Cross correlation is a frequently used technique to obtain the Doppler shifts of digitized celestial spectra. This method, suggested by Tonry & Davis (1979), cross correlates the observed spectrum against an assumed template, and obtains the stellar radial velocity by the location of the correlation maximum (Wyatt 1985). The technique finds the correct radial velocity even for extremely low S/N spectra.
Spectra composed of two components present a potential difficulty to this technique. The cross correlation of these spectra usually displays a double peak which can not be resolved whenever the relative velocity of the two components is small. To overcome this difficulty, we developed TODCOR — a new TwO-Dimensional CORrelation algorithm which can simultaneously derive the Doppler shifts of the two components.
TODCOR assumes that the observed spectrum is a combination of two known spectra with unknown shifts. Following the one-dimensional technique, the algorithm calculates the correlation of the observed spectrum against a set of combinations of two templates, with all possible shifts. The correlation, thus, is a two-dimensional function, whose two independent variables are the radial velocities of the two components. The location of the maximum of this function corresponds to the actual Doppler shifts of the two components.