Experimental demonstration of spectral linear dark field control at NASA's high contrast imaging testbeds

Due to the low flux of exoEarths, long exposure times are required to spectrally characterize them. During these long exposures, the contrast in the dark hole will degrade as the the optical system drifts from its initial DH state. To prevent such contrast drift, a wavefront sensing and control (WFSC) algorithm running in parallel to the science acquisition can stabilize the contrast. However, pairwise probing (PWP) cannot be reused to efficiently stabilize the contrast since it relies on strong temporal modulation of the intensity in the image plane, which would interrupt the science acquisition. The use of small amplitude probes has been demonstrated but requires multiple measurements from each science sub-band to converge. Conversely, spectral linear dark field control (LDFC) takes advantage of the linear relationship between the change in intensity of the post-coronagraph out-of-band image and small changes in wavefront in the science band to preserve the DH region during science exposures. In this paper, we show experimental results that demonstrate spectral LDFC stabilizes the contrast to levels of a few $10^{-9}$ on a Lyot coronagraph testbed which is housed in a vacuum chamber. Promising results show that spectral LDFC is able to correct for disturbances that degrade the contrast by more than 100$\times$. To our knowledge, this is the first experimental demonstration of spectral LDFC and the first demonstration of spatial or spectral LDFC on a vacuum coronagraph testbed and at contrast levels less than $10^{-8}$.