2D probability histogram of the total proton column density N_H and the column density of molecular hydrogen N(H₂) obtained with the standard simulation (see Table 2). Upper panel: original data where all lines of sight have a size L= 200 pc. Bottom panel: outcome of the reconstruction algorithm described in Sect. 3.8 that produces a sample of lines of sight ranging from 100 to 3200 pc. The color code indicates the fraction of lines of sight (in logarithmic scale) contained in each bin. Dotted lines are isocontours of the molecular fraction for , 10⁻⁶, 10⁻⁴, 10⁻², and 1.