Deconvolution accuracy of the half maximum sizes for the critical Bonnor-Ebert sphere (Fig. 4), separated from the flat (top), convex (middle), and concave (bottom) backgrounds, for background over-subtraction levels 0 ≤ ϵ_l ≤ 0.3 and size factors 1 ≤ ƒ_k ≤ 2. The convolution kernels, besides a Gaussian shape, assumed the PSF shapes of Berschel PACS at 160 µm, Berschel SPIRE at 250 µm, and Spitzer MIPS at 160 µm (Aniano et al. 2011) with progressively larger deviations from the Gaussian shape. The ratio of the modified deconvolved sizes C_j to the true model size H_BE = 10″ is plotted as a function of the source resolvedness . Some curves display small irregularities in their shapes, similar to the jumps appearing in Fig. A.2, discussed in Sect. 3.2. They are also caused by the appearance of the secondary minima in the source profiles, induced by the wavy profiles of the PSFs (Fig. 14). For reference, the thin black curves display D_j/H_BE and the dashed curves visualize (O_j/2)/H_BE for ϵ_l = {0,0.3} and f_k = {1,2}.