Illustration of the AOD computations. Upper panel: the three Si II lines in this analysis shown together, with the zero-velocity bin marked with a vertical red line. Lower panel: from this bin, the three measured relative intensities are plotted against ﹩f\lambda ﹩ as black dots, with vertical error bars showing the error spectrum from the COS pipeline. The best-fit function ﹩I/{I}_{0}(f\lambda )﹩ as defined above is drawn in magenta. Also shown for illustration are the two extreme examples of a very high column density and unchanged covering fraction, and of a very high covering fraction but significantly lower column density.