Excalibur: A Non-Parametric, Hierarchical Wavelength-Calibration Method for a Precision Spectrograph

TL;DR

Excalibur is a hierarchical, non-parametric wavelength calibration method that leverages dense calibration data and instrument stability to improve precision in spectrographs, demonstrated on EXPRES with significant residuals reduction.

Contribution

It introduces a non-parametric, hierarchical calibration framework that adapts to instrument oddities and improves wavelength accuracy over traditional polynomial methods.

Findings

Residual RMS reduced by a factor of five compared to polynomial fits.

Radial velocity RMS scatter decreased from 1.17 to 1.05 m/s over 10 months.

Effective calibration of EXPRES with laser frequency combs using Excalibur.

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 $1.05\, m\,s^{-1}$.