_T, as detected by ICA, and the observed mean number of counts λ₀, as reported by ICA after the background reduction and binning are applied. In this figure, the relation is averaged over all energies for clarity ; in a real application, the correction factor is different for each energy bin. The observed mean λ₀ is significantly reduced for low true mean values λ_T. The deviation vanishes for larger λ_T ≳ 3 (inset). Bottom panel: ratio between the true mean number of counts and the observed mean number of counts. In all panels, the analytical estimate matches very well (within the MC uncertainties) the MC simulation, validating both approaches. The undistorted unit response is shown by the dashed line in all panels.