The optical velocity convention

Optical spectrometers (e.g., grates) naturally delivers a spectral axis regularly spaced in wavelength. Eq. [*] can then be rewritten as

  $\displaystyle \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{o...
...ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}}.
$ (70)
The first order approximation gives
  $\displaystyle \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{o...
...{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
$ (71)
In frequency this gives
  $\displaystyle \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}...
...nsuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}}.
$ (72)
Following the same path as in Sect. [*] but now in wavelenght, it is easy to show that we can establish a linear velocity scale proportional to the wavelength axis
  $\displaystyle \ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{ob...
...ensuremath{\lambda_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
$ (73)
This velocity scale is called the optical velocity convention. The relation between this velocity scale and the frequency spectral axis is non-linear. This is why it is not used in CLASS.