Evolution of the anti-truncated stellar profiles of S0 galaxies since
  $z=0.6$ in the SHARDS survey: I - Sample and Methods
  The controversy about the origin of the structure of S0--E/S0 galaxies may be
due to the difficulty of comparing surface brightness profiles with different
depths, photometric corrections and PSF effects (almost always ignored). We aim
to quantify the properties of Type-III (anti-truncated) discs in a sample of S0
galaxies at 0.2<z<0.6. In this paper, we present the sample selection and
describe in detail the methods to robustly trace the structure in their
outskirts and correct for PSF effects. We have selected and classified a sample
of 150 quiescent galaxies at 0.2<z<0.6 in the GOODS-N field. We perform a
quantitative structural analysis of 44 S0-E/S0 galaxies. We corrected their
surface brightness profiles for PSF distortions and analysed the biases in the
structural and photometric parameters when the PSF correction is not applied.
Additionally, we have developed Elbow, an automatic statistical method to
determine whether a possible break is significant - or not - and its type and
made it publicly available. We found 14 anti-truncated S0-E/S0 galaxies in the
range 0.2<z<0.6 (~30% of the final sample). This fraction is similar to the
those reported in the local Universe. In our sample, ~25% of the Type-III
breaks observed in PSF-uncorrected profiles are artifacts, and their profiles
turn into a Type I after PSF correction. PSF effects also soften Type-II
profiles. We found that the profiles of Type-I S0 and E/S0 galaxies of our
sample are compatible with the inner profiles of the Type-III, in contrast with
the outer profiles. We have obtained the first robust and reliable sample of 14
anti-truncated S0--E/S0 galaxies beyond the local Universe, in the range
0.2<z<0.6. PSF effects significantly affect the shape of the surface brightness
profiles in galaxy discs even in the case of the narrow PSF of HST/ACS images,
so future studies on the subject should make an effort to correct them.
