Feature- calibration polynomials in the wavelength domain

[gully]

Starfish currently supports calibration polynomials in the flux domain, parameterized as Chebyshev polynomials (c.f. Czekala et al. 2015). In principle there could be calibration uncertainties attributable to wavelength-domain instrumental artifacts-- basically bad wavelength solution in your data reduction pipeline. The v_z term takes up the zeroth order instrumental artifact, a wavelength shift (of course, in perfectly or near-perfectly calibrated spectra, v_z has astrophysical significance!). However linear or higher-order distortions of your wavelength solutions are possible. In fact, they're not only possible, they're omni-present, but just at a level that may be negligible for most applications.

In any case, if for some reason you are stuck with spectra with poor wavelength calibration, one could straightforwardly implement wavelength-domain calibration polynomials. Such a feature would need to modify the over-sampled wavelength axis in the update_theta() step. This change would add negligibly to the computation time-- the FFT would proceed as normal.

To be clear this is a feature idea enabled by this powerful spectral inference framework, not some inadequacy as might be misconstrued by the GitHub label "Issue", which takes on multiple meanings.

[mveyette]

You're bringing up some great points today, Gully. I've thought about this too and have implemented Chebyshev polynomials before to correct for bad wavelength calibration. I didn't care about RVs when I did it, but for people who might care about the v_z parameter from Starfish, the zeroth order component is no longer going to be the v_z of the star. Just something to think about.