Mean PSF of open and closed-loop LDFC datasets with a static aberration introduced on the DM, and quantification of the raw contrast and residual wavefront error improvements. We note that a different aberration has been injected by the DM compared to Fig. 8: (a) Open-loop PSFl (b) Closed-loop PSFl (c) Aberration introduced by the DM; (d) 1σ raw contrasts as a function of spatial frequency in the DH of the reference PSF, and the mean of the open and closed-loop LDFC dataset; (e) Gain in raw contrast over the spatial frequencies in the DH; (f) Residual wavefront error, calculated by adding the introduced aberration to the derived LDFC correction.