Same as Fig. 3 but for a 250 μm image with an additional population of synthetic filaments. The population of synthetic filaments has a lognormal distribution of contrasts in the range 0.3 <  δ_c <  2.0 with a broad peak around δ_peak ∼ 0.9. The overall area filling factor of the synthetic filaments is A_fil ∼ 3% and the A_fil parameter (see Sect. 3) is 0.023. Panel b: solid black curve shows the total power spectrum of the original Polaris image plus synthetic filaments. The best-fit power-law (red curve) has γ = −2.7 ± 0.1, slightly steeper than the slope of the original power spectrum of the Polaris image shown by the dashed green curve. The blue curve is the power spectrum of the image containing only synthetic filaments. Panel c: black triangles are the same as in Fig. 3c and the red dots show the residuals between the best-fit power-law model and the power spectrum of the image including synthetic filaments. The of the residuals between k_min <  k <  1.5 k_fil is 0.037. The vertical dashed line marks the angular frequency k_fil ∼ (0.6/θ_fil) corresponding to the characteristic ∼0.1 pc width of the synthetic filaments.