All this means is that you need to bin your spectra in equal intervals of log wavelength for each pixel to be a constant interval in velocity.
First consider the case whereeachpixel is worth a constant interval in linear wavelength. Here we have
fracDeltalambdalambda=fracDeltavc,
and the Deltav represented by each pixel depends on lambda, which changes across the spectrum.
But now if you bin in equal increments of
Deltaloglambda=fracDeltalambdalambda=fracDeltavc
and each pixel has the same fixed velocity interval, Deltav=cDeltaloglambda, independent of lambda.
This log wavelength binning is a prerequisite for cross-correlation procedures that yield velocities.
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