Apodization due to the spatial filtering caused by single-mode fibres as a function of the angular separation α between the star and the exoplanet, in the K band (upper panel) and in the I band (lower panel). The green curves show ${\eta }_{●}^{\text{inj}}$, the injection of the exoplanet flux into interferometer 2, while the blue and orange curves represent the injection of the stellar flux ${\eta }_{\star }^{\text{inj}}$. The blue curves are without a phase apodization (Ψ_α = 0), while the orange curves are with phase apodization (Ψ_α = aH₁ + bH₂). The solid curves include the residuals of atmospheric correction by an extreme AO system, giving a Strehl ratio of 98% in the K band and 72% in the I band. The dotted curves are obtained assuming no atmospheric residuals: Φ(u) = 0, hence a Strehl ratio of 100%. The red curves correspond to the contrast limit, C_shot in Eq. (56), that would be achieved when limited by photon noise, for an observation with parameters as stipulated in Table 2. The phase apodizer is efficient at decreasing the flux injected into the fibre in the K band. However, at shorter wavelengths, the lower Strehl ratio makes it less effective, with the injected flux mostly due to the atmospheric halo.