  context: The combination of image restoration and a Fabry-P\'{e}rot
interferometer (FPI) based instrument in solar observations results in specific
calibration issues. FPIs generally show variations over the field-of-view,
while in the image restoration process, the 1-to-1 relation between pixel space
and image space is lost, thus complicating any correcting for such variations.
aims: We develop a data reduction method that takes these issues into account
and minimizes the resulting errors. methods: By accounting for the time
variations in the telescope's Mueller matrix and using separate calibration
data optimized for the wavefront sensing in the MOMFBD image restoration
process and for the final deconvolution of the data, we have removed most of
the calibration artifacts from the resulting data. results: Using this method
to reduce full Stokes data from CRISP at the SST, we find that it drastically
reduces the instrumental and image restoration artifacts resulting from cavity
errors, reflectivity variations, and the polarization dependence of flatfields.
The results allow for useful scientific interpretation. Inversions of restored
data from the $\delta$ sunspot AR11029 using the Nicole inversion code, reveal
strong (~10 km/s) downflows near the disk center side of the umbra.
conclusions: The use of image restoration in combination with an FPI-based
instrument leads to complications in the calibrations and intrinsic limitations
to the accuracy that can be achieved. We find that for CRISP, the resulting
errors can be kept mostly below the polarimetric accuracy of ~10^-3. Similar
instruments aiming for higher polarimetric and high spectroscopic accuracy,
will, however, need to take these problems into account. keywords: Techniques:
image processing, polarimetric, imaging spectroscopy, Sun: surface magnetism,
sunspots, activity
