Distributions of ΔPA^{gal − opt} and ΔPA^{gal − kin}. This figure presents the distributions of ΔPA^{gal − opt}, the 2D misalignment angle between the projected stellar angular momentum vector of the galaxy and the optical position angle, defined as the orientation of the minor axis of the projected light ellipse. The first and second columns correspond to synthetic DESI-LS and Euclid images, respectively, with optical PAs estimated at one effective radius (top row) and at two effective radii (middle row). The third column shows the distributions of ΔPA^{gal − kin}, defined as the angle between the projected spin vector of the galaxy and the kinematic PA derived from synthetic MaNGA-like stellar velocity fields. In all panels, hatched red histograms indicate results when only good cases (i.e., more reliable PA measurements) are selected. We also specify the number of “sources” or images used to derive the different histograms.