The impact of atmospheric dispersion in the performance of high-resolution spectrographs

Differential atmospheric dispersion is a wavelength-dependent effect introduced by the atmosphere. It is one of the instrumental errors that can affect the position of the target as perceived on the sky and its flux distribution. This effect will affect the results of astronomical observations if not corrected by an atmospheric dispersion corrector (ADC). In high-resolution spectrographs, in order to reach a radial velocity (RV) precision of 10 cm s^-1, an ADC is expected to return residuals at only a few tens of milliarcseconds (mas). In fact, current state-of-the-art spectrograph conservatively require this level of residuals, although no work has been done to quantify the impact of atmospheric dispersion. In this work, we test the effect of atmospheric dispersion on astronomical observations in general, and in particular on RV precision degradation and flux losses. Our scientific objective was to quantify the amount of residuals needed to fulfil the requirements set on an ADC during the design phase. We found that up to a dispersion of 100 mas, the effect on the RV is negligible. However, on the flux losses, such a dispersion can create a loss of ∼2 per cent at 380 nm, a significant value when efficiency is critical. The requirements set on ADC residuals should take into consideration the atmospheric conditions where the ADC will function, and also all the aspects related with not only the RV precision requirements but also the guiding camera used, the tolerances on the flux loss, and the different melt data of the chosen glasses.