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tokens: avoid the Galactic disk where a fraction of the dust is farther than 4.5 , and therefore, traced by dust in emission, but not present in the SGF absorption map. Fig. 10 Comparison between the renormalized DL estimates (), and those derived from optical stellar observations (). The top row shows the maps derived from optical stellar observations. The lines have been added for reference. The bottom row left panel compares the renormalized estimates with those derived from optical stellar observations in the sky. The agreement of these independent estimates is a successful test of our empirical renormalization. The bottom row right panel show the histogram of the difference of the two estimates, also in the sky. Figure 10 shows the comparison between the renormalized DL estimates () with the stellar observations based estimates in the sky. The agreement between both estimates is remarkable. The difference between the estimates () has a mean of 0.02 mag and scatter (variance) of 0.12 mag. This comparison validates our renormalized DL estimates as a good tracer of the dust optical extinction in the sky. Our optical extinction estimate () was tailored to match the QSOs estimates. QSOs were observed in diffuse diffuse Galactic lines of sight (most of the QSOs have ). The agreement of the and estimates extends the validity of the DL renormalized estimate () to greater column densities. The scatter of – provides an estimate of the uncertainties in the different estimates. 7. FIR SEDs per unit of optical extinction The DL model parameter and the QSO data are used to compress the FIR IRAS and sub-mm Planck observations of the diffuse ISM to a set of 20 SEDs normalized per , which we present and discuss. The parameter is mainly determined by the wavelength where the SED peaks; as a corollary, SEDs for different values of differ significantly. The values obtained from the QSO analysis,, allow us to normalize the observed SEDs (per unit of optical extinction) and generate a one-parameter family of . This family is indexed by the parameter; the QSO lines of sight are grouped according to the fitted Galactic value. We divide the sample of good QSOs in 20 bins, containing QSOs each 15 . To obtain the values we proceed as follows. For each band and , we would like to perform a linear regression of the values as a function of. The large scatter and non-Gaussian distribution of and the scatter on make it challenging to determine such a slope robustly. Therefore, we smooth the maps to a Gaussian PSF with FWHM to reduce the scatter on , redo the dust modelling (to obtain a coherent estimate), and perform the regression on the smoothed (less noisy) maps. The non-Gaussian distribution of do not introduce any bias in the slope found 16 . Figure F11 presents the set of SEDs. The left panel shows the SEDs for the different values. The right panel shows each SED divided by the mean to highlight the differences between the individual SEDs. The complex statistics of the