This work is part of an ongoing project which aims to detect terrestrial planets in our neighbouring star system $alpha$ Centauri using the Doppler method. Owing to the small angular separation between the two components of the $alpha$ Cen AB binary system, the observations will to some extent be contaminated with light coming from the other star. We are accurately determining the amount of contamination for every observation by measuring the relative strengths of the H-$alpha$ and NaD lines. Furthermore, we have developed a modified version of a well established Doppler code that is modelling the observations using two stellar templates simultaneously. With this method we can significantly reduce the scatter of the radial velocity measurements due to spectral cross-contamination and hence increase our chances of detecting the tiny signature caused by potential Earth-mass planets. After correcting for the contamination we achieve radial velocity precision of $sim 2.5,mathrm{m,s^{-1}}$ for a given night of observations. We have also applied this new Doppler code to four southern double-lined spectroscopic binary systems (HR159, HR913, HR7578, HD181958) and have successfully recovered radial velocities for both components simultaneously.
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