  Telluric correction of spectroscopic observations is either performed via
standard stars that are observed close in time and airmass along with the
science target, or recently growing in importance, by theoretical telluric
absorption modeling. Both approaches work fine when the telluric lines are
resolved, i.e. at spectral resolving power larger than about 10000, and it is
sufficient to facilitate the detection of spectral features at lower
resolution. However, a meaningful quantitative analysis requires also a
reliable recovery of line strengths. Here, we show for the Fraunhofer A-band of
molecular O2 that the standard telluric correction approach fails in this at
lower spectral resolutions, as an example for the general problem.
Doppler-shift dependent errors of the restored flux may arise, which can amount
to more than 50% in extreme cases, depending on the line shapes of the target
spectral features. Two applications are discussed: the recovery of the O2-band
in the reflected light of an Earth analog atmosphere, as facilitated
potentially in the future using an orbiting starshade and a ground-based
extremely large telescope; and the recovery of the intrinsic ratio of the K I
lines in the post-nova V4332 Sgr tracing the optical depth of the emitting
region, to exemplify the relevance using present-day instrumentation. We show
how one should derive correction functions for the compensation of the error in
dependence of radial velocity shift, spectral resolution and target
line-profile function by use of high resolution atmospheric transmission
modeling, which has to be solved for the individual case.
