  The new CRISP filter at the Swedish 1-m Solar Telescope provides
opportunities for observing the solar atmosphere with unprecedented spatial
resolution and cadence. In order to benefit from the high quality of
observational data from this instrument, we have developed methods for
calibrating and restoring polarized Stokes images, obtained at optical and near
infrared wavelengths, taking into account field-of-view variations of the
filter properties.
  In order to facilitate velocity measurements, a time series from a 3D
hydrodynamical granulation simulation is used to compute quiet Sun spectral
line profiles at different heliocentric angles. The synthetic line profiles,
with their convective blueshifts, can be used as absolute references for
line-of-sight velocities.
  Observations of the Ca II 8542 {\AA} line are used to study magnetic fields
in chromospheric fibrils. The line wings show the granulation pattern at
mid-photospheric heights whereas the overlying chromosphere is seen in the core
of the line. Using full Stokes data, we have attempted to observationally
verify the alignment of chromospheric fibrils with the magnetic field. Our
results suggest that in most cases fibrils are aligned along the magnetic field
direction, but we also find examples where this is not the case.
  Detailed interpretation of Stokes data from spectral lines formed in the
chromospheric data can be made using non-LTE inversion codes. For the first
time, we use a realistic 3D MHD chromospheric simulation of the quiet Sun to
assess how well NLTE inversions recover physical quantities from
spectropolarimetric observations of Ca II 8542 {\AA}. We demonstrate that
inversions provide realistic estimates of depth-averaged quantities in the
chromosphere, although high spectral resolution and high sensitivity are needed
to measure quiet Sun chromospheric magnetic fields.
