Geometric distortion and astrometric calibration of the JWST MIRI Medium Resolution Spectrometer

The Medium-Resolution integral field Spectrometer (MRS) of MIRI on board JWST performs spectroscopy between 5 and 28~$\mu$m. The optics of the MRS introduce substantial distortion, and this needs to be rectified in order to reconstruct the observed astrophysical scene. We use data from the JWST/MIRI commissioning and cycle 1 calibration phase, to derive the MRS geometric distortion and astrometric solution, a critical step in the calibration of MRS data. These solutions come in the form of transform matrices that map the detector pixels to spatial coordinates of a local MRS coordinate system called $\alpha$/$\beta$, to the global JWST observatory coordinates V2/V3. For every MRS spectral band and each slice dispersed on the detector, the transform of detector pixels to $\alpha$/$\beta$ is fit by a two-dimensional polynomial, using a raster of point source observations. A polynomial transform is used to map the coordinates from $\alpha$/$\beta$ to V2/V3. We calibrated the distortion of all 198 discrete slices of the MIRI/MRS IFUs, and derived an updated Field of View (FoV) for each MRS spectral band. The precision of the distortion solution is estimated to be better than one tenth of a spatial resolution element, with a root mean square (rms) of 10 milli-arcsecond (mas) at 5 $\mu$m, to 23 mas at 27 $\mu$m. Finally we find that the wheel positioning repeatability causes an additional astrometric error of rms 30 mas. We have demonstrated the MRS astrometric calibration strategy and analysis enabling the calibration of MRS spectra, a critical step in the data pipeline especially for science with spatially resolved objects. The distortion calibration was folded into the JWST pipeline in Calibration Reference Data System (CRDS) context jwst\_1094.pmap. The distortion calibration precision meets the pre-launch requirement, and the estimated total astrometric uncertainty is 50 mas.