Illustrations of the noise distribution in the (Q, U) plane. The solid and dashed blue lines represent the 1σ probability contours around the true polarization values (Q0, U0), also parameterized by (p0, ψ0). Left: the canonical case (ε = 1, ρ = 0) is shown as a solid line. The dashed line shows the introduction of a correlation ρ = 0.5, leading to an effective ellipticity (εeff> 1) rotated by an angle θ. Right: same transformation, starting from the elliptical case (ε = 2, ρ = 0).
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