Distributions obtained from the convolution of a log-normal cloud PDF (Eq. (2) with σ_η,cloud = 0.5) with a Gaussian noise PDF (Eq. (5)) as a function of the noise amplitude (σ_noise) relative to the peak of the log-normal distribution (N_peak). Contours and colors visualize the same data, given on a logarithmic scale. The individual contour levels are marked in the color bar. The left edge of the figure represents the original log-normal PDF. When increasing the noise level σ_noise in the right direction, we see the distortion of the PDF mainly at low column densities η. The dashed line indicates the peak of the distribution, to better follow the shift of the PDF maximum to larger column densities with increasing noise level.