Demonstration of the impact of the kernel processing. Top panel: experimental Fourier phase extracted from a single aberrated image shown in Fig. 2 (the blue curve) bears little ressemblance with the theoretical expected binary signal (in orange). Contrasting with the raw Fourier phase, the bottom panel shows how the projection onto the kernel subspace efficiently erases the impact of the aberration and brings the experimental kernel-phase curve (K ⋅ Φ), which is also plotted with a solid blue line, much closer to its theoretical counterpart (K ⋅ Φ₀), which is now plotted with a dashed orange line so as to better distinguish them.