The study of Earth-mass extrasolar planets via the radial-velocity technique and the measurement of the potential cosmological variability of fundamental constants call for very-high-precision spectroscopy at the level of $updeltalambda/lambda<10^{-9}$. Wavelength accuracy is obtained by providing two fundamental ingredients: 1) an absolute and information-rich wavelength source and 2) the ability of the spectrograph and its data reduction of transferring the reference scale (wavelengths) to a measurement scale (detector pixels) in a repeatable manner. The goal of this work is to improve the wavelength calibration accuracy of the HARPS spectrograph by combining the absolute spectral reference provided by the emission lines of a thorium-argon hollow-cathode lamp (HCL) with the spectrally rich and precise spectral information of a Fabry-Perot-based calibration source. On the basis of calibration frames acquired each night since the Fabry-Perot etalon was installed on HARPS in 2011, we construct a combined wavelength solution which fits simultaneously the thorium emission lines and the Fabry-Perot lines. The combined fit is anchored to the absolute thorium wavelengths, which provide the `zero-point of the spectrograph, while the Fabry-Perot lines are used to improve the (spectrally) local precision. The obtained wavelength solution is verified for auto-consistency and tested against a solution obtained using the HARPS Laser-Frequency Comb (LFC). The combined thorium+Fabry-Perot wavelength solution shows significantly better performances compared to the thorium-only calibration. The presented techniques will therefore be used in the new HARPS and HARPS-N pipeline, and will be exported to the ESPRESSO spectrograph.
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