  Tunable filters are a powerful way of implementing narrow-band imaging mode
over wide wavelength ranges, without the need of purchasing a large number of
narrow-band filters covering all strong emission or absorption lines at any
redshift. However, one of its main features is a wavelength variation across
the field of view, sometimes termed the phase effect. In this work, an
anomalous phase effect is reported and characterized for the OSIRIS instrument
at the 10.4m Gran Telescopio Canarias. The transmitted wavelength across the
field of view of the instrument depends, not only on the distance to the
optical centre, but on wavelength. This effect is calibrated for the red
tunable filter of OSIRIS by measuring both normal-incidence light at laboratory
and spectral lamps at the telescope at non-normal incidence.
  This effect can be explained by taking into account the inner coatings of the
etalon. In a high spectral resolution etalon, the gap between plates is much
larger than the thickness of the inner reflective coatings. In the case of a
tunable filter, like that in OSIRIS, the coatings thickness could be of the
order of the cavity, which changes drastically the effective gap of the etalon.
We show that by including thick and dispersive coatings into the interference
equations, the observed anomalous phase effect can be perfectly reproduced. In
fact, we find that, for the OSIRIS red TF, a two-coatings model fits the data
with a rms of 0.5\AA\ at all wavelengths and incidence angles. This is a
general physical model that can be applied to other tunable-filter instruments.
