Proflies of the sources and (Fig. 2), separated from the flat, convex, and concave backgrounds by subtraction of their interpolated planar backgrounds, according to Eq. (8). The profiles (solid lines) correspond to the angular resolutions O_j = {4,32, 256}″, background error ϵ_l = 0.05, and background size factor f_k = 1.54 used in Fig. 2. The profiles completely overlap with each other at O_j = 256″. For reference, the dotted curves reproduce the true model profiles from Fig. 1. For comparison, the black dashed curves for models Ƥ_{a|c} with ϵ_l = 0 and f_k = 1 display the background-separated profiles that get almost no distortions of their shapes for O_j = 4″ in the process of background subtraction. To preserve clarity of the plots, similar profiles for models 𝒢 and Ƥ_{B|D} are not shown.