Simulated structure function of the fitting residuals D_ϵ normalised by for the different profiles. Each panel shows the structure function simulated via Monte Carlo simulations (MC, upper-left corner), via the analytical PSD (upper-right corner), and via the analytical structure function (SF₁ and SF₂, lower-left and -right corners, respectively). Two 2D maps produced via the analytical structure function are displayed: D_ϵ(x, 0) (SF₁) and D_ϵ(x + Δ/2, Δ/2) (SF₂). The dots emphasise the actuator positions. Panel a: 2D local piston. Panel b: 2D pyramid. Panel c: 2D axisymmetric Gaussian profile. Panel d: 2D axisymmetric ALPAO profile. Panel e: 2D sinc function. Panel f: Binary mask analytical model. Panel g: x₁ -profiles of Panels a-f of the Monte Carlo simulations (solid lines) and the PSD analytical models (dashed lines). – Aperture: disc of diameter 95%D.