Distributions obtained from the convolution of a log-normal cloud PDF (Eq. (2), σ_η,cloud = 0.5) with a second log-normal PDF (Eq. (6), σ_contam = 0.5) as a function of the typical density of the contaminating structure, N_contam, relative to the peak of the log-normal cloud distribution, N_peak. The left edge of the figure represents the original cloud PDF shown in colors of the logarithm of p_η. When increasing the contamination level N_contam in the right direction, we see the shift of the PDF towards higher logarithmic column densities, η.