Top: map of the polarization angle dispersion function 𝒮⁽⁰⁾ for the input sky of the E2E simulations, at 60′ resolution and a lag of δ = 30′. Middle: map of the difference between the average ⟨𝒮⟩ and the input 𝒮⁽⁰⁾ in the E2E simulations. Bottom: distribution function of the difference between the output and input polarization angle dispersion function. The solid blue curve shows the average of 100 histograms of 𝒮 − 𝒮⁽⁰⁾ from the 100 simulations, with the 1σ dispersion shown as the blue area between dashed lines (barely visible).