  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
$10^{-8}$.
