  We investigate theoretically dark resonance spectroscopy for a dilute atomic
vapor confined in a thin (micro-metric) cell. We identify the physical
parameters characterizing the spectra and study their influence. We focus on a
Hanle-type situation, with an optical irradiation under normal incidence and
resonant with the atomic transition. The dark resonance spectrum is predicted
to combine broad wings with a sharp maximum at line-center, that can be singled
out when detecting a derivative of the dark resonance spectrum. This narrow
signal derivative, shown to broaden only sub-linearly with the cell length, is
a signature of the contribution of atoms slow enough to fly between the cell
windows in a time as long as the characteristic ground state optical pumping
time. We suggest that this dark resonance spectroscopy in micro-metric thin
cells could be a suitable tool for probing the effective velocity distribution
in the thin cell arising from the atomic desorption processes, and notably to
identify the limiting factors affecting desorption under a grazing incidence.
