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 $f_2=185.70pm0.17,$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$8arcmin$times$8arcmin), 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 $Rlesssim 2arcmin$.
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