Abstract
Excalibur is a non-parametric, hierarchical framework for precision
wavelength-calibration of spectrographs. It is designed with the needs of
extreme-precision radial velocity (EPRV) in mind, which require that
instruments be calibrated or stabilized to better than $10^-4$ pixels.
Instruments vary along only a few dominant degrees of freedom, especially EPRV
instruments that feature highly stabilized optical systems and detectors.
Excalibur takes advantage of this property by using all calibration data to
construct a low-dimensional representation of all accessible calibration states
for an instrument. Excalibur also takes advantage of laser frequency combs or
etalons, which generate a dense set of stable calibration points. This density
permits the use of a non-parametric wavelength solution that can adapt to any
instrument or detector oddities better than parametric models, such as a
polynomial. We demonstrate the success of this method with data from the
EXtreme PREcision Spectrograph (EXPRES), which uses a laser frequency comb.
When wavelengths are assigned to laser comb lines using excalibur, the RMS of
the residuals is about five times lower than wavelengths assigned using
polynomial fits to individual exposures. Radial-velocity measurements of HD
34411 showed a reduction in RMS scatter over a 10-month time baseline from
$1.17$ to $1.05\, m\,s^-1$.
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