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tokens: length: this value is extracted from Sbordone Ledoux ( 2018 ) and is equal to 50 mas (0.5 per cent of the slit length, 10 000 mas). This accuracy, as well as the one of the binary separation, are considered in our measurements as rectangular distributions, by excess, where we account for the factor to convert them into normal distributions. standard deviation: as stated above, each point is the mean of all the data of 1-nm bins. In the example we show, we had 49 data points to average. We consider the standard deviation of the mean as another source of uncertainty. It is equal to 0.02 pixel in our example. Using equation ( 4 ), we can derive the combined uncertainty on the pixel scale. It is equal to 0.87 mas using equation ( 5 ). where u 1 is the uncertainty on the angular separation in mas, u 2 and u 3 are the uncertainties of the fits and the standard deviation in pixels, respectively, is the distance of the binary system in pixels (18 pixels in our example), and is the distance of the binary system in mas (4680 mas in our example). Instrumental dispersion calibration: The uncertainty of this component is the standard deviation of the measurements (at airmass 1), and is considered constant over the range. It is equal to 8.3 mas. Atmospheric dispersion measurement: This component has similar subcomponents as the ones of the accuracy of the fits as well as the standard deviation. In addition, we take into consideration the total uncertainty of the pixel scale (equation 5 ). The combined uncertainty on the atmospheric dispersion measurement is also derived from equation ( 4 ). It is equal to 16.18 mas using equation ( 6 ). where is the measured atmospheric dispersion in pixels ( in our example), and PS is the computed pixel scale in mas. Figure 8. Top: Measured atmospheric dispersion, before and after correction by the instrumental dispersion in the blue range. We also show the expected dispersion using Filippenko’s model; bottom: Atmospheric dispersion residuals, before and after correction by the instrumental dispersion. The results obtained for the red arm are shown in Figs A3 and A4 . Table 2. Atmospheric parameters at the time of observation. Table 3. Uncertainties budget showing in details what each source of error is introducing. The contribution of each subsource is computed using equation ( 4 ) and show the results at the wavelength 315 nm of one exposure. The total uncertainty of each source is computed using the root sum squared of its contributions. The last column represents the references used in these computations: (1) Pourbaix Boffin ( 2016 ); (2) study with generated data; (3) experimental standard deviation of the mean value; and (4) Sbordone Ledoux ( 2018 ). The final uncertainty of the method listed, taking into consideration the components described above, is computed using equation ( 7 ). The accuracy of the method is as follows: ±18 mas in the blue range, ±17 mas in the red range. These results are for a 1σ interval.