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The optical velocity convention

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

\begin{displaymath}
\ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\ma...
...nsuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}}.
\end{displaymath} (70)

The first order approximation gives
\begin{displaymath}
\ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\ma...
...el}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
\end{displaymath} (71)

In frequency this gives
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{o...
...\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}}.
\end{displaymath} (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
\begin{displaymath}
\ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mat...
...da_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath} (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.



Gildas manager 2023-06-01