GALACTICNUCLEUS: A high-angular-resolution $JHK_s$ imaging survey of the
  Galactic centre. IV. Extinction maps and de-reddened photometry
  The extreme extinction ($A_V\sim30$\,mag) and its variation on arc-second
scales towards the Galactic centre hamper the study of its stars. Their
analysis is restricted to the near infrared (NIR) regime, where the extinction
curve can be approximated by a broken power law. Therefore, correcting for
extinction is fundamental to analyse the structure and stellar population of
the central regions of our Galaxy. We aim to, (1) discuss different strategies
to de-redden the photometry and check the usefulness of extinction; (2) build
extinction maps for the NIR bands $JHK_s$ and make them publicly available; (3)
create a de-reddened catalogue of the GALACTICNUCLEUS (GNS) survey, identifying
foreground stars; and (4) perform a preliminary analysis of the de-reddened
$K_s$ luminosity functions (KLFs). We used photometry from the GNS survey to
create extinction maps for the whole catalogue. We took red clump (RC) and red
giant stars of similar brightnesses as a reference to build the maps and
de-reddened the GNS photometry. We discussed the limitations of the process and
analysed non-linear effects of the de-reddening. We obtained high resolution
($\sim3''$) extinction maps with low uncertainties ($\lesssim5$\,\%) and
computed average extinctions for each of the regions covered by the GNS. We
checked that our maps effectively correct the differential extinction reducing
the spread of the RC features by a factor of $\sim2$. We assessed the validity
of the broken power law approach computing two equivalent extinction maps $A_H$
using either $JH$ and $HK_s$ photometry for the same reference stars and
obtained compatible average extinctions within the uncertainties. Finally, we
analysed de-reddened KLFs for different lines of sight and found that the
regions belonging to the NSD contain a homogeneous stellar population that is
significantly different from that in the innermost bulge regions.
