The JWST has been collecting scientific data for over two years now.
Scientists are now looking deeper into the data, which introduces the need to
correct known systematic effects. Important limiting factors for the MIRI/MRS
are the pointing accuracy, non-linearity, detector charge migration, detector
scattering, the accuracy of the PSF model, and the complex interplay between
these. The Cycle 2 programme 3779 proposed a 72-point intra-pixel dither raster
of the calibration star 10-Lac. In this first work of the paper series, we aim
to address the degeneracy between the non-linearity and BFE that affect the
pixel voltage integration ramps of the MRS. Due to the low flux in the longer
wavelengths, we only do this in the 4.9 to 11.7 micron region. We fitted the
ramps per pixel and dither, in order to fold in the deviations from classical
non-linearity that are caused by charge migration. The ramp shapes should be
repeatable depending on the part of the PSF that is sampled. By doing so, we
defined both a grid-based linearity correction, and an interpolated linearity
correction. We find significant improvements compared to the uniform
illumination assumption. The standard deviation on the pixel ramp residual
non-linearity is between 70-90% smaller than the current standard pipeline when
self-calibrating with the grid. We are able to interpolate these coefficients
to apply to any unresolved source not on the grid points, resulting in an up to
70% smaller standard deviation on the residual deviation from linearity. The
FWHM is up to 20% narrower. The depth of the fringes is now consistent up the
ramp. Pointing-specific linearity corrections allow us to fix the systematic
deviation in the slopes. We demonstrated this for unresolved sources. The
discovered trends with PSF sampling suggest that, we may be able to model ramps
for spatially extended and resolved illumination as well.Comment: 18 pages, 20 figures, Accepted for publication in A&