Wavelength calibration for OSIRIS/GTC* tunable filters

OSIRIS (Optical System for Imaging and low Resolution Integrated Spectroscopy) is the first light instrument of the Gran Telescopio Canarias (GTC). It provides a flexible and competitive tunable filter (TF). Since it is based on a Fabry-Perot interferometer working in collimated beam, the TF transmission wavelength depends on the position of the target with respect to the optical axis. This effect is non-negligible and must be accounted for in the data reduction. Our paper establishes a wavelength calibration for OSIRIS TF with the accuracy required for spectrophotometric measurements using the full field of view (FOV) of the instrument. The variation of the transmission wavelength $\lambda(R)$ across the FOV is well described by $\lambda(R)=\lambda(0)/\sqrt{1+(R/f_2)^2}$, where $\lambda(0)$ is the central wavelength, $R$ represents the physical distance from the optical axis, and $f_2=185.70\pm0.17\,$mm is the effective focal length of the camera lens. This new empirical calibration yields an accuracy better than 1\,\AA\ across the entire OSIRIS FOV ($\sim$8\arcmin$\times$8\arcmin), provided that the position of the optical axis is known within 45 $\mu$m ($\equiv$ 1.5 binned pixels). We suggest a calibration protocol to grant such precision over long periods, upon re-alignment of OSIRIS optics, and in different wavelength ranges. This calibration differs from the calibration in OSIRIS manual which, nonetheless, provides an accuracy $\lesssim1$\AA\, for $R\lesssim 2\arcmin$.