Map of the χ²− variance of the residuals between the best power-law fit and the output power spectrum as a function of column density contrast (δ_c) and area filling factor (A_fil) in a grid of simulations based on a set of 20 × 20 populations of Gaussian synthetic filaments, all 0.1 pc in width (see text of Sect. 7 for details). The white solid curve marks the fiducial limit A_fil = 0.1 above which the effect of the characteristic filament width can be detected in the power spectrum (see Fig. 12 below). The white plus and cross symbols mark the positions of the observed populations of filaments in the Aquila and Polaris clouds, respectively (cf. Arzoumanian et al. 2019).