Examples of ellipse fitting and Fourier decomposition of barred galaxies (top row) and unbarred galaxies (bottom row) in TNG100 (left) and TNG50 (right). The right-hand column in each panel displays the face-on stellar surface density maps of the galaxies, with each pixel corresponding to 0.35 × 0.35 kpc² for TNG100, and 0.15 × 0.15 kpc² for TNG50. The left-hand column of each galaxy presents the radial profiles of ellipticity (ϵ) and position angle (PA) measured via ellipse fitting, along with A₂ and Φ₂ from Fourier decomposition. Horizontal dotted lines at ϵ = 0.25 and A₂ = 0.2 are included for reference in each panel. For the barred galaxies: the blue solid and dashed lines represent R_max and R₈₅, respectively; for TNG50, the adjusted measurements R_max, new and R_85, new, calculated with an inner boundary limit of 1.4 kpc, are shown in red; the green solid and dashed line represent R_2, max and R_2, 50, respectively; in the stellar surface density maps, the red line represents the bar size measured by R₈₅ for TNG100 and R_85, new for TNG50.