Empirical correction of the 1-MBB optical depth estimates of the IRDC cloud model. Frame a shows the ratio τ/τ₀ between the original estimates and the true optical depths. Frame b shows the quantity Σ(ΔI_v/I_v) that characterises the difference between each observed spectrum and the 1-MBB fit. Frame c shows the correlation between this quantity and the τ error, and Frame d shows the τ/τ₀ ratio corrected for the trend in frame c. In frames a and d, the inserts show histograms of the τ/τ₀ values (with linear y-axis). In frame c, the colour scale corresponds to logarithmic point density.