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 $2sigma$ 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 $2sigma$ 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 $2sigma$ galaxies represents only a lower limit of the stellar counter-rotation phenomenon.
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