Raw contrast of atmospheric residual as a function of wavelength. Upper left panel: Instantaneous phase map obtained using HCIPy simulations (parameters for the AO system are detailed in Section 2.5.3), yielding a Strehl ratio of 97.8% in the K band. Upper right panel: Normalised autocorrelation function of the phase map, C_Φ(u,v) (blue curve), overlaid with the real part of e^{−ikα⋅(u,v)} for an object at a separation of 200 mas in the I band. The scalar product of these two functions gives the residual flux injected into the fibre, $\mathbb{E}\left[{\eta }_{\star }^{\text{inj}}\right]$. Lower panel: Raw contrast as a function of wavelength and angular separation, assuming two cases: (i) solid lines represent $\mathbb{E}\left[{\eta }_{\star }^{\text{inj}}\right]$ assuming a correlated phase noise (as in our simulation), and (ii) dashed lines represent the raw contrast if we would have uncorrelated phase noise (C_Φ(u,v) = cte).