  In recent years integral-field spectroscopic surveys have revealed that the
presence of kinematically decoupled stellar components is not a rare phenomenon
in nearby galaxies. However, complete statistics are still lacking because they
depend on the detection limit of these objects. We investigate the kinematic
signatures of two large-scale counter-rotating stellar disks in mock
integral-field spectroscopic data to address their detection limits as a
function of the galaxy properties and instrumental setup. We built a set of
mock data of two large-scale counter-rotating stellar disks as if they were
observed with the Multi-Unit Spectroscopic Explorer (MUSE). We accounted for
different photometric, kinematic, and stellar population properties of the two
counter-rotating components as a function of galaxy inclination. We extracted
the stellar kinematics in the wavelength region of the calcium triplet
absorption lines by adopting a Gauss-Hermite (GH) parameterization of the
line-of-sight velocity distribution (LOSVD). We confirm that the strongest
signature of the presence of two counter-rotating stellar disks is the
symmetric double peak in the velocity dispersion map, already known as the
$2\sigma$ feature. The size, shape, and slope of the 2$\sigma$ peak strongly
depend on the velocity separation and relative light contribution of the two
counter-rotating stellar disks. When the $2\sigma$ peak is difficult to detect
due to the low signal-to-noise ratio of the data, the large-scale structure in
the $h_3$ map can be used as a diagnostic for strong and weak counter-rotation.
The counter-rotating kinematic signatures become fainter at lower viewing
angles as an effect of the smaller projected velocity separation between the
two counter-rotating components. We confirm that the observed frequency of
$2\sigma$ galaxies represents only a lower limit of the stellar
counter-rotation phenomenon.
