5.4.1. Why is saturation of absorption lines important?
Wampler  suggested that the low D/H values might be inaccurate because in some cases the H absorption lines have zero flux in their cores; they are saturated. Songaila, Wampler & Cowie  suggested that this well known problem might lead to errors in the H column density, but later work, using better data and more detailed analyses  has shown that these concerns were not significant, and that the initial result  was reliable.
Neutral deuterium (D I) is detected in Lyman series absorption lines, which are adjacent to the H I lines. The separation of 82 km s-1 is easily resolved in high resolution spectra, but it is not enough to move D out of the absorption by the H. The Lyman series lines lie between 1216 Å and 912 Å , and can be observed from the ground at redshifts > 2.5.
Ideally, many (in the best cases > 20) Lyman lines are observed, to help determine the column density (NHI , measured in H I atoms per cm-2 along the line of sight) and velocity width (b values, b = 2 , measured in km s-1) of the H. But in some cases only Ly has been observed (Q1718+4807, APM 08279+5255), and these give highly uncertain D/H, or no useful information.
The column densities of H and D are estimated from the precise shapes of their absorption lines in the spectra. For H, the main difficulties are the accuracy of the column density and the measurement of the distribution in velocity of this H. For D the main problem is contamination by H, which we discuss below.
It is well known that column densities are harder to measure when absorption lines become saturated. The amount of absorption increases linearly with the column density as long as only a small fraction of the photons at the line central wavelength are absorbed. Lines saturate when most photons are absorbed. The amount of absorption then increases with the log of the column density.
Wampler  has suggested that D/H values could be 3 - 4 times higher in Q1937-1009 than measured by Tytler, Fan & Burles . He argued that saturation of the H Lyman series lines could allow lower NHI . This would lead to residual flux in the Lyman continuum, which would contradict the data, but Wampler suggested that the background subtraction might have been faulty, which was not a known problem with HIRES.
Tytler & Burles  explained why Wampler's general concerns were not applicable to the existing data on Q1937-1009. Thirteen Lyman series lines were observed and used to obtain the NHI . The cross section for absorption (oscillator strength) decreases by 2000 from the Ly to the Ly-19 line. This means that the lines vary significantly in shape, and this is readily seen in spectra with high resolution and high signal to noise. The background subtraction looked excellent because the line cores were near zero flux, as expected.
Songaila, Wampler & Cowie  measured the residual flux in the Lyman continuum of the D/H absorber in Q1937-1009. They found a lower NHI and hence a higher D/H. Burles & Tytler  presented a more detailed analysis of better data, and found a lower NHI , consistent with that obtained from the fitting of Lyman series lines. They explained that Songaila, Wampler and Cowie  had underestimated NHI because they used poor estimates of the continuum level and the flux in the Lyman continuum.
In summary, saturation does make the estimation of NHI harder. Column densities of H might be unreliable in data with low spectral resolution, or low signal to noise, and when only a few Lyman lines are observed. The above studies show that it is not a problem with the data available on Q1937-1009, Q1009+2956, Q0014+8118 and Q0130-4021. For the first two quasars, we obtain the same answer by two independent methods, and for the last three the higher order Lyman lines are not saturated.
Saturation is avoided in absorbers with lower NHI , but then the D lines are weaker, and contamination by H lines becomes the dominant problem.