Imaging planets in reflected light, a key focus of future NASA missions and ELTs, requires advanced wavefront control to maintain a deep, temporally correlated null of stellar halo -- i.e. a dark hole -- at just several diffraction beam widths. Using the Ames Coronagraph Experiment testbed, we present the first laboratory tests of Spatial Linear Dark Field Control (LDFC) approaching raw contrasts ($sim$ 5$times$10$^{-7}$) and separations (1.5--5.2 $lambda$/D) needed to image jovian planets around Sun-like stars with space-borne coronagraphs like WFIRST-CGI and image exo-Earths around low-mass stars with future ground-based 30m class telescopes. In four separate experiments and for a range of different perturbations, LDFC largely restores (to within a factor of 1.2--1.7) and maintains a dark hole whose contrast is degraded by phase errors by an order of magnitude. Our implementation of classical speckle nulling requires a factor of 2--5 more iterations and 20--50 DM commands to reach contrasts obtained by spatial LDFC. Our results provide a promising path forward to maintaining dark holes without relying on DM probing and in the low-flux regime, which may improve the duty cycle of high-contrast imaging instruments, increase the temporal correlation of speckles, and thus enhance our ability to image true solar system analogues in the next two decades.
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