Range of recovered corrected velocity dispersions σ_corr, out as a function of the input corrected velocity dispersion σ_corr, in for several set-ups. The red dotted line corresponds to the analytical propagation of uncertainty of the MUSE set-up, where σ_LSF = 50 km s⁻¹, δσ_obs = 5 km s⁻¹, and δσ_LSF = 1 km s⁻¹. The interval determined from the Monte Carlo approach for this set-up is shown as the green area, which is partially hidden by the blue areas for visual convenience. The blue areas correspond to the Fabry-Perot set-ups, where σ_LSF = 13 km s⁻¹ and δσ_LSF = 1 km s⁻¹. The light blue area, which is again partially hidden by the dark blue area, corresponds to the MUSE-like uncertainties (case 1), where δσ_obs = 5 km s⁻¹, whereas the darker blue area corresponds to the most realistic hypothesis (case 2), where δσ_obs = 2.5 km s⁻¹. The black line shows the one-to-one relation. The three dashed lines (green, light, and dark blue) correspond to the three set-ups. The vertical lines show the corrected velocity dispersion in which the lower limit gets larger than zero. The horizontal lines show the corresponding upper limit, which defines the range of reliable corrected velocity dispersion.