  Context. Narrow-band interference filters can be tuned toward shorter
wavelengths by tilting them from the perpendicular to the optical axis. This
can be used as a cheap alternative to real tunable filters, such as
Fabry-P\'erot interferometers and Lyot filters. At the Swedish 1-m Solar
Telescope, such a setup is used to scan through the blue wing of the Ca II H
line. Because the filter is mounted in a converging beam, the incident angle
varies over the pupil, which causes a variation of the transmission over the
pupil, different for each wavelength within the passband. This causes
broadening of the filter transmission profile and degradation of the image
quality. Aims. We want to characterize the properties of our filter, at normal
incidence as well as at different tilt angles. Knowing the broadened profile is
important for the interpretation of the solar images. Compensating the images
for the degrading effects will improve the resolution and remove one source of
image contrast degradation. In particular, we need to solve the latter problem
for images that are also compensated for blurring caused by atmospheric
turbulence. Methods. We simulate the process of image formation through a
tilted interference filter in order to understand the effects. We test the
hypothesis that they are separable from the effects of wavefront aberrations
for the purpose of image deconvolution. We measure the filter transmission
profile and the degrading PSF from calibration data. Results. We find that the
filter transmission profile differs significantly from the specifications.We
demonstrate how to compensate for the image-degrading effects. Because the
filter tilt effects indeed appear to be separable from wavefront aberrations in
a useful way, this can be done in a final deconvolution, after standard image
restoration with MFBD/Phase Diversity based methods. We illustrate the
technique with real data.
