Let's assume that the user wishes to observe a line that appears at the
rest frequency,
, for a source that has a systemic velocity,
, in a given velocity convention #1. The rest frame and
observatory frame frequencies are linked by the Doppler effect through
,
, or
, depending on the assumed convention. For
instance, the Doppler function of the optical convention is
Now, let's assume that the analysis exactly uses the same observed
frequency,
, and systemic velocity,
, but it
interprets it using another Doppler convention and thus Doppler function,
. The spectral axis in the rest frame is then computed as