Total polarization spinor in the filament of the toy model for ψ^bg = 22.5° and various values of the filament polarization angle ψ^fl. Left: Modulus of the total signal at 100 GHz normalized by the pivot MBB (red) and modulus of the analytical derivation from the spin-moment expansion up to second order (black dashed line). The modulus of each term is displayed: order 0: |𝒲₀| (blue), order 1: (orange), and order 2: (green). Right: Difference of the polarization angles between the two frequencies (red), prediction from the complex Δβ correction (blue) and from the spin-moment expansion up to second order (black dashed line).