Upper panel: convergence power spectra for source redshift z_s = 1 (top) and z_s = 0.5 (bottom) derived with the OBB (magenta) and the SPL (green) methods. The more aggressive smoothing of this latter method translates into a faster high-ℓ fall-off. The cyan curves (DM) only account for the DM component (rescaled by 1 + Ω_b/Ω_M). The red curve corresponds to the direct integration of the three-dimensional total matter power spectrum (Limber approximation) in the Horizon-AGN simulation (Hz-AGN). The blue curves are the direct integration of the Horizon-DM (DM-only) matter power spectrum (Hz-DM). Dashes reflect regimes where the three-dimensional spectra of Chisari et al. (2018) were extrapolated by a simple power law (extrapolation). The yellow lines show the particle shot-noise contribution at two different redshifts. Middle panel: ratio of the z_s = 0.5 convergence power spectra obtained with the Born approximation and the proper multiple lens plane integration showing only very small changes up to ℓ ∼ 10⁵. Bottom panel: ratio of the DM-only to total convergence power spectra at z_s = 0.5,  1.0, and 1.5 for the SPL method.