Context. The detectors of the JWST Mid-Infrared Instrument (MIRI) Medium Resolution Spectrometer (MRS) form low-finesse resonating cavities that cause periodic count rate modulations (fringes) with peak amplitudes of up to 15% for sources external to MIRI. To detect weak features on a strong continuum and reliably measure line fluxes and line-flux ratios, fringe correction is crucial. Aims. This paper describes the first of two steps implemented in the JWST Science Calibration Pipeline, which is the division by a static fringe flat that removes the bulk of the fringes for extended sources. Methods. Fringe flats were derived by fitting a numerical model to observations of spatially extended sources. The model includes fringes that originate from two resonating cavities in the detector substrate (a third fringe component that originates from the dichroic filters is not included). The model, numerical implementation, and resulting fringe flats are described, and the efficiency of the calibration was evaluated for sources of various spatial extents on the detector. Results. Flight fringe flats are obtained from observations of the planetary nebula NGC 7027. The two fringe components are well recovered and fitted by the model. The derived parameters are used to build a fringe flat for each MRS spectral band, except for 1A and 1B due to the low signal-to-noise ratio of NGC 7027 in these bands. When applied to extended sources, fringe amplitudes are reduced to the sub-percent level on individual spaxels. For point sources, they are reduced to amplitudes between 1 and 5% considering individual spaxels and a single dither position, and decrease to the 1 to 2% level after two-dimensional residual fringe correction. Conclusions. The fringe flats derived from this work are the reference files currently in use by the JWST Science Calibration Pipeline. They provide an efficient calibration for extended sources, and are less efficient for point sources. Future improvements of these fringe flats are possible. The fringe modelling method could also be tested on individual semi-extended or point sources.

Exoplanet Proxima b will be an important laboratory for the search for extraterrestrial life for the decades ahead. Here, we discuss the prospects of detecting carbon dioxide at 15 μm using a spectral filtering technique with the Medium Resolution Spectrograph (MRS) mode of the Mid-Infrared Instrument (MIRI) on the James Webb Space Telescope (JWST). At superior conjunction, the planet is expected to show a contrast of up to 100 ppm with respect to the star. At a spectral resolving power of R = 1790-2640, about 100 spectral CO₂ features are visible within the 13.2-15.8 μm (3B) band, which can be combined to boost the planet atmospheric signal by a factor of 3-4, depending on the atmospheric temperature structure and CO₂ abundance. If atmospheric conditions are favorable (assuming an Earth-like atmosphere), with this new application to the cross-correlation technique, carbon dioxide can be detected within a few days of JWST observations. However, this can only be achieved if both the instrumental spectral response and the stellar spectrum can be determined to a relative precision of ≤1 10^-4 between adjacent spectral channels. Absolute flux calibration is not required, and the method is insensitive to the strong broadband variability of the host star. Precise calibration of the spectral features of the host star may only be attainable by obtaining deep observations of the system during inferior conjunction that serve as a reference. The high-pass filter spectroscopic technique with the MIRI MRS can be tested on warm Jupiters, Neptunes, and super-Earths with significantly higher planet/star contrast ratios than the Proxima system.