Notes. Thefirst row corresponds to the most challenging scenario presented in Fig. 5. Strehl ratio (SR) estimates are calculated normalised encircled energy measurements of the PSF core and first Airy ring, as described by Eq. (10). Final RMS error is estimated from the residual wavefront map implemented on the SLM, or theMaréchal approximation when significant non-SLM induced aberrations are involved. The quoted 1σ errors on S/N, Strehl ratio, and residual RMS are calculated from the final five frames in each test sequence, and as such are a reflection of post-convergence stability. The final three rows denote test cases attempting to force F&F to avoid correcting specific wavefront errors, by manipulating the correction basis or subtracting reference offsets from F&F output wavefronts. ⁽¹⁾ Low-order static wavefront, consisting of the first 19 non-trivial Zernike modes (excluding PTT) with randomly drawn coefficients. ⁽²⁾ LWE aberration is applied via the weak static phase pattern included in the MITHIC turbulence module (Vigan et al. 2016b), instead of via the SLM. ⁽³⁾ Residual astigmatism-dominated MITHIC bench alignment errors, which were measured by the HASO SH-WFS and pre-compensated for all other tests. ⁽⁴⁾ RMS residuals are estimated via Maréchal approximation, as the majority of wavefront error is not applied via the SLM and thus residual phase is poorly known. ⁽⁵⁾No DM-like spatial filter is applied to F&F outputs, hence wavefront corrections are applied at the full SLM resolution. ⁽⁶⁾ Global tip-tilt is subtracted from F&F estimates before projection onto the PTT basis. The PSF is initially shifted by 1 × 1 pixels from the F&F reference centroid. ⁽⁷⁾ F&F exhibits divergent behaviour within ten closed-loop iterations. ⁽⁸⁾43 nm of focus is subtracted from each F&F output wavefront estimate before projection onto the PTT basis, in an attempt to apply a zero-point offset.