Stokes imaging polarimetry using image restoration: A calibration strategy for Fabry-P\'{e}rot based instruments

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